Psych 221 Image Systems Engineering - User contributions [en]

Pupil Shape in the Animal Kingdom

2024-12-13T19:01:17Z

Leiyu: /* Limitations of using diffraction-limited optics and pupil models in this work */

== Introduction ==

Animals exhibit a wide variety of pupil shapes, unlike the uniform round pupils in humans. These shapes are closely related to the ecological niches of the animals, which refers to their behavioral and environmental needs.
In recent times, researchers are looking into biologically inspired artificial vision systems to achieve novel imaging capabilities. Examples include an artificial vision system with a vertically elongated pupil for object detection and recognition under diverse light conditions, inspired by the cat’s eye, and an artificial vision system with a W-shaped pupil for imaging under uneven light conditions, inspired by the cuttlefish eye. A deeper understanding of how vision systems function in animals could inspire the development of advanced optical systems for various applications such as robotics, surveillance and autonomous vehicles.
Hence, the goal of our project is to study the impact of different pupil shapes on vision, particularly focusing on the vertical slit pupil, horizontal slit pupil, W-shaped pupil, and multiple slit pupil, using ISETCam and ISETBio in MATLAB.

== Background ==
===Point spread function and apertures===
Point spread function is a measure of how an imaging system responds to a point source of light. It reflects the blurring of light caused by diffraction, aberrations and other imperfections in the imaging system. A circular aperture results in a pattern called an Airy Disk. A smaller aperture size increases diffraction and the spread of the airy disk, causing more blurring.
Non-circular apertures, such as square and triangle, produce unique PSFs compared to circular apertures. When the aperture is elongated in one axis, such as a rectangle, the diffraction pattern is extended in the direction perpendicular to the aperture extension.
Most species, including humans, have circular pupils as a circular aperture allows symmetrical distribution of light across the retina. This minimizes distortions and provides consistent image sharpness across the entire visual field, making it optimal for general vision tasks. This suggests that species with non-circular pupils must have evolved them for specialized purposes.

===Theories for various pupil shapes===
Studies have shown that vertical slit pupils are common in ambush predators, as they enable the predators to keep vertical features in focus across different depths of field, while using the amount of defocus blur of horizontal features to estimate distance accurately. Conversely, horizontal slit pupils help terrestrial prey gain panoramic views of their surroundings, helping them detect predators more effectively.
Research has also highlighted the role of pupil dynamics in regulating light entry. For example, many species with vertical pupil shapes are nocturnal, so there is a need to control the amount of light entering during daylight. Another example is the cuttlefish, which lives in shallow waters, a high dynamic range environment with the top surface bright due to sunlight and the bottom sea floor dark. The cuttlefish’s W-shaped pupil is said to help balance out the vertically uneven light field entering its eye.
Another intriguing aspect of pupil shape is its connection to color vision. Cephalopods, such as cuttlefish, have only one type of photoreceptor. However, their W-shaped pupil is believed to enhance chromatic aberration, allowing them to perceive color by adjusting the lens-to-retina distance.

== Methods ==
In this project, we utilized ISETCam and ISETBio to simulate the imaging process that occurs within an animal's eye.
[[File:Schematic.PNG|800px|thumb|center|Figure 1. The flow chart illustrates the simulation process, with the examples below for each step. ]]

===Scene===
We created two types of scenes for our simulations: sceneCreate.m to generate gridlines and sceneFromFile.m to read an image. The gridlines illustrate the effects along different axes, while the image provides a visualization of what the animal might be seeing.

===Aperture===
The aperture represents the pupil shape and is modeled as a 201x201 matrix. In this matrix, ones indicate the regions where light can pass through (white), while zeros denote the areas where light is blocked (black).
For the single-slit elliptical aperture, we can adjust both the size and the orientation of the ellipse (vertical or horizontal). For the multiple-slit aperture, we can modify the slit length, slit width, and the number of slits. For the w-shaped aperture, we intake the w-shape black and white image to generate the aperture matrix, and are able to change the size of it.

===Point spread function and optical image===
The point spread function was simulated for each aperture to analyze the impact of aperture shapes on light passing through the aperture. This was achieved by creating a diffraction-limited wavefront structure using wvfCreate.m and computing the point spread function with wvf.Compute.m with the aperture matrix as input.
The optical image was generated using oiCompute.m taking in the scene and the aperture matrix as inputs. The simulation process assumes that the optical lens is diffraction-limited.
===Cone mosaic and absorptions===
To simulate how the eye’s sensor processes the scene, we modeled the human cone mosaic using cMosaic.m in ISETbio, and used cm.compute.m to simulate the cone excitations and absorptions. Due to time constraints, we only tried the human cone distribution, but it would be highly valuable to try incorporating known cone distributions from the literature for various animals in the future.

== Results ==

===Horizontal goat pupil and vertical cat pupil===
The horizontal slit pupil introduces blurring along the vertical direction, evident in the scene by the horizontal gridlines appearing blurred while the vertical gridlines remain sharply in focus. This effect is also replicated in the cone mosaic plot, confirming the impact on visual perception. Conversely, for the vertical slit pupil, the phenomenon is observed along the opposite axis. The horizontal gridlines remain sharply focused, while the vertical gridlines appear blurred. This demonstrates that a vertical pupil causes blurring in the horizontal direction while maintaining clarity along the vertical axis.

[[File: Horizontal_vertical_pupil.PNG|800px|thumb|center|Figure 2. Horizontal pupil has enhanced features identification along the vertical direction compared with vertical pupil. (A) Horizontal pupil and vertical pupil. (B) Point spread function of each pupil case. (C) Optical images of the grid scene.(D) Cone mosaic absorption of the optical image.]]

These plots align with our understanding of the functional advantages of pupil shapes in animals. For prey animals with horizontal slit pupils, having sharp focus across the horizontal axis is advantageous, as it allows them to effectively monitor their surroundings for predators. Additionally, the laterally placed eyes of these animals provide a wide field of view, further enhancing their ability to detect threats. On the other hand, predator animals with vertical slit pupils benefit from sharp focus along the vertical axis, which aids in keeping their prey in view. This vertical focus is particularly useful when combined with head or eye movements to track prey's horizontal motion, supporting their hunting strategies.

===Slit pupil vs. circular pupil===

When comparing a slit pupil to a circular pupil of the same area, we observe that for a smaller aperture, the circular pupil leads to blurring across the entire scene. This occurs because diffraction becomes more pronounced in smaller apertures, causing the loss of sharp focus. In contrast, a slit pupil of the same area can retain focus along one axis. Specifically, for a vertical slit pupil, the image remains sharp along the vertical direction while blurring occurs along the horizontal axis.

[[File: Figure 1 vertical_vs_round .png|800px|thumb|center|Figure 3. Vertical pupil has enhanced features identification along the vertical direction compared with round pupil with the same size. (A) Round pupils in comparison with the vertical pupils with the same size (B) Point Spread Function of each pupil case. (C) Optical images of the grid scene. (D) Cone mosaic absorption of the optical image and (E) the horizontal integration of the absorption intensity. ]]

These plots support our understanding of the behavior of predator animals. Many predators with vertical slit pupils are also nocturnal. During the day, their pupils constrict to a small area to limit the amount of light entering the eye. If their pupils were circular, the small aperture would cause significant diffraction, leading to a loss of visual clarity. However, the vertical slit pupil allows them to maintain good focus along one axis, despite the reduced aperture size, enabling them to retain functional vision even in bright conditions. This ability is particularly beneficial for nocturnal predators, allowing them to effectively navigate and hunt in varying lighting conditions.

===Effect of W-shaped pupil on chromatic aberration===

Cuttlefish are an interesting case in the animal kingdom. They are famous for their colorful displays and ability to dynamically camouflage themselves, yet they are actually monochromats, effectively colorblind. One paper [10] suggests they make use of chromatic aberration to distinguish between colours using their single photoreceptor type (at the cost of requiring more processing power behind their visual system).

[[File: Cuttlefish eye.png| 200px|thumb|center|Figure 4. The eye of a cuttlefish. Source: Adobe Stock]]

To test the theory that their unique W-shaped pupil produced chromatic aberrations, a custom aperture mask was created and resulting optical image generated with a gridline scene. In the case of a larger pupil size, clear vertical lines and slightly blurred horizontal lines are seen, as expected given its overall horizontal slit-like aspect ratio. Additionally, clear red colour fringing is seen in the vertical lines, supporting this theory that one purpose of their unique pupil shape is to produce chromatic aberrations on their cone mosaic.

Interestingly, once the pupil size was reduced by 17% whilst preserving aspect ratio, the resulting optical image loses almost all contrast and becomes overly blurred, suggesting this pupil shape effectively only works for the animal at larger aspect ratios. Indeed in brighter light, the cuttlefish eye becomes more of a U-shaped slit than a 'W'.

Furthermore, in 3D the W/U shape has the effect of being a vertical slit when viewed from the front, and a horizontal slit from the side. Potentially this could help the cuttlefish as an ambush predator, whilst still being able to scan for threats in the periphery.

[[File: W-shape pupil figure.png| 800px|thumb|center|Figure 5. W-shape pupil PSF and optical image of a grid scene. Upper figure has a 453px major axis length; lower figure has a 350px major axis length.]]

===Multiple-slit pupil: Mantis Shrimp===
The mantis shrimp is a case in of an animal from the same biome with a completely opposing approach to colour vision. It has an incredibly complex visual system with up to 16 different photoreceptor types, and an eye split into 3 bands capable of detecting even UV and circularly polarized light. However it has limited brain processing power behind this visual system, unlike the cuttlefish.

[[File: Mantis Shrimp Eye.png| 200px|thumb|center|Figure 6. The eye of a mantis shrimp showing its distinct 3-band eye structure and psueudopupils. Credit: Roy L. Caldwell/University of California, Berkeley]]

The midband of the mantis shrimp eye is the only portion with multiple photoreceptor types. One study [9] showed that although they have a huge resolution in terms of sampled wavelengths, they are only effectively able to distinguish colours up to 25nm apart in the visible light spectrum. In order to investigate whether chromatic aberration plays a part in their colour vision like the cuttlefish, the triple-slit pupil was simulated in the same way as above. Also, a triple parallel slit pupil was simulated out of academic interest, although no animal is known to us to have this pupil shape.

[[File: Multiple slit.png| 800px|thumb|center|Figure 7. Multiple slit pupil PSF and resulting OI of a gridline scene. The upper set of images is close to the real mantis shrimp pupil, whilst the lower set is a tri-parallel slit simulated out of curiosity. Chromatic aberration is seen mostly in the second, suggesting that is the optimal design if chromatic aberration is desired]]

It can be seen that for the multiple slit colinear pupil, there is actually not much difference to the single horizontal slit. No significant chromatic aberrations can be seen, suggesting that it does not use chromatic aberration for colour vision like the cuttlefish; it instead relies on the multiple photoreceptor types.

This does raise the question of when the mantis shrimp makes use of the multiple-slit pupil, instead of a single pupil (it can indeed change between the two). Watching a video of them shows the typical saccade-fixation eye movement pattern. In the scanning phase of its eye movements is when the multiple-slit pupil can be seen. Furthermore, the mantis shrimp is rather unique in its ability to yaw its eyeball in a third degree of freedom. Perhaps it makes use of the multiple slit to detect general oriented edges in the scene, yawing to adjust for orientation, before fixating with a single pupil in the outer hemisphere of its vision.

Following is a link to a video taken of a Mantis shrimp in Monad Shoal, Malapascua, Philippines. The eye movements can be seen: https://www.youtube.com/watch?v=WnkQmnUcKyA

===Limitations of using diffraction-limited optics and pupil models in this work===
While diffraction can affect optical systems, when it comes to the human or animal eyes, especially regarding how light enters through the pupil, diffraction issue is not the major concern, instead, the chromatic aberration in cornea and lens is. Chromatic aberration occurs when different wavelengths of light are focused at different points, leading to color fringing around objects. This effect is more pronounced in the cornea due to its curved surface and varying refractive indices for different wavelengths.

== Conclusions ==
*Our results support the theory that a vertical slit is used for the predators like cats to focus the vertical direction when hunting; we see the vertical gridlines across the horizontal axis blurring.
*For a horizontal slit, improved horizontal contrast is perhaps beneficial to prey animals that need to constantly scan left/right for threats whilst grazing.
*For smaller pupil areas (bright lighting conditions) a vertical slit is superior in providing more general scene contrast compared to a circular pupil of the same area
**For a horizontal slit, this could have the added benefit of reducing glare from sunlight above
*In the case of a ‘W’ shaped pupil, chromatic aberration with neat colour fringing is seen whilst preserving horizontal contrast, supporting the theory that chromatic aberration is used to perceive colour in the monochromat
**Reducing the size of a ‘W’ pupil greatly reduces contrast and blends colours too much, hence the cuttlefish needs to employ a more slit-like pupil at brighter conditions
*The mantis shrimp split pupil does not produce significant chromatic aberration, it is very close to a single slit but with the added ability to control the orientation.
**When combined with the fact that it uses the multiple slit in the saccadic phase of eye movements (with yaw control), perhaps this is used to detect oriented edges.

Future work could include:
*Using ISET3D to simulate the depth of field effect for all the asymmetrical pupils
*incorporate various lighting conditions into the simulations
*Adapt the coded in ISETbio to replicate the cone mosaic of specific animals for simulation instead of using human mosaic for all.
*Treating the optics in a non diffraction-limited way to closer emulate a real biological visual system.
**Indeed some papers explored produced differing results to ours for the vertical pupil, notably when taking into account depth of field effects.

==References==
[1]M. S. Banks, W. W. Sprague, J. Schmoll, J. A. Q. Parnell, and G. D. Love, “Why do animal eyes have pupils of different shapes?,” Science Advances, vol. 1, no. 7, p. e1500391, Aug. 2015, doi: https://doi.org/10.1126/sciadv.1500391.

[2]Min Su Kim et al., “Feline eye–inspired artificial vision for enhanced camouflage breaking under diverse light conditions,” Science Advances, vol. 10, no. 38, Sep. 2024, doi: https://doi.org/10.1126/sciadv.adp2809.

[3]M. Kim et al., “Cuttlefish eye–inspired artificial vision for high-quality imaging under uneven illumination conditions,” Science Robotics, vol. 8, no. 75, Feb. 2023, doi: https://doi.org/10.1126/scirobotics.ade4698.

[4]S. Chang, D.-J. Kong, and Young Min Song, “Advanced visual components inspired by animal eyes,” Nanophotonics, vol. 0, no. 0, Mar. 2024, doi: https://doi.org/10.1515/nanoph-2024-0014.

[5]“The Science Behind Cat Eyes,” Small Cat Advocacy and Research (SCAR), Sep. 28, 2021. https://scar.lk/the-science-behind-cat-eyes/ (accessed Dec. 11, 2024).

[6]“Diversity in Pupil Dimensions across the Animal Kingdom – An Aesthetic Creation with Visual Significance,” Vision Science Academy, Oct. 01, 2020. https://visionscienceacademy.org/diversity-in-pupil-dimensions-across-the-animal-kingdom-an-aesthetic-creation-with-visual-significance/

[7]L. M. Mäthger, R. T. Hanlon, J. Håkansson, and D.-E. Nilsson, “The W-shaped pupil in cuttlefish (Sepia officinalis): Functions for improving horizontal vision,” Vision Research, vol. 83, pp. 19–24, May 2013, doi: https://doi.org/10.1016/j.visres.2013.02.016.

[8]T. W. Cronin, M. J. Bok, N. J. Marshall, and R. L. Caldwell, “Filtering and polychromatic vision in mantis shrimps: themes in visible and ultraviolet vision,” Philosophical Transactions of the Royal Society B: Biological Sciences, vol. 369, no. 1636, Feb. 2014, doi: https://doi.org/10.1098/rstb.2013.0032.

[9]J. Morrison, “Mantis shrimp’s super colour vision debunked,” Nature, Jan. 2014, doi: https://doi.org/10.1038/nature.2014.14578.

[10]A. L. Stubbs and C. W. Stubbs, “Spectral discrimination in color blind animals via chromatic aberration and pupil shape,” Proceedings of the National Academy of Sciences, vol. 113, no. 29, pp. 8206–8211, Jul. 2016, doi: https://doi.org/10.1073/pnas.1524578113.

[11]“How mantis shrimp make sense of the world | NSF - National Science Foundation,” new.nsf.gov, Dec. 04, 2019. https://new.nsf.gov/news/how-mantis-shrimp-make-sense-world

== Appendix I==
===Diffraction effect from pupil size===
[[File: Circuilar pupil.PNG|800px|thumb|center|Figure S1. Decreased diffraction effect increasing the pupil size. (A) Round pupil with increasing sizes from left to right. (B) Point Spread Function of each pupil case. (C) Optical Images of the grid scene and (D) Optical images of mouse image for the corresponding pupil size. ]]

===Source codes===
MATLAB codes and data file: <ins>https://github.com/riannehere/pupil-project</ins>

== Appendix II==
===Work breakdown===
Wei Lin Puah: In-person liaising with mentor, MATLAB code for vertical and horizontal pupil, literature review for validating accuracy of simulations, written report and presentation

Lei Yu: MATLAB code for vertical, horizontal and multiple slit pupil, generation of PSF plots, optical images and cone mosaic, email liaising with mentor, written report and presentation

Rahul Swaminathan: MATLAB code for vertical and horizontal pupil, MATLAB code for W-shaped pupil, literature review for the Mantis shrimp, written report and presentation

Pupil Shape in the Animal Kingdom

2024-12-13T18:59:00Z

Leiyu:

== Introduction ==

Animals exhibit a wide variety of pupil shapes, unlike the uniform round pupils in humans. These shapes are closely related to the ecological niches of the animals, which refers to their behavioral and environmental needs.
In recent times, researchers are looking into biologically inspired artificial vision systems to achieve novel imaging capabilities. Examples include an artificial vision system with a vertically elongated pupil for object detection and recognition under diverse light conditions, inspired by the cat’s eye, and an artificial vision system with a W-shaped pupil for imaging under uneven light conditions, inspired by the cuttlefish eye. A deeper understanding of how vision systems function in animals could inspire the development of advanced optical systems for various applications such as robotics, surveillance and autonomous vehicles.
Hence, the goal of our project is to study the impact of different pupil shapes on vision, particularly focusing on the vertical slit pupil, horizontal slit pupil, W-shaped pupil, and multiple slit pupil, using ISETCam and ISETBio in MATLAB.

== Background ==
===Point spread function and apertures===
Point spread function is a measure of how an imaging system responds to a point source of light. It reflects the blurring of light caused by diffraction, aberrations and other imperfections in the imaging system. A circular aperture results in a pattern called an Airy Disk. A smaller aperture size increases diffraction and the spread of the airy disk, causing more blurring.
Non-circular apertures, such as square and triangle, produce unique PSFs compared to circular apertures. When the aperture is elongated in one axis, such as a rectangle, the diffraction pattern is extended in the direction perpendicular to the aperture extension.
Most species, including humans, have circular pupils as a circular aperture allows symmetrical distribution of light across the retina. This minimizes distortions and provides consistent image sharpness across the entire visual field, making it optimal for general vision tasks. This suggests that species with non-circular pupils must have evolved them for specialized purposes.

===Theories for various pupil shapes===
Studies have shown that vertical slit pupils are common in ambush predators, as they enable the predators to keep vertical features in focus across different depths of field, while using the amount of defocus blur of horizontal features to estimate distance accurately. Conversely, horizontal slit pupils help terrestrial prey gain panoramic views of their surroundings, helping them detect predators more effectively.
Research has also highlighted the role of pupil dynamics in regulating light entry. For example, many species with vertical pupil shapes are nocturnal, so there is a need to control the amount of light entering during daylight. Another example is the cuttlefish, which lives in shallow waters, a high dynamic range environment with the top surface bright due to sunlight and the bottom sea floor dark. The cuttlefish’s W-shaped pupil is said to help balance out the vertically uneven light field entering its eye.
Another intriguing aspect of pupil shape is its connection to color vision. Cephalopods, such as cuttlefish, have only one type of photoreceptor. However, their W-shaped pupil is believed to enhance chromatic aberration, allowing them to perceive color by adjusting the lens-to-retina distance.

== Methods ==
In this project, we utilized ISETCam and ISETBio to simulate the imaging process that occurs within an animal's eye.
[[File:Schematic.PNG|800px|thumb|center|Figure 1. The flow chart illustrates the simulation process, with the examples below for each step. ]]

===Scene===
We created two types of scenes for our simulations: sceneCreate.m to generate gridlines and sceneFromFile.m to read an image. The gridlines illustrate the effects along different axes, while the image provides a visualization of what the animal might be seeing.

===Aperture===
The aperture represents the pupil shape and is modeled as a 201x201 matrix. In this matrix, ones indicate the regions where light can pass through (white), while zeros denote the areas where light is blocked (black).
For the single-slit elliptical aperture, we can adjust both the size and the orientation of the ellipse (vertical or horizontal). For the multiple-slit aperture, we can modify the slit length, slit width, and the number of slits. For the w-shaped aperture, we intake the w-shape black and white image to generate the aperture matrix, and are able to change the size of it.

===Point spread function and optical image===
The point spread function was simulated for each aperture to analyze the impact of aperture shapes on light passing through the aperture. This was achieved by creating a diffraction-limited wavefront structure using wvfCreate.m and computing the point spread function with wvf.Compute.m with the aperture matrix as input.
The optical image was generated using oiCompute.m taking in the scene and the aperture matrix as inputs. The simulation process assumes that the optical lens is diffraction-limited.
===Cone mosaic and absorptions===
To simulate how the eye’s sensor processes the scene, we modeled the human cone mosaic using cMosaic.m in ISETbio, and used cm.compute.m to simulate the cone excitations and absorptions. Due to time constraints, we only tried the human cone distribution, but it would be highly valuable to try incorporating known cone distributions from the literature for various animals in the future.

== Results ==

===Horizontal goat pupil and vertical cat pupil===
The horizontal slit pupil introduces blurring along the vertical direction, evident in the scene by the horizontal gridlines appearing blurred while the vertical gridlines remain sharply in focus. This effect is also replicated in the cone mosaic plot, confirming the impact on visual perception. Conversely, for the vertical slit pupil, the phenomenon is observed along the opposite axis. The horizontal gridlines remain sharply focused, while the vertical gridlines appear blurred. This demonstrates that a vertical pupil causes blurring in the horizontal direction while maintaining clarity along the vertical axis.

[[File: Horizontal_vertical_pupil.PNG|800px|thumb|center|Figure 2. Horizontal pupil has enhanced features identification along the vertical direction compared with vertical pupil. (A) Horizontal pupil and vertical pupil. (B) Point spread function of each pupil case. (C) Optical images of the grid scene.(D) Cone mosaic absorption of the optical image.]]

These plots align with our understanding of the functional advantages of pupil shapes in animals. For prey animals with horizontal slit pupils, having sharp focus across the horizontal axis is advantageous, as it allows them to effectively monitor their surroundings for predators. Additionally, the laterally placed eyes of these animals provide a wide field of view, further enhancing their ability to detect threats. On the other hand, predator animals with vertical slit pupils benefit from sharp focus along the vertical axis, which aids in keeping their prey in view. This vertical focus is particularly useful when combined with head or eye movements to track prey's horizontal motion, supporting their hunting strategies.

===Slit pupil vs. circular pupil===

When comparing a slit pupil to a circular pupil of the same area, we observe that for a smaller aperture, the circular pupil leads to blurring across the entire scene. This occurs because diffraction becomes more pronounced in smaller apertures, causing the loss of sharp focus. In contrast, a slit pupil of the same area can retain focus along one axis. Specifically, for a vertical slit pupil, the image remains sharp along the vertical direction while blurring occurs along the horizontal axis.

[[File: Figure 1 vertical_vs_round .png|800px|thumb|center|Figure 3. Vertical pupil has enhanced features identification along the vertical direction compared with round pupil with the same size. (A) Round pupils in comparison with the vertical pupils with the same size (B) Point Spread Function of each pupil case. (C) Optical images of the grid scene. (D) Cone mosaic absorption of the optical image and (E) the horizontal integration of the absorption intensity. ]]

These plots support our understanding of the behavior of predator animals. Many predators with vertical slit pupils are also nocturnal. During the day, their pupils constrict to a small area to limit the amount of light entering the eye. If their pupils were circular, the small aperture would cause significant diffraction, leading to a loss of visual clarity. However, the vertical slit pupil allows them to maintain good focus along one axis, despite the reduced aperture size, enabling them to retain functional vision even in bright conditions. This ability is particularly beneficial for nocturnal predators, allowing them to effectively navigate and hunt in varying lighting conditions.

===Effect of W-shaped pupil on chromatic aberration===

Cuttlefish are an interesting case in the animal kingdom. They are famous for their colorful displays and ability to dynamically camouflage themselves, yet they are actually monochromats, effectively colorblind. One paper [10] suggests they make use of chromatic aberration to distinguish between colours using their single photoreceptor type (at the cost of requiring more processing power behind their visual system).

[[File: Cuttlefish eye.png| 200px|thumb|center|Figure 4. The eye of a cuttlefish. Source: Adobe Stock]]

To test the theory that their unique W-shaped pupil produced chromatic aberrations, a custom aperture mask was created and resulting optical image generated with a gridline scene. In the case of a larger pupil size, clear vertical lines and slightly blurred horizontal lines are seen, as expected given its overall horizontal slit-like aspect ratio. Additionally, clear red colour fringing is seen in the vertical lines, supporting this theory that one purpose of their unique pupil shape is to produce chromatic aberrations on their cone mosaic.

Interestingly, once the pupil size was reduced by 17% whilst preserving aspect ratio, the resulting optical image loses almost all contrast and becomes overly blurred, suggesting this pupil shape effectively only works for the animal at larger aspect ratios. Indeed in brighter light, the cuttlefish eye becomes more of a U-shaped slit than a 'W'.

Furthermore, in 3D the W/U shape has the effect of being a vertical slit when viewed from the front, and a horizontal slit from the side. Potentially this could help the cuttlefish as an ambush predator, whilst still being able to scan for threats in the periphery.

[[File: W-shape pupil figure.png| 800px|thumb|center|Figure 5. W-shape pupil PSF and optical image of a grid scene. Upper figure has a 453px major axis length; lower figure has a 350px major axis length.]]

===Multiple-slit pupil: Mantis Shrimp===
The mantis shrimp is a case in of an animal from the same biome with a completely opposing approach to colour vision. It has an incredibly complex visual system with up to 16 different photoreceptor types, and an eye split into 3 bands capable of detecting even UV and circularly polarized light. However it has limited brain processing power behind this visual system, unlike the cuttlefish.

[[File: Mantis Shrimp Eye.png| 200px|thumb|center|Figure 6. The eye of a mantis shrimp showing its distinct 3-band eye structure and psueudopupils. Credit: Roy L. Caldwell/University of California, Berkeley]]

The midband of the mantis shrimp eye is the only portion with multiple photoreceptor types. One study [9] showed that although they have a huge resolution in terms of sampled wavelengths, they are only effectively able to distinguish colours up to 25nm apart in the visible light spectrum. In order to investigate whether chromatic aberration plays a part in their colour vision like the cuttlefish, the triple-slit pupil was simulated in the same way as above. Also, a triple parallel slit pupil was simulated out of academic interest, although no animal is known to us to have this pupil shape.

[[File: Multiple slit.png| 800px|thumb|center|Figure 7. Multiple slit pupil PSF and resulting OI of a gridline scene. The upper set of images is close to the real mantis shrimp pupil, whilst the lower set is a tri-parallel slit simulated out of curiosity. Chromatic aberration is seen mostly in the second, suggesting that is the optimal design if chromatic aberration is desired]]

It can be seen that for the multiple slit colinear pupil, there is actually not much difference to the single horizontal slit. No significant chromatic aberrations can be seen, suggesting that it does not use chromatic aberration for colour vision like the cuttlefish; it instead relies on the multiple photoreceptor types.

This does raise the question of when the mantis shrimp makes use of the multiple-slit pupil, instead of a single pupil (it can indeed change between the two). Watching a video of them shows the typical saccade-fixation eye movement pattern. In the scanning phase of its eye movements is when the multiple-slit pupil can be seen. Furthermore, the mantis shrimp is rather unique in its ability to yaw its eyeball in a third degree of freedom. Perhaps it makes use of the multiple slit to detect general oriented edges in the scene, yawing to adjust for orientation, before fixating with a single pupil in the outer hemisphere of its vision.

Following is a link to a video taken of a Mantis shrimp in Monad Shoal, Malapascua, Philippines. The eye movements can be seen: https://www.youtube.com/watch?v=WnkQmnUcKyA

===Limitations of using diffraction-limited optics and pupil models in this work===
While diffraction can affect optical systems, when it comes to the human or animal eye, especially regarding how light enters through the pupil, diffraction issue is not the major concern, instead, the chromatic aberration in cornea and lens is. Chromatic aberration occurs when different wavelengths of light are focused at different points, leading to color fringing around objects. This effect is more pronounced in the cornea due to its curved surface and varying refractive indices for different wavelengths.

== Conclusions ==
*Our results support the theory that a vertical slit is used for the predators like cats to focus the vertical direction when hunting; we see the vertical gridlines across the horizontal axis blurring.
*For a horizontal slit, improved horizontal contrast is perhaps beneficial to prey animals that need to constantly scan left/right for threats whilst grazing.
*For smaller pupil areas (bright lighting conditions) a vertical slit is superior in providing more general scene contrast compared to a circular pupil of the same area
**For a horizontal slit, this could have the added benefit of reducing glare from sunlight above
*In the case of a ‘W’ shaped pupil, chromatic aberration with neat colour fringing is seen whilst preserving horizontal contrast, supporting the theory that chromatic aberration is used to perceive colour in the monochromat
**Reducing the size of a ‘W’ pupil greatly reduces contrast and blends colours too much, hence the cuttlefish needs to employ a more slit-like pupil at brighter conditions
*The mantis shrimp split pupil does not produce significant chromatic aberration, it is very close to a single slit but with the added ability to control the orientation.
**When combined with the fact that it uses the multiple slit in the saccadic phase of eye movements (with yaw control), perhaps this is used to detect oriented edges.

Future work could include:
*Using ISET3D to simulate the depth of field effect for all the asymmetrical pupils
*incorporate various lighting conditions into the simulations
*Adapt the coded in ISETbio to replicate the cone mosaic of specific animals for simulation instead of using human mosaic for all.
*Treating the optics in a non diffraction-limited way to closer emulate a real biological visual system.
**Indeed some papers explored produced differing results to ours for the vertical pupil, notably when taking into account depth of field effects.

==References==
[1]M. S. Banks, W. W. Sprague, J. Schmoll, J. A. Q. Parnell, and G. D. Love, “Why do animal eyes have pupils of different shapes?,” Science Advances, vol. 1, no. 7, p. e1500391, Aug. 2015, doi: https://doi.org/10.1126/sciadv.1500391.

[2]Min Su Kim et al., “Feline eye–inspired artificial vision for enhanced camouflage breaking under diverse light conditions,” Science Advances, vol. 10, no. 38, Sep. 2024, doi: https://doi.org/10.1126/sciadv.adp2809.

[3]M. Kim et al., “Cuttlefish eye–inspired artificial vision for high-quality imaging under uneven illumination conditions,” Science Robotics, vol. 8, no. 75, Feb. 2023, doi: https://doi.org/10.1126/scirobotics.ade4698.

[4]S. Chang, D.-J. Kong, and Young Min Song, “Advanced visual components inspired by animal eyes,” Nanophotonics, vol. 0, no. 0, Mar. 2024, doi: https://doi.org/10.1515/nanoph-2024-0014.

[5]“The Science Behind Cat Eyes,” Small Cat Advocacy and Research (SCAR), Sep. 28, 2021. https://scar.lk/the-science-behind-cat-eyes/ (accessed Dec. 11, 2024).

[6]“Diversity in Pupil Dimensions across the Animal Kingdom – An Aesthetic Creation with Visual Significance,” Vision Science Academy, Oct. 01, 2020. https://visionscienceacademy.org/diversity-in-pupil-dimensions-across-the-animal-kingdom-an-aesthetic-creation-with-visual-significance/

[7]L. M. Mäthger, R. T. Hanlon, J. Håkansson, and D.-E. Nilsson, “The W-shaped pupil in cuttlefish (Sepia officinalis): Functions for improving horizontal vision,” Vision Research, vol. 83, pp. 19–24, May 2013, doi: https://doi.org/10.1016/j.visres.2013.02.016.

[8]T. W. Cronin, M. J. Bok, N. J. Marshall, and R. L. Caldwell, “Filtering and polychromatic vision in mantis shrimps: themes in visible and ultraviolet vision,” Philosophical Transactions of the Royal Society B: Biological Sciences, vol. 369, no. 1636, Feb. 2014, doi: https://doi.org/10.1098/rstb.2013.0032.

[9]J. Morrison, “Mantis shrimp’s super colour vision debunked,” Nature, Jan. 2014, doi: https://doi.org/10.1038/nature.2014.14578.

[10]A. L. Stubbs and C. W. Stubbs, “Spectral discrimination in color blind animals via chromatic aberration and pupil shape,” Proceedings of the National Academy of Sciences, vol. 113, no. 29, pp. 8206–8211, Jul. 2016, doi: https://doi.org/10.1073/pnas.1524578113.

[11]“How mantis shrimp make sense of the world | NSF - National Science Foundation,” new.nsf.gov, Dec. 04, 2019. https://new.nsf.gov/news/how-mantis-shrimp-make-sense-world

== Appendix I==
===Diffraction effect from pupil size===
[[File: Circuilar pupil.PNG|800px|thumb|center|Figure S1. Decreased diffraction effect increasing the pupil size. (A) Round pupil with increasing sizes from left to right. (B) Point Spread Function of each pupil case. (C) Optical Images of the grid scene and (D) Optical images of mouse image for the corresponding pupil size. ]]

===Source codes===
MATLAB codes and data file: <ins>https://github.com/riannehere/pupil-project</ins>

== Appendix II==
===Work breakdown===
Wei Lin Puah: In-person liaising with mentor, MATLAB code for vertical and horizontal pupil, literature review for validating accuracy of simulations, written report and presentation

Lei Yu: MATLAB code for vertical, horizontal and multiple slit pupil, generation of PSF plots, optical images and cone mosaic, email liaising with mentor, written report and presentation

Rahul Swaminathan: MATLAB code for vertical and horizontal pupil, MATLAB code for W-shaped pupil, literature review for the Mantis shrimp, written report and presentation

Pupil Shape in the Animal Kingdom

2024-12-13T17:36:24Z

Leiyu:

== Introduction ==

Animals exhibit a wide variety of pupil shapes, unlike the uniform round pupils in humans. These shapes are closely related to the ecological niches of the animals, which refers to their behavioral and environmental needs.
In recent times, researchers are looking into biologically inspired artificial vision systems to achieve novel imaging capabilities. Examples include an artificial vision system with a vertically elongated pupil for object detection and recognition under diverse light conditions, inspired by the cat’s eye, and an artificial vision system with a W-shaped pupil for imaging under uneven light conditions, inspired by the cuttlefish eye. A deeper understanding of how vision systems function in animals could inspire the development of advanced optical systems for various applications such as robotics, surveillance and autonomous vehicles.
Hence, the goal of our project is to study the impact of different pupil shapes on vision, particularly focusing on the vertical slit pupil, horizontal slit pupil, W-shaped pupil, and multiple slit pupil, using ISETCam and ISETBio in MATLAB.

== Background ==
===Point spread function and apertures===
Point spread function is a measure of how an imaging system responds to a point source of light. It reflects the blurring of light caused by diffraction, aberrations and other imperfections in the imaging system. A circular aperture results in a pattern called an Airy Disk. A smaller aperture size increases diffraction and the spread of the airy disk, causing more blurring.
Non-circular apertures, such as square and triangle, produce unique PSFs compared to circular apertures. When the aperture is elongated in one axis, such as a rectangle, the diffraction pattern is extended in the direction perpendicular to the aperture extension.
Most species, including humans, have circular pupils as a circular aperture allows symmetrical distribution of light across the retina. This minimizes distortions and provides consistent image sharpness across the entire visual field, making it optimal for general vision tasks. This suggests that species with non-circular pupils must have evolved them for specialized purposes.

===Theories for various pupil shapes===
Studies have shown that vertical slit pupils are common in ambush predators, as they enable the predators to keep vertical features in focus across different depths of field, while using the amount of defocus blur of horizontal features to estimate distance accurately. Conversely, horizontal slit pupils help terrestrial prey gain panoramic views of their surroundings, helping them detect predators more effectively.
Research has also highlighted the role of pupil dynamics in regulating light entry. For example, many species with vertical pupil shapes are nocturnal, so there is a need to control the amount of light entering during daylight. Another example is the cuttlefish, which lives in shallow waters, a high dynamic range environment with the top surface bright due to sunlight and the bottom sea floor dark. The cuttlefish’s W-shaped pupil is said to help balance out the vertically uneven light field entering its eye.
Another intriguing aspect of pupil shape is its connection to color vision. Cephalopods, such as cuttlefish, have only one type of photoreceptor. However, their W-shaped pupil is believed to enhance chromatic aberration, allowing them to perceive color by adjusting the lens-to-retina distance.

== Methods ==
In this project, we utilized ISETCam and ISETBio to simulate the imaging process that occurs within an animal's eye.
[[File:Schematic.PNG|800px|thumb|center|Figure 1. The flow chart illustrates the simulation process, with the examples below for each step. ]]

===Scene===
We created two types of scenes for our simulations: sceneCreate.m to generate gridlines and sceneFromFile.m to read an image. The gridlines illustrate the effects along different axes, while the image provides a visualization of what the animal might be seeing.

===Aperture===
The aperture represents the pupil shape and is modeled as a 201x201 matrix. In this matrix, ones indicate the regions where light can pass through (white), while zeros denote the areas where light is blocked (black).
For the single-slit elliptical aperture, we can adjust both the size and the orientation of the ellipse (vertical or horizontal). For the multiple-slit aperture, we can modify the slit length, slit width, and the number of slits. For the w-shaped aperture, we intake the w-shape black and white image to generate the aperture matrix, and are able to change the size of it.

===Point spread function and optical image===
The point spread function was simulated for each aperture to analyze the impact of aperture shapes on light passing through the aperture. This was achieved by creating a diffraction-limited wavefront structure using wvfCreate.m and computing the point spread function with wvf.Compute.m with the aperture matrix as input.
The optical image was generated using oiCompute.m taking in the scene and the aperture matrix as inputs. The simulation process assumes that the optical lens is diffraction-limited.
===Cone mosaic and absorptions===
To simulate how the eye’s sensor processes the scene, we modeled the human cone mosaic using cMosaic.m in ISETbio, and used cm.compute.m to simulate the cone excitations and absorptions. Due to time constraints, we only tried the human cone distribution, but it would be highly valuable to try incorporating known cone distributions from the literature for various animals in the future.

== Results ==

===Horizontal goat pupil and vertical cat pupil===
The horizontal slit pupil introduces blurring along the vertical direction, evident in the scene by the horizontal gridlines appearing blurred while the vertical gridlines remain sharply in focus. This effect is also replicated in the cone mosaic plot, confirming the impact on visual perception. Conversely, for the vertical slit pupil, the phenomenon is observed along the opposite axis. The horizontal gridlines remain sharply focused, while the vertical gridlines appear blurred. This demonstrates that a vertical pupil causes blurring in the horizontal direction while maintaining clarity along the vertical axis.

[[File: Horizontal_vertical_pupil.PNG|800px|thumb|center|Figure 2. Horizontal pupil has enhanced features identification along the vertical direction compared with vertical pupil. (A) Horizontal pupil and vertical pupil. (B) Point spread function of each pupil case. (C) Optical images of the grid scene.(D) Cone mosaic absorption of the optical image.]]

These plots align with our understanding of the functional advantages of pupil shapes in animals. For prey animals with horizontal slit pupils, having sharp focus across the horizontal axis is advantageous, as it allows them to effectively monitor their surroundings for predators. Additionally, the laterally placed eyes of these animals provide a wide field of view, further enhancing their ability to detect threats. On the other hand, predator animals with vertical slit pupils benefit from sharp focus along the vertical axis, which aids in keeping their prey in view. This vertical focus is particularly useful when combined with head or eye movements to track prey's horizontal motion, supporting their hunting strategies.

===Slit pupil vs. circular pupil===

When comparing a slit pupil to a circular pupil of the same area, we observe that for a smaller aperture, the circular pupil leads to blurring across the entire scene. This occurs because diffraction becomes more pronounced in smaller apertures, causing the loss of sharp focus. In contrast, a slit pupil of the same area can retain focus along one axis. Specifically, for a vertical slit pupil, the image remains sharp along the vertical direction while blurring occurs along the horizontal axis.

[[File: Figure 1 vertical_vs_round .png|800px|thumb|center|Figure 3. Vertical pupil has enhanced features identification along the vertical direction compared with round pupil with the same size. (A) Round pupils in comparison with the vertical pupils with the same size (B) Point Spread Function of each pupil case. (C) Optical images of the grid scene. (D) Cone mosaic absorption of the optical image and (E) the horizontal integration of the absorption intensity. ]]

These plots support our understanding of the behavior of predator animals. Many predators with vertical slit pupils are also nocturnal. During the day, their pupils constrict to a small area to limit the amount of light entering the eye. If their pupils were circular, the small aperture would cause significant diffraction, leading to a loss of visual clarity. However, the vertical slit pupil allows them to maintain good focus along one axis, despite the reduced aperture size, enabling them to retain functional vision even in bright conditions. This ability is particularly beneficial for nocturnal predators, allowing them to effectively navigate and hunt in varying lighting conditions.

===Effect of W-shaped pupil on chromatic aberration===

Cuttlefish are an interesting case in the animal kingdom. They are famous for their colorful displays and ability to dynamically camouflage themselves, yet they are actually monochromats, effectively colorblind. One paper [10] suggests they make use of chromatic aberration to distinguish between colours using their single photoreceptor type (at the cost of requiring more processing power behind their visual system).

[[File: Cuttlefish eye.png| 200px|thumb|center|Figure 4. The eye of a cuttlefish. Source: Adobe Stock]]

To test the theory that their unique W-shaped pupil produced chromatic aberrations, a custom aperture mask was created and resulting optical image generated with a gridline scene. In the case of a larger pupil size, clear vertical lines and slightly blurred horizontal lines are seen, as expected given its overall horizontal slit-like aspect ratio. Additionally, clear red colour fringing is seen in the vertical lines, supporting this theory that one purpose of their unique pupil shape is to produce chromatic aberrations on their cone mosaic.

Interestingly, once the pupil size was reduced by 17% whilst preserving aspect ratio, the resulting optical image loses almost all contrast and becomes overly blurred, suggesting this pupil shape effectively only works for the animal at larger aspect ratios. Indeed in brighter light, the cuttlefish eye becomes more of a U-shaped slit than a 'W'.

Furthermore, in 3D the W/U shape has the effect of being a vertical slit when viewed from the front, and a horizontal slit from the side. Potentially this could help the cuttlefish as an ambush predator, whilst still being able to scan for threats in the periphery.

[[File: W-shape pupil figure.png| 800px|thumb|center|Figure 5. W-shape pupil PSF and optical image of a grid scene. Upper figure has a 453px major axis length; lower figure has a 350px major axis length.]]

===Multiple-slit pupil: Mantis Shrimp===
The mantis shrimp is a case in of an animal from the same biome with a completely opposing approach to colour vision. It has an incredibly complex visual system with up to 16 different photoreceptor types, and an eye split into 3 bands capable of detecting even UV and circularly polarized light. However it has limited brain processing power behind this visual system, unlike the cuttlefish.

[[File: Mantis Shrimp Eye.png| 200px|thumb|center|Figure 6. The eye of a mantis shrimp showing its distinct 3-band eye structure and psueudopupils. Credit: Roy L. Caldwell/University of California, Berkeley]]

The midband of the mantis shrimp eye is the only portion with multiple photoreceptor types. One study [9] showed that although they have a huge resolution in terms of sampled wavelengths, they are only effectively able to distinguish colours up to 25nm apart in the visible light spectrum. In order to investigate whether chromatic aberration plays a part in their colour vision like the cuttlefish, the triple-slit pupil was simulated in the same way as above. Also, a triple parallel slit pupil was simulated out of academic interest, although no animal is known to us to have this pupil shape.

[[File: Multiple slit.png| 800px|thumb|center|Figure 7. Multiple slit pupil PSF and resulting OI of a gridline scene. The upper set of images is close to the real mantis shrimp pupil, whilst the lower set is a tri-parallel slit simulated out of curiosity. Chromatic aberration is seen mostly in the second, suggesting that is the optimal design if chromatic aberration is desired]]

It can be seen that for the multiple slit colinear pupil, there is actually not much difference to the single horizontal slit. No significant chromatic aberrations can be seen, suggesting that it does not use chromatic aberration for colour vision like the cuttlefish; it instead relies on the multiple photoreceptor types.

This does raise the question of when the mantis shrimp makes use of the multiple-slit pupil, instead of a single pupil (it can indeed change between the two). Watching a video of them shows the typical saccade-fixation eye movement pattern. In the scanning phase of its eye movements is when the multiple-slit pupil can be seen. Furthermore, the mantis shrimp is rather unique in its ability to yaw its eyeball in a third degree of freedom. Perhaps it makes use of the multiple slit to detect general oriented edges in the scene, yawing to adjust for orientation, before fixating with a single pupil in the outer hemisphere of its vision.

Following is a link to a video taken of a Mantis shrimp in Monad Shoal, Malapascua, Philippines. The eye movements can be seen: https://www.youtube.com/watch?v=WnkQmnUcKyA

== Conclusions ==
*Our results support the theory that a vertical slit is used for the predators like cats to focus the vertical direction when hunting; we see the vertical gridlines across the horizontal axis blurring.
*For a horizontal slit, improved horizontal contrast is perhaps beneficial to prey animals that need to constantly scan left/right for threats whilst grazing.
*For smaller pupil areas (bright lighting conditions) a vertical slit is superior in providing more general scene contrast compared to a circular pupil of the same area
**For a horizontal slit, this could have the added benefit of reducing glare from sunlight above
*In the case of a ‘W’ shaped pupil, chromatic aberration with neat colour fringing is seen whilst preserving horizontal contrast, supporting the theory that chromatic aberration is used to perceive colour in the monochromat
**Reducing the size of a ‘W’ pupil greatly reduces contrast and blends colours too much, hence the cuttlefish needs to employ a more slit-like pupil at brighter conditions
*The mantis shrimp split pupil does not produce significant chromatic aberration, it is very close to a single slit but with the added ability to control the orientation.
**When combined with the fact that it uses the multiple slit in the saccadic phase of eye movements (with yaw control), perhaps this is used to detect oriented edges.

Future work could include:
*Using ISET3D to simulate the depth of field effect for all the asymmetrical pupils
*incorporate various lighting conditions into the simulations
*Adapt the coded in ISETbio to replicate the cone mosaic of specific animals for simulation instead of using human mosaic for all.
*Treating the optics in a non diffraction-limited way to closer emulate a real biological visual system.
**Indeed some papers explored produced differing results to ours for the vertical pupil, notably when taking into account depth of field effects.

==References==
[1]M. S. Banks, W. W. Sprague, J. Schmoll, J. A. Q. Parnell, and G. D. Love, “Why do animal eyes have pupils of different shapes?,” Science Advances, vol. 1, no. 7, p. e1500391, Aug. 2015, doi: https://doi.org/10.1126/sciadv.1500391.

[2]Min Su Kim et al., “Feline eye–inspired artificial vision for enhanced camouflage breaking under diverse light conditions,” Science Advances, vol. 10, no. 38, Sep. 2024, doi: https://doi.org/10.1126/sciadv.adp2809.

[3]M. Kim et al., “Cuttlefish eye–inspired artificial vision for high-quality imaging under uneven illumination conditions,” Science Robotics, vol. 8, no. 75, Feb. 2023, doi: https://doi.org/10.1126/scirobotics.ade4698.

[4]S. Chang, D.-J. Kong, and Young Min Song, “Advanced visual components inspired by animal eyes,” Nanophotonics, vol. 0, no. 0, Mar. 2024, doi: https://doi.org/10.1515/nanoph-2024-0014.

[5]“The Science Behind Cat Eyes,” Small Cat Advocacy and Research (SCAR), Sep. 28, 2021. https://scar.lk/the-science-behind-cat-eyes/ (accessed Dec. 11, 2024).

[6]“Diversity in Pupil Dimensions across the Animal Kingdom – An Aesthetic Creation with Visual Significance,” Vision Science Academy, Oct. 01, 2020. https://visionscienceacademy.org/diversity-in-pupil-dimensions-across-the-animal-kingdom-an-aesthetic-creation-with-visual-significance/

[7]L. M. Mäthger, R. T. Hanlon, J. Håkansson, and D.-E. Nilsson, “The W-shaped pupil in cuttlefish (Sepia officinalis): Functions for improving horizontal vision,” Vision Research, vol. 83, pp. 19–24, May 2013, doi: https://doi.org/10.1016/j.visres.2013.02.016.

[8]T. W. Cronin, M. J. Bok, N. J. Marshall, and R. L. Caldwell, “Filtering and polychromatic vision in mantis shrimps: themes in visible and ultraviolet vision,” Philosophical Transactions of the Royal Society B: Biological Sciences, vol. 369, no. 1636, Feb. 2014, doi: https://doi.org/10.1098/rstb.2013.0032.

[9]J. Morrison, “Mantis shrimp’s super colour vision debunked,” Nature, Jan. 2014, doi: https://doi.org/10.1038/nature.2014.14578.

[10]A. L. Stubbs and C. W. Stubbs, “Spectral discrimination in color blind animals via chromatic aberration and pupil shape,” Proceedings of the National Academy of Sciences, vol. 113, no. 29, pp. 8206–8211, Jul. 2016, doi: https://doi.org/10.1073/pnas.1524578113.

[11]“How mantis shrimp make sense of the world | NSF - National Science Foundation,” new.nsf.gov, Dec. 04, 2019. https://new.nsf.gov/news/how-mantis-shrimp-make-sense-world

== Appendix I==
===Diffraction effect from pupil size===
[[File: Circuilar pupil.PNG|800px|thumb|center|Figure S1. Decreased diffraction effect increasing the pupil size. (A) Round pupil with increasing sizes from left to right. (B) Point Spread Function of each pupil case. (C) Optical Images of the grid scene and (D) Optical images of mouse image for the corresponding pupil size. ]]

===Source codes===
MATLAB codes and data file: <ins>https://github.com/riannehere/pupil-project</ins>

== Appendix II==
===Work breakdown===
Wei Lin Puah: In-person liaising with mentor, MATLAB code for vertical and horizontal pupil, literature review for validating accuracy of simulations, written report and presentation

Lei Yu: MATLAB code for vertical, horizontal and multiple slit pupil, generation of PSF plots, optical images and cone mosaic, email liaising with mentor, written report and presentation

Rahul Swaminathan: MATLAB code for vertical and horizontal pupil, MATLAB code for W-shaped pupil, literature review for the Mantis shrimp, written report and presentation

Pupil Shape in the Animal Kingdom

2024-12-13T08:30:43Z

Leiyu: /* Methods */

File:Schematic.PNG

2024-12-13T08:29:28Z

Leiyu:

Pupil Shape in the Animal Kingdom

2024-12-13T08:28:43Z

Leiyu: /* Methods */

Pupil Shape in the Animal Kingdom

2024-12-13T08:28:29Z

Leiyu: /* Methods */

Pupil Shape in the Animal Kingdom

2024-12-13T08:22:59Z

Leiyu: /* Methods */

Pupil Shape in the Animal Kingdom

2024-12-13T08:15:00Z

Leiyu: /* Diffraction effect from pupil size */

Pupil Shape in the Animal Kingdom

2024-12-13T08:13:49Z

Leiyu: /* Source codes */

Pupil Shape in the Animal Kingdom

2024-12-13T08:13:19Z

Leiyu: /* Source codes */

Pupil Shape in the Animal Kingdom

2024-12-13T08:11:26Z

Leiyu: /* Source codes */

Pupil Shape in the Animal Kingdom

2024-12-13T08:07:03Z

Leiyu: /* Source codes */

Image Optimization for Optical Projector Arrays

2024-12-13T08:06:38Z

Leiyu: /* Appendix */

== Introduction ==
This project addresses the core challenges of geometric distortion and luminance inconsistency in projection systems, particularly at ultra-short throw ratios. Traditional projection lens arrays must be designed for a limited range of throw distances due to their static lens arrays, leading to issues in maintaining spatial fidelity and consistent brightness across the projection surface as the throw distance changes. To overcome these challenges, we consider a computational framework that improves projection quality without relying on expensive corrective optics. This approach demonstrates significant improvements in image clarity and uniformity. By dynamically adjusting geometric distortions and blending outputs from multiple projectors, we achieve projections with improved spatial fidelity at throw ratios as low as 0.10.

== Background ==
Projection systems face challenges such as glare, geometric distortions, and uneven luminance, especially at ultra-short throw ratios. These issues limit projector placement to specific configurations—such as ceiling-mounted, floor-mounted, or ultra-short throw setups—while requiring precise alignment and costly optical lens arrays to correct distortions. Misalignment can lead to geometric warping, reduced coverage, diminished clarity, glare, and inconsistent luminance, making deployment in dynamic or unconventional scenarios particularly difficult.

[[File:Common Projector Orientations.png|thumb|center|600px|Common projector orientations. Glare lines illustrate undesirable projection angles where reflected light reaches the audience's eyes.]]

To address these challenges, we can utilize a computational framework comprising two key methods:
* '''Perspective Alignment''': Dynamically adjusts projector input to ensure consistent projection in suboptimal configurations.
* '''Multi-Projector Blending''': Utilizes overlapping projections from multiple projectors to eliminate blind spots and improve luminance uniformity.

== Methods ==
Projection quality is heavily influenced by the throw ratio, defined as the distance between the projector and the screen divided by the height of the projection screen. For this project, we analyzed throw ratios on a logarithmic scale ranging from 0.1 to 100. Testing was conducted using a base test image with a height of 180 pixels and a width of 270 pixels, upscaled by a factor of 2. The upscaling allows us to simulate the effects of decreasing throw distances while maintaining visible distortion patterns. Although higher upscaling ratios and resolutions could yield more precise results, they significantly increase computational costs. The chosen parameters strike a balance between computational efficiency and the accuracy required for this project. All image processing was conducted using a custom Python library built specifically for this work, providing lossless geometric transformations and total control over the image alignment process. The code is available in the appendix.

[[File:Projector Spacing at Various Throw Distances.png|thumb|center|600px|Projector spacing visualized at different throw ratios.]]
[[File:Test Image.png|thumb|center|600px|The test image used in experiments to evaluate projection quality.]]

=== Perspective Alignment ===
Perspective Alignment dynamically adjusts the input image to correct geometric distortions caused by suboptimal projector placement or low throw ratios. By using back-projection, this method computes the geometric distortions introduced by the projector’s position and orientation and applies transformations to the input image to counteract them. The result is a projection where the proportions and scaling of objects are preserved, even at extremely low throw ratios such as τ = 0.10, where spatial distortion is most severe.

While Perspective Alignment ensures that the relative size and shape of objects on the projection surface are maintained, it introduces some trade-offs. Portions of the original image that fall outside the accessible projection area at very short throw distances must be cropped. Additionally, luminance tends to decrease in areas of the display farther from the projector, and the projected pixel size increases in these regions, leading to noticeable pixelation. These limitations will be addressed with the introduction of additional projectors.

[[File:Perspective Alignment Process.png|thumb|center|600px|Overview of Perspective Alignment and its role in correcting geometric distortions.]]
[[File:Perspective Alignment Examples.png|thumb|center|600px|Examples of projection quality with and without Perspective Alignment at various throw ratios.]]

=== Multi-Projector Blending ===
Multi-Projector Blending addresses luminance inconsistencies and blind spots inherent to single-projector setups by combining overlapping projection areas from multiple projectors. This technique leverages the aligned perspectives of projectors placed at different positions around the display, ensuring that regions inaccessible to some projectors are covered by others. The result is a more uniform and evenly lit projection, even at extreme throw ratios.

By blending the projections, the output image more closely matches the target image, with enhanced brightness and reduced gaps in coverage. However, some artifacts can still be observed, particularly at the edges of individual projections, and some vignetting occurs in regions covered by fewer projectors. These issues can be mitigated by increasing the simulation resolution to reduce aliasing and by adding additional projectors to improve luminance consistency. Despite these minor limitations, Multi-Projector Blending significantly enhances projection quality, especially in large-scale or ultra-short throw setups where single-projector solutions are insufficient without corrective lenses. Future refinements to the computational blending process, including improved algorithms, could further reduce these artifacts and optimize performance.

[[File:Multi-Projector Blending Process.png|thumb|center|600px|Overview of Multi-Projector Blending for enhanced coverage.]]
[[File:Multi-Projector Blending Examples.png|thumb|center|600px|Examples of Multi-Projector Blending.]]

== Results ==
The combination of Perspective Alignment and Multi-Projector Blending resulted in:
* Reduced spatial warping at ultra-short throw ratios.
* Improved luminance uniformity across the projection surface.
* Enhanced image quality even without advanced corrective optics.

To evaluate the effectiveness of these methods, ten different test images were tested at each of the ten selected throw ratios, ranging from 0.1 to 100. The average Delta E and SSIM were calculated for each image, and these values were then averaged across all ten images to produce the data for the plots below.

[[File:Multi-Projector Blending Delta E.png|thumb|center|600px|Delta E analysis for Perspective Alignment and Multi-Projector Blending.]]
[[File:Multi-Projector Blending Performance Statistics.png|thumb|center|600px|Performance statistics for Normal Input, Perspective Alignment, and Multi-Projector Blending.]]

From the Delta E analysis, we observe that Perspective Alignment significantly reduced the average Delta E across the projection surface at low throw ratios. However, at very short throw distances, large portions of the display are excluded and regions far from the projector still exhibited notable Delta E values due to reduced luminance and geometric distortions.

By incorporating Multi-Projector Blending, some of this Delta E was recovered, leading to further improvements in luminance uniformity. Despite those improvements, overlapping projections introduced slight blurring, which reduced sharpness and contributed to increased Delta E in certain regions. Overall, Perspective Alignment and Multi-Projector Blending were most effective at reducing Delta E for throw ratios less than approximately 4, where spatial distortions and luminance inconsistencies are most severe.

Additionally, by examining the graphs of SSIM over throw ratios, we see that spatial error introduced by varying throw ratios loosely correlates with chromatic error. This relationship arises because as the throw ratio decreases, the projected pixel size and shape deviate from their ideal configuration. Spatial and chromatic information are condensed, as the average color value of the pixels covered by each projected pixel is applied to the entire covered area.

== Conclusions ==
This project demonstrates a improvement in the spatial fidelity and luminance uniformity of projection systems in ultra-short throw environments through the combination of two computational methods: Perspective Alignment and Multi-Projector Blending.

* '''Perspective Alignment''' effectively mitigates geometric distortions by dynamically adjusting the input image to correct for suboptimal projector placement and orientation.
* '''Multi-Projector Blending''' enhances luminance consistency by overlapping projection areas from multiple projectors. This method eliminates blind spots and improves overall brightness, although overlapping regions introduce slight blurring that can increase Delta E in certain areas.

Together, these techniques are most effective at throw ratios less than approximately 4, significantly reducing spatial and chromatic distortions while enabling high-quality image projection without expensive corrective optics. Performance metrics such as Delta E and SSIM demonstrate that this computational approach significantly reduces spatial and chromatic distortions, particularly at extreme throw ratios. However, further refinement of the simulation is necessary to explore the full extent to which these methods can be optimized for distortion reduction.

=== Limitations ===
While the computational methods developed here show great promise, certain limitations remain:
* Minor aliasing artifacts are introduced due to the limited resolution of the simulation.
* Blurring in overlapping regions during Multi-Projector Blending contributes to slight reductions in sharpness.
* Computational cost increases with higher resolutions and the addition of more projectors, limiting scalability in real-time applications.

=== Future Work ===
Real-world testing and hardware development are ongoing to further refine these methods and validate their effectiveness. A 3D-printed projector array has been designed as part of this effort, and Perspective Alignment has been successfully tested in a real-world setting, but those results are beyond the scope of this project. Future work will focus on:
* Verifying results with real-world testing:
** Build a multi-projector testbed to validate trends observed in simulations.
** Design custom projection hardware to accelerate image computation and improve real-time applicability.
* Optimizing individual projector inputs with machine learning:
** Implement convolutional neural networks (CNNs) to refine the accuracy of individual input adjustments.
** Develop GAN or diffusion models to compute individual node inputs more efficiently.
** Incorporate SSIM and S-CIELAB into the loss function for more perceptually accurate corrections.

[[File:3D Printable LCD Mini Projector.png|thumb|center|600px|3D-printed mini projector used for testing and hardware development.]]
[[File:Perspective Alignment Real World Test.png|thumb|center|600px|Real-world test setup demonstrating Perspective Alignment.]]

This work provides a foundation for improving projection quality in constrained or unconventional setups. Further developments in real-world testing and algorithm refinement will determine the practical applicability of these techniques to scenarios such as large-scale displays and portable projection systems.

== Appendix ==
* [https://github.com/chilman98/scheimpflug-blur/tree/main GitHub Repository]

Image Optimization for Optical Projector Arrays

2024-12-13T08:05:34Z

Leiyu: /* Appendix */

Pupil Shape in the Animal Kingdom

2024-12-13T07:55:40Z

Leiyu:

Pupil Shape in the Animal Kingdom

2024-12-13T07:50:55Z

Leiyu:

Pupil Shape in the Animal Kingdom

2024-12-13T07:50:01Z

Leiyu:

Pupil Shape in the Animal Kingdom

2024-12-13T07:47:48Z

Leiyu:

Pupil Shape in the Animal Kingdom

2024-12-13T07:45:54Z

Leiyu:

Pupil Shape in the Animal Kingdom

2024-12-13T07:40:27Z

Leiyu:

Pupil Shape in the Animal Kingdom

2024-12-13T07:35:06Z

Leiyu:

Pupil Shape in the Animal Kingdom

2024-12-13T07:28:32Z

Leiyu: /* Horizontal goat pupil and vertical cat pupil */

== Introduction ==

== Background ==

== Methods ==
In this project, we utilized ISETCam and ISETBio to simulate the imaging process that occurs within an animal's eye.

[[File: Figure. schematic.png|800px|thumb|center|Figure 1. The flow chart illustrates the simulation process, with the examples below each step. ]]

===Scene===
We created two types of scenes for our simulations: sceneCreate.m to generate gridlines and sceneFromFile.m to read an image. The gridlines illustrate the effects along different axes, while the image provides a visualization of what the animal might be seeing.

===Aperture===
The aperture represents the pupil shape and is modeled as a 201x201 matrix. In this matrix, ones indicate the regions where light can pass through (white), while zeros denote the areas where light is blocked (black).
For the single-slit elliptical aperture, we can adjust both the size and the orientation of the ellipse (vertical or horizontal). For the multiple-slit aperture, we can modify the slit length, slit width, and the number of slits. For the w-shaped aperture, we intake the w-shape black and white image to generate the aperture matrix, and are able to change the size of it.

===Point spread function and Optical image===
The point spread function was simulated for each aperture to analyze the impact of aperture shapes on light passing through the aperture. This was achieved by creating a diffraction-limited wavefront structure using wvfCreate.m and computing the point spread function with wvf.Compute.m with the aperture matrix as input.
The optical image was generated using oiCompute.m taking in the scene and the aperture matrix as inputs. The simulation process assumes that the optical lens is diffraction-limited.
===Cone Mosaic and Absorptions===
To simulate how the eye’s sensor processes the scene, we modeled the human cone mosaic using cMosaic.m in ISETbio, and used cm.compute.m to simulate the cone excitations and absorptions. Due to time constraints, we only tried the human cone distribution, but it would be highly valuable to try incorporating known cone distributions from the literature for various animals in the future.

== Results ==

===Horizontal goat pupil and vertical cat pupil===
The horizontal slit pupil introduces blurring along the vertical direction, evident in the scene by the horizontal gridlines appearing blurred while the vertical gridlines remain sharply in focus. This effect is also replicated in the cone mosaic plot, confirming the impact on visual perception. Conversely, for the vertical slit pupil, the phenomenon is observed along the opposite axis. The horizontal gridlines remain sharply focused, while the vertical gridlines appear blurred. This demonstrates that a vertical pupil causes blurring in the horizontal direction while maintaining clarity along the vertical axis.

[[File: Horizontal_vertical_pupil.PNG|800px|thumb|center|Figure 2. Horizontal pupil has enhanced features identification along the vertical direction compared with vertical pupil. (A) Horizontal pupil and vertical pupil. (B) Point spread function of each pupil case. (C) Optical images of the grid scene.(D) Cone mosaic absorption of the optical image.]]

These plots align with our understanding of the functional advantages of pupil shapes in animals. For prey animals with horizontal slit pupils, having sharp focus across the horizontal axis is advantageous, as it allows them to effectively monitor their surroundings for predators. Additionally, the laterally placed eyes of these animals provide a wide field of view, further enhancing their ability to detect threats. On the other hand, predator animals with vertical slit pupils benefit from sharp focus along the vertical axis, which aids in keeping their prey in view. This vertical focus is particularly useful when combined with head or eye movements to track prey's horizontal motion, supporting their hunting strategies.

===Slit pupil vs. circular pupil===

When comparing a slit pupil to a circular pupil of the same area, we observe that for a smaller aperture, the circular pupil leads to blurring across the entire scene. This occurs because diffraction becomes more pronounced in smaller apertures, causing the loss of sharp focus. In contrast, a slit pupil of the same area can retain focus along one axis. Specifically, for a vertical slit pupil, the image remains sharp along the vertical direction while blurring occurs along the horizontal axis.

[[File: Figure 1 vertical_vs_round .png|900px|thumb|center|Figure 3. Vertical pupil has enhanced features identification along the vertical direction compared with round pupil with the same size. (A) Round pupils in comparison with the vertical pupils with the same size (B) Point Spread Function of each pupil case. (C) Optical images of the grid scene. (D) Cone mosaic absorption of the optical image and (E) the horizontal integration of the absorption intensity. ]]

These plots support our understanding of the behavior of predator animals. Many predators with vertical slit pupils are also nocturnal. During the day, their pupils constrict to a small area to limit the amount of light entering the eye. If their pupils were circular, the small aperture would cause significant diffraction, leading to a loss of visual clarity. However, the vertical slit pupil allows them to maintain good focus along one axis, despite the reduced aperture size, enabling them to retain functional vision even in bright conditions. This ability is particularly beneficial for nocturnal predators, allowing them to effectively navigate and hunt in varying lighting conditions.

== Conclusions ==

== Appendix ==

You can write math equations as follows:
<math>y = x + 5 </math>

You can include images as follows (you will need to upload the image first using the toolbox on the left bar, using the "Upload file" link).

[[File:Snip 20210106183207.png|200px]]

Pupil Shape in the Animal Kingdom

2024-12-13T07:27:30Z

Leiyu:

== Introduction ==

== Background ==

== Methods ==
In this project, we utilized ISETCam and ISETBio to simulate the imaging process that occurs within an animal's eye.

[[File: Figure. schematic.png|800px|thumb|center|Figure 1. The flow chart illustrates the simulation process, with the examples below each step. ]]

===Scene===
We created two types of scenes for our simulations: sceneCreate.m to generate gridlines and sceneFromFile.m to read an image. The gridlines illustrate the effects along different axes, while the image provides a visualization of what the animal might be seeing.

===Aperture===
The aperture represents the pupil shape and is modeled as a 201x201 matrix. In this matrix, ones indicate the regions where light can pass through (white), while zeros denote the areas where light is blocked (black).
For the single-slit elliptical aperture, we can adjust both the size and the orientation of the ellipse (vertical or horizontal). For the multiple-slit aperture, we can modify the slit length, slit width, and the number of slits. For the w-shaped aperture, we intake the w-shape black and white image to generate the aperture matrix, and are able to change the size of it.

===Point spread function and Optical image===
The point spread function was simulated for each aperture to analyze the impact of aperture shapes on light passing through the aperture. This was achieved by creating a diffraction-limited wavefront structure using wvfCreate.m and computing the point spread function with wvf.Compute.m with the aperture matrix as input.
The optical image was generated using oiCompute.m taking in the scene and the aperture matrix as inputs. The simulation process assumes that the optical lens is diffraction-limited.
===Cone Mosaic and Absorptions===
To simulate how the eye’s sensor processes the scene, we modeled the human cone mosaic using cMosaic.m in ISETbio, and used cm.compute.m to simulate the cone excitations and absorptions. Due to time constraints, we only tried the human cone distribution, but it would be highly valuable to try incorporating known cone distributions from the literature for various animals in the future.

== Results ==

===Horizontal goat pupil and vertical cat pupil===
The horizontal slit pupil introduces blurring along the vertical direction, evident in the scene by the horizontal gridlines appearing blurred while the vertical gridlines remain sharply in focus. This effect is also replicated in the cone mosaic plot, confirming the impact on visual perception. Conversely, for the vertical slit pupil, the phenomenon is observed along the opposite axis. The horizontal gridlines remain sharply focused, while the vertical gridlines appear blurred. This demonstrates that a vertical pupil causes blurring in the horizontal direction while maintaining clarity along the vertical axis.

[[File: Horizontal vertical pupil .png|800px|thumb|center|Figure 2. Horizontal pupil has enhanced features identification along the vertical direction compared with vertical pupil. (A) Horizontal pupil and vertical pupil. (B) Point spread function of each pupil case. (C) Optical images of the grid scene.(D) Cone mosaic absorption of the optical image.]]

These plots align with our understanding of the functional advantages of pupil shapes in animals. For prey animals with horizontal slit pupils, having sharp focus across the horizontal axis is advantageous, as it allows them to effectively monitor their surroundings for predators. Additionally, the laterally placed eyes of these animals provide a wide field of view, further enhancing their ability to detect threats. On the other hand, predator animals with vertical slit pupils benefit from sharp focus along the vertical axis, which aids in keeping their prey in view. This vertical focus is particularly useful when combined with head or eye movements to track prey's horizontal motion, supporting their hunting strategies.

===Slit pupil vs. circular pupil===

When comparing a slit pupil to a circular pupil of the same area, we observe that for a smaller aperture, the circular pupil leads to blurring across the entire scene. This occurs because diffraction becomes more pronounced in smaller apertures, causing the loss of sharp focus. In contrast, a slit pupil of the same area can retain focus along one axis. Specifically, for a vertical slit pupil, the image remains sharp along the vertical direction while blurring occurs along the horizontal axis.

[[File: Figure 1 vertical_vs_round .png|900px|thumb|center|Figure 3. Vertical pupil has enhanced features identification along the vertical direction compared with round pupil with the same size. (A) Round pupils in comparison with the vertical pupils with the same size (B) Point Spread Function of each pupil case. (C) Optical images of the grid scene. (D) Cone mosaic absorption of the optical image and (E) the horizontal integration of the absorption intensity. ]]

These plots support our understanding of the behavior of predator animals. Many predators with vertical slit pupils are also nocturnal. During the day, their pupils constrict to a small area to limit the amount of light entering the eye. If their pupils were circular, the small aperture would cause significant diffraction, leading to a loss of visual clarity. However, the vertical slit pupil allows them to maintain good focus along one axis, despite the reduced aperture size, enabling them to retain functional vision even in bright conditions. This ability is particularly beneficial for nocturnal predators, allowing them to effectively navigate and hunt in varying lighting conditions.

== Conclusions ==

== Appendix ==

You can write math equations as follows:
<math>y = x + 5 </math>

You can include images as follows (you will need to upload the image first using the toolbox on the left bar, using the "Upload file" link).

[[File:Snip 20210106183207.png|200px]]

Pupil Shape in the Animal Kingdom

2024-12-13T07:14:27Z

Leiyu: /* Methods */

Pupil Shape in the Animal Kingdom

2024-12-13T07:13:53Z

Leiyu: /* Methods */

== Introduction ==

== Background ==

== Methods ==
In this project, we utilized ISETCam and ISETBio to simulate the imaging process that occurs within an animal's eye.

[[File: Horizontal vertical pupil.PNG|800px|thumb|center|The flow chart illustrates the simulation process, with the examples below each step. ]]

===Scene===
We created two types of scenes for our simulations: sceneCreate.m to generate gridlines and sceneFromFile.m to read an image. The gridlines illustrate the effects along different axes, while the image provides a visualization of what the animal might be seeing.

===Aperture===
The aperture represents the pupil shape and is modeled as a 201x201 matrix. In this matrix, ones indicate the regions where light can pass through (white), while zeros denote the areas where light is blocked (black).
For the single-slit elliptical aperture, we can adjust both the size and the orientation of the ellipse (vertical or horizontal). For the multiple-slit aperture, we can modify the slit length, slit width, and the number of slits. For the w-shaped aperture, we intake the w-shape black and white image to generate the aperture matrix, and are able to change the size of it.

===Point spread function and Optical image===
The point spread function was simulated for each aperture to analyze the impact of aperture shapes on light passing through the aperture. This was achieved by creating a diffraction-limited wavefront structure using wvfCreate.m and computing the point spread function with wvf.Compute.m with the aperture matrix as input.
The optical image was generated using oiCompute.m taking in the scene and the aperture matrix as inputs. The simulation process assumes that the optical lens is diffraction-limited.
===Cone Mosaic and Absorptions===
To simulate how the eye’s sensor processes the scene, we modeled the human cone mosaic using cMosaic.m in ISETbio, and used cm.compute.m to simulate the cone excitations and absorptions. Due to time constraints, we only tried the human cone distribution, but it would be highly valuable to try incorporating known cone distributions from the literature for various animals in the future.

== Results ==

== Conclusions ==

== Appendix ==

You can write math equations as follows:
<math>y = x + 5 </math>

You can include images as follows (you will need to upload the image first using the toolbox on the left bar, using the "Upload file" link).

[[File:Snip 20210106183207.png|200px]]

File:Circuilar pupil.PNG

2024-12-13T07:04:02Z

Leiyu:

File:Horizontal vertical pupil.PNG

2024-12-13T06:47:12Z

Leiyu:

File:Multiple slit.png

2024-12-13T06:45:58Z

Leiyu:

File:Figure 1 vertical vs round .png

2024-12-13T06:29:52Z

Leiyu:

Pupil Shape in the Animal Kingdom

2024-12-13T06:25:33Z

Leiyu: /* Methods */ trial, how to insert image?

== Introduction ==

== Background ==

== Methods ==
In this project, we utilized ISETCam and ISETBio to simulate the imaging process that occurs within an animal's eye.

Scene
We created two types of scenes for our simulations: sceneCreate.m to generate gridlines and sceneFromFile.m to read an image. The gridlines illustrate the effects along different axes, while the image provides a visualization of what the animal might be seeing.

== Results ==

== Conclusions ==

== Appendix ==

You can write math equations as follows:
<math>y = x + 5 </math>

You can include images as follows (you will need to upload the image first using the toolbox on the left bar, using the "Upload file" link).

[[File:Snip 20210106183207.png|200px]]