MichaelAlissa - Revision history

imported>Student221: /* Methods */

2019-12-14T19:24:24Z

Methods

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	* Calculate the centroid for each set of points, given by the following equation:		* Calculate the centroid for each set of points, given by the following equation:
	::<math>A_{centroid} = \frac{1}{N}\sum^N_{i=1}{A_i}</math>		::<math>A_{centroid} = \frac{1}{N}\sum^N_{i=1}{A_i}</math>
	:Shown in Figure #, this is simply the average of the x, y, and z values for all points in a set.		:Shown in Figure 9, this is simply the average of the x, y, and z values for all points in a set.
	* Center both sets of points at the origin (Figure 9). This is accomplished subtracting the centroid of each set from all the points in the corresponding set.		* Center both sets of points at the origin (Figure 9). This is accomplished subtracting the centroid of each set from all the points in the corresponding set.
	* To find the rotation from A to B in Figure 9, we take the singular value decomposition (SVD) of the cross-covariance matrix of A and B. This cross covariance matrix can be calculated as		* To find the rotation from A to B in Figure 9, we take the singular value decomposition (SVD) of the cross-covariance matrix of A and B. This cross covariance matrix can be calculated as

imported>Student221: /* References */

2019-12-14T19:24:02Z

References

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	3. Gao, Peiran, and Surya Ganguli. "On simplicity and complexity in the brave new world of large-scale neuroscience." Current opinion in neurobiology 32 (2015): 148-155.		3. Gao, Peiran, and Surya Ganguli. "On simplicity and complexity in the brave new world of large-scale neuroscience." Current opinion in neurobiology 32 (2015): 148-155.

			4. "Least-Squares Fitting of Two 3-D Point Sets", Arun, K. S. and Huang, T. S. and Blostein, S. D, IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 9 Issue 5, May 1987

	== Appendix ==		== Appendix ==

	Our code can be found at [[https://code.stanford.edu/aling96/intel code.stanford.edu]]		Our code can be found at [[https://code.stanford.edu/aling96/intel code.stanford.edu]]

imported>Student221: /* Results */

2019-12-14T00:19:00Z

Results

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	We repeated this process at greater distances from the two cameras to relate our multi-camera point cloud reconstruction to the beginning quantitative analysis of depth error. Figure 11 shows the heatmap of for both cameras of the object at distances of 0.4, 0.6, 0.8, and 1 meter away from the camera. The object is sharper and has a higher resolution in depths thats are less than 0.6 meters, but as the depth increases past 0.8 meters, the object's resolution dramatically decreases. The depth data for calibration tool at farther depths shows more noise and spread than the depths closer to the camera.		We repeated this process at greater distances from the two cameras to relate our multi-camera point cloud reconstruction to the beginning quantitative analysis of depth error. Figure 11 shows the heatmap of for both cameras of the object at distances of 0.4, 0.6, 0.8, and 1 meter away from the camera. The object is sharper and has a higher resolution in depths thats are less than 0.6 meters, but as the depth increases past 0.8 meters, the object's resolution dramatically decreases. The depth data for calibration tool at farther depths shows more noise and spread than the depths closer to the camera.
	As depicted in Figure 12, the point cloud reconstruction quality dramatically decreases. The data becomes noisier, the alignment between the cameras worsens, and it becomes difficult to distinguish finer details in the calibration tool. The rapid increase in measurement noise that occurs as distance increases—a phenomenon characterized above for a single camera—is a significant drawback of the RealSense d435, limiting its ability to perform 3d reconstruction outside of close range measurements.		As depicted in Figure 12, the point cloud reconstruction quality dramatically decreases. The data becomes noisier, the alignment between the cameras worsens, and it becomes difficult to distinguish finer details in the calibration tool. The rapid increase in measurement noise that occurs as distance increases—a phenomenon characterized above for a single camera—is a significant drawback of the RealSense d435, limiting its ability to perform 3d reconstruction outside of close range measurements.
	[[File:Point creation.png\|300px\|thumb\|~~right~~\|alt text\| Figure 10: 3D Point cloud reconstruction at a depth of 0.2 meters]]		[[File:Point creation.png\|300px\|thumb\|left\|alt text\| Figure 10: 3D Point cloud reconstruction at a depth of 0.2 meters]]
	[[File:Pointclouds.png\|300px\|thumb\|~~left~~\|alt text\| Figure 12: 3D Point cloud reconstruction at depths of 0.4, 0.6, 0.8, and 1 meter]]		[[File:Pointclouds.png\|300px\|thumb\|right\|alt text\| Figure 12: 3D Point cloud reconstruction at depths of 0.4, 0.6, 0.8, and 1 meter]]
	[[File:Image1016.png\|300px\|thumb\|center\|alt text\| Figure 11: Heatmap of depth images from two cameras at depths of 0.4, 0.6, 0.8, and 1 meter]]		[[File:Image1016.png\|300px\|thumb\|center\|alt text\| Figure 11: Heatmap of depth images from two cameras at depths of 0.4, 0.6, 0.8, and 1 meter]]

imported>Student221: /* Results */

2019-12-14T00:15:26Z

Results

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	With this algorithm, we can successfully locate the four ball positions, providing four common points which we can use to align our camera system. Templates 3 and 4 in Figure 8 provide examples of successful template matches. Once the template is matched to a sphere on the calibration tool, the midpoint of the sphere is automatically found by taking the pixel coordinate in the center of the bounding box. For our two camera set up, the cameras were positions close enough together that the midpoint of the the spheres in both pictures provided a good estimate of similar points within the two images. We then used these similar points to calculate the rotation and translation matrices of one camera with respect to the other camera.		With this algorithm, we can successfully locate the four ball positions, providing four common points which we can use to align our camera system. Templates 3 and 4 in Figure 8 provide examples of successful template matches. Once the template is matched to a sphere on the calibration tool, the midpoint of the sphere is automatically found by taking the pixel coordinate in the center of the bounding box. For our two camera set up, the cameras were positions close enough together that the midpoint of the the spheres in both pictures provided a good estimate of similar points within the two images. We then used these similar points to calculate the rotation and translation matrices of one camera with respect to the other camera.

	In its current state, however, our algorithm can provide false positive matches. For example, templates 1 and 2 in Figure 8 correspond to templates that do not match the spheres on our calibration tool, yet find high confidence matching locations outside of the tool. Currently, these false positives must be manually excluded when running the algorithm, but future iterations of this calibration technique will look to remedy this issue.		In its current state, however, our algorithm can provide false positive matches. For example, templates 1 and 2 in Figure 8 correspond to templates that do not match the spheres on our calibration tool, yet find high confidence matching locations outside of the tool. Currently, these false positives must be manually excluded when running the algorithm, but future iterations of this calibration technique will look to remedy this issue. Future iterations of the algorithm will also account for different orientations of camera placement. Instead of using the midpoint as similar points between the two cameras, we will template match to the curvature of the sphere to find the exact location of the full sphere. This way, we will be able to find similar points between any camera orientation.
	[[File:temp_matching.png\|300px\|thumb\|center\|alt text\| Figure 8: Template Matching algorithm to find the center of the spheres on the calibration tool]]		[[File:temp_matching.png\|300px\|thumb\|center\|alt text\| Figure 8: Template Matching algorithm to find the center of the spheres on the calibration tool]]

imported>Student221: /* Results */

2019-12-14T00:13:03Z

Results

← Older revision		Revision as of 00:13, 14 December 2019
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	===Results===		===Results===
	With this algorithm, we can successfully locate the four ball positions, providing four common points which we can use to align our camera system. Templates 3 and 4 in Figure 8 provide examples of successful template matches. Once the template is matched to a sphere on the calibration tool, the midpoint of the sphere is automatically found by taking the pixel coordinate in the center of the bounding box.		With this algorithm, we can successfully locate the four ball positions, providing four common points which we can use to align our camera system. Templates 3 and 4 in Figure 8 provide examples of successful template matches. Once the template is matched to a sphere on the calibration tool, the midpoint of the sphere is automatically found by taking the pixel coordinate in the center of the bounding box. For our two camera set up, the cameras were positions close enough together that the midpoint of the the spheres in both pictures provided a good estimate of similar points within the two images. We then used these similar points to calculate the rotation and translation matrices of one camera with respect to the other camera.

	In its current state, however, our algorithm can provide false positive matches. For example, templates 1 and 2 in Figure 8 correspond to templates that do not match the spheres on our calibration tool, yet find high confidence matching locations outside of the tool. Currently, these false positives must be manually excluded when running the algorithm, but future iterations of this calibration technique will look to remedy this issue.		In its current state, however, our algorithm can provide false positive matches. For example, templates 1 and 2 in Figure 8 correspond to templates that do not match the spheres on our calibration tool, yet find high confidence matching locations outside of the tool. Currently, these false positives must be manually excluded when running the algorithm, but future iterations of this calibration technique will look to remedy this issue.

imported>Student221: /* Methods */

2019-12-14T00:07:02Z

Methods

← Older revision		Revision as of 00:07, 14 December 2019
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	===Methods===		===Methods===

	To establish a baseline of the error present in the point cloud ~~construction from~~ multi-camera setup, we first characterized the accuracy and temporal noise for a single camera. To accomplish this, we designed an experimental rig—depicted in Figures 4a and 4b—which ~~allowed~~ the imaging plane of the camera and the ~~surfaced~~ of the wall to ~~oriented~~ parallel to each other. The camera could then be adjusted to different distances from the wall while maintaining this orientation. We performed recordings ranging from 0.2 – 2 meters at increments of 0.2 meters. Five, 1-minute recording with a sampling rate of 90 frames per second were taken at each measurement distance, analysis for all recordings was confined to the same section of wall, which possessed a matte, textured finish.		To establish a baseline of the error present in the camera's depth measurements, later used in the point cloud reconstruction using a multi-camera setup, we first characterized the depth measurement accuracy and temporal noise for a single camera. To accomplish this, we designed an experimental rig—depicted in Figures 4a and 4b—which oriented the imaging plane of the camera and the surface of the wall to be parallel to each other. The camera could then be adjusted to different distances from the wall while maintaining this orientation. The depth value reported back from the camera is the distance of the object (in this experiment, the wall) to the plane of the camera sensors. With our setup, we measured exactly how far away the front of the camera was to the wall. We used this measurement as ground truth, and compared the reported depth measurement from the camera to calculate the error of the depth measurements. We performed recordings ranging from 0.2 – 2 meters at increments of 0.2 meters. Five, 1-minute recording with a sampling rate of 90 frames per second were taken at each measurement distance, analysis for all recordings was confined to the same section of wall, which possessed a matte, textured finish.

	[[File:exp_rig.png\|300px\|thumb\|center\|alt text\| Figure 4: Experimental setup to quantify depth error]]		[[File:exp_rig.png\|300px\|thumb\|center\|alt text\| Figure 4: Experimental setup to quantify depth error]]

imported>Student221: /* Background */

2019-12-13T23:57:53Z

Background

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	The Intel RealSense D400 Series depth cameras are commercial stereo tracking solutions that are low cost, lightweight, and powerful that are capable of recording both depth and RGB data. There are two types of cameras in the D400 Series, the D415 and the D435 depth cameras. Both have the same maximum depth resolution of 1280x720 and provide RGB-D data over USB 3. However, there are important differences between the two with regards to field of view and shutter type, which factored into our consideration of which camera to use.		The Intel RealSense D400 Series depth cameras are commercial stereo tracking solutions that are low cost, lightweight, and powerful that are capable of recording both depth and RGB data. There are two types of cameras in the D400 Series, the D415 and the D435 depth cameras. Both have the same maximum depth resolution of 1280x720 and provide RGB-D data over USB 3. However, there are important differences between the two with regards to field of view and shutter type, which factored into our consideration of which camera to use.

	The [https://www.intelrealsense.com/depth-camera-d415/ Intel RealSense D415] camera has a small field of view of about 70 degrees that provides a higher quality depth per degree. It is useful for imaging smaller objects and getting precise measurements because of its high depth resolution. However, it uses rolling shutters, which scan the image sequentially from one side of the sensor to the other. There are spatial distortions in rolling shutter due to the fact that the the image has pixels that are not taken at the exact same time throughout the scene. In scenes with motion, this is especially apparent because the image will capture the motion at different times. For our research purposes, the D415 is not suitable because it will cause spatial distortion when we image and reconstruct limb and body movements.		The [https://www.intelrealsense.com/depth-camera-d415/ Intel RealSense D415] camera has a small field of view of about 70 degrees that provides a higher quality depth per degree. It is useful for imaging smaller objects and getting precise measurements because of its high depth resolution. However, it uses rolling shutters, which scan the image sequentially from one side of the sensor to the other. There are spatial distortions in images captured by rolling shutter sensors due to the fact that the the image has pixels that are not taken at the exact same time throughout the scene. In scenes with motion, this is especially apparent because the image will capture the motion at different times. For our research purposes, the D415 is not suitable because it will cause spatial distortion when we image and reconstruct limb and body movements.

	The [https://www.intelrealsense.com/depth-camera-d435/ Intel RealSense D435] (Figure 2) depth camera provides a wide field of view and global shutter sensor. This depth stream employs a global shutter, which scan the entire area of the image simultaneously, has a diagonal field of view of approximately 95 degrees, and at a resolution of 848x480 pixels can achieve frame rates of up to 90 frames per second. Able to detect depths from 0.1 to 10 meters, this camera calculates depth using two monochrome sensors, as shown in Figure 2. These monochrome sensors—which detect both visible and infrared light—perform stereoscopic matching to calculate the frame depth values. Depicted in Figure 3, stereoscopic matching consists of first calculating the disparity (i.e. shift in the horizontal axis) between images created by the two cameras. As the focal length and baseline distance (i.e. the distance between the imaging sensors), depth values can be calculated with the following equation:		The [https://www.intelrealsense.com/depth-camera-d435/ Intel RealSense D435] (Figure 2) depth camera provides a wide field of view and global shutter sensor. This depth stream employs a global shutter, which scan the entire area of the image simultaneously, has a diagonal field of view of approximately 95 degrees, and at a resolution of 848x480 pixels can achieve frame rates of up to 90 frames per second. Able to detect depths from 0.1 to 10 meters, this camera calculates depth using two monochrome sensors, as shown in Figure 2. These monochrome sensors—which detect both visible and infrared light—perform stereoscopic matching to calculate the frame depth values. Depicted in Figure 3, stereoscopic matching consists of first calculating the disparity (i.e. shift in the horizontal axis) between images created by the two cameras. As the focal length and baseline distance (i.e. the distance between the imaging sensors), depth values can be calculated with the following equation:

imported>Student221: /* Background */

2019-12-13T23:57:09Z

Background

← Older revision		Revision as of 23:57, 13 December 2019
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	The Intel RealSense D400 Series depth cameras are commercial stereo tracking solutions that are low cost, lightweight, and powerful that are capable of recording both depth and RGB data. There are two types of cameras in the D400 Series, the D415 and the D435 depth cameras. Both have the same maximum depth resolution of 1280x720 and provide RGB-D data over USB 3. However, there are important differences between the two with regards to field of view and shutter type, which factored into our consideration of which camera to use.		The Intel RealSense D400 Series depth cameras are commercial stereo tracking solutions that are low cost, lightweight, and powerful that are capable of recording both depth and RGB data. There are two types of cameras in the D400 Series, the D415 and the D435 depth cameras. Both have the same maximum depth resolution of 1280x720 and provide RGB-D data over USB 3. However, there are important differences between the two with regards to field of view and shutter type, which factored into our consideration of which camera to use.

	The [https://www.intelrealsense.com/depth-camera-d415/ Intel RealSense D415] camera has a small field of view of ~~<math>~~ 70~~^{\circ}\pm 3^{\circ}</math>~~ that provides a higher quality depth per degree. It is useful for imaging smaller objects and getting precise measurements because of its high depth resolution. However, it uses rolling shutters, which scan the image sequentially from one side of the sensor to the other. There are spatial distortions in rolling shutter due to the fact that the the image has pixels that are not taken at the exact same time throughout the scene. In scenes with motion, this is especially apparent because the image will capture the motion at different times. For our research purposes, the D415 is not suitable because it will cause spatial distortion when we image and reconstruct limb and body movements.		The [https://www.intelrealsense.com/depth-camera-d415/ Intel RealSense D415] camera has a small field of view of about 70 degrees that provides a higher quality depth per degree. It is useful for imaging smaller objects and getting precise measurements because of its high depth resolution. However, it uses rolling shutters, which scan the image sequentially from one side of the sensor to the other. There are spatial distortions in rolling shutter due to the fact that the the image has pixels that are not taken at the exact same time throughout the scene. In scenes with motion, this is especially apparent because the image will capture the motion at different times. For our research purposes, the D415 is not suitable because it will cause spatial distortion when we image and reconstruct limb and body movements.

	The [https://www.intelrealsense.com/depth-camera-d435/ Intel RealSense D435] (Figure 2) depth camera provides a wide field of view and global shutter sensor. This depth stream employs a global shutter, which scan the entire area of the image simultaneously, has a diagonal field of view of approximately 95 degrees, and at a resolution of 848x480 pixels can achieve frame rates of up to 90 frames per second. Able to detect depths from 0.1 to 10 meters, this camera calculates depth using two monochrome sensors, as shown in Figure 2. These monochrome sensors—which detect both visible and infrared light—perform stereoscopic matching to calculate the frame depth values. Depicted in Figure 3, stereoscopic matching consists of first calculating the disparity (i.e. shift in the horizontal axis) between images created by the two cameras. As the focal length and baseline distance (i.e. the distance between the imaging sensors), depth values can be calculated with the following equation:		The [https://www.intelrealsense.com/depth-camera-d435/ Intel RealSense D435] (Figure 2) depth camera provides a wide field of view and global shutter sensor. This depth stream employs a global shutter, which scan the entire area of the image simultaneously, has a diagonal field of view of approximately 95 degrees, and at a resolution of 848x480 pixels can achieve frame rates of up to 90 frames per second. Able to detect depths from 0.1 to 10 meters, this camera calculates depth using two monochrome sensors, as shown in Figure 2. These monochrome sensors—which detect both visible and infrared light—perform stereoscopic matching to calculate the frame depth values. Depicted in Figure 3, stereoscopic matching consists of first calculating the disparity (i.e. shift in the horizontal axis) between images created by the two cameras. As the focal length and baseline distance (i.e. the distance between the imaging sensors), depth values can be calculated with the following equation:

imported>Student221: /* Introduction */

2019-12-13T23:55:56Z

Introduction

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	[[File:playcage.png\|500px\|thumb\|right\|alt text\| Figure 1: Behavioral movements in a freely moving experimental rig will be imaged and translated into a skeletal model to calculate kinematics. ]]		[[File:playcage.png\|500px\|thumb\|right\|alt text\| Figure 1: Behavioral movements in a freely moving experimental rig will be imaged and translated into a skeletal model to calculate kinematics. ]]

	Systems neuroscience~~, the study of~~ how the brain works at the scale of systems (neural circuits, cortical regions, etc.) ~~is the foundation of Brain Machine Interfaces used in robotic prosthetics that are controlled by the brain~~. With the emergence of multichannel recordings over recent decades, the field has been revolutionized by access to hundreds of simultaneously recorded neurons, and awake behaving animal experiments have become even more critical to advancing our understanding (1). Classical nonhuman primate (NHP) in-rig experiments constrain most bodily movements except the movement of interest to reduce confounding variables to draw tight correlations between the desired behavior and neural population dynamics (2). However, it is unclear if these results generalize to ambulatory behavior. Further, some evidence suggests that the complexity/variability of the neural recordings is constrained by the complexity of the task being performed, artificially and unintentionally limiting the observed neural data (3). To address this, experiments with higher task complexity need to be conducted.		Systems neuroscience is concerned with understanding how the brain works at the scale of systems (neural circuits, cortical regions, etc). With the emergence of multichannel recordings over recent decades, the field has been revolutionized by access to hundreds of simultaneously recorded neurons, and awake behaving animal experiments have become even more critical to advancing our understanding (1). Classical nonhuman primate (NHP) in-rig experiments constrain most bodily movements except the movement of interest to reduce confounding variables to draw tight correlations between the desired behavior and neural population dynamics (2). However, it is unclear if these results generalize to ambulatory behavior. Further, some evidence suggests that the complexity/variability of the neural recordings is constrained by the complexity of the task being performed, artificially and unintentionally limiting the observed neural data (3). To address this, experiments with higher task complexity need to be conducted.

	Our lab will conduct freely moving experiments to directly ask whether increasing task complexity yields greater neural variance and how the extra neural variance correlates to various limb kinematics. To do this, we aim to simultaneously record neural data from motor regions of cortex of a freely moving rhesus macaque using a commercial wireless electrophysiology system and capture video of kinematic movements using multiple stereo depth cameras surrounding a large, transparent, observational rig (Figure 1a). This 3D data will yield a point cloud which will be fit to a skeleton to extract the kinematics of the monkey.		Our lab will conduct freely moving experiments to directly ask whether increasing task complexity yields greater neural variance and how the extra neural variance correlates to various limb kinematics. To do this, we aim to simultaneously record neural data from motor regions of cortex of a freely moving rhesus macaque using a commercial wireless electrophysiology system and capture video of kinematic movements using multiple stereo depth cameras surrounding a large, transparent, observational rig (Figure 1a). This 3D data will yield a point cloud which will be fit to a skeleton to extract the kinematics of the monkey.

imported>Student221: /* Results */

2019-12-13T23:53:10Z

Results

← Older revision		Revision as of 23:53, 13 December 2019
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	=== Results ===		=== Results ===

	Using the method above to calculate the rotation matrix and translation vector, aligned point cloud reconstruction was performed using the two-camera setup. This setup was used to image the calibration tool 0.2 meter increments from 0.2 – 1 meter. As shown in Figure 10, by applying the appropriate rotation and translation, data from the first camera can be aligned with the coordinate space of camera 2, allowing this data to be combined. While each separate camera image (Figure 10a, 10b) contains only a partial depiction of the calibration tool, these images can be combined to provide a more complete representation of the object. ~~When~~ this process ~~is repeated~~ at greater distances from the two cameras, as depicted in Figure 11, the point cloud reconstruction quality dramatically decreases. The data becomes noisier, the alignment between the cameras worsens, and it becomes difficult to distinguish finer details in the calibration tool. The rapid increase in measurement noise that occurs as distance increases—a phenomenon characterized above for a single camera—is a significant drawback of the RealSense d435, limiting its ability to perform 3d reconstruction outside of close range measurements.		Using the method above to calculate the rotation matrix and translation vector, aligned point cloud reconstruction was performed using the two-camera setup. This setup was used to image the calibration tool 0.2 meter increments from 0.2 – 1 meter. As shown in Figure 10, by applying the appropriate rotation and translation, data from the first camera can be aligned with the coordinate space of camera 2, allowing this data to be combined. While each separate camera image (Figure 10a, 10b) contains only a partial depiction of the calibration tool, these images can be combined to provide a more complete representation of the object. The parts of the object that were occluded in camera one could be seen in camera two, so when the two point clouds were combined, the resulting image was one that was more a complete representation of the object.
			We repeated this process at greater distances from the two cameras to relate our multi-camera point cloud reconstruction to the beginning quantitative analysis of depth error. Figure 11 shows the heatmap of for both cameras of the object at distances of 0.4, 0.6, 0.8, and 1 meter away from the camera. The object is sharper and has a higher resolution in depths thats are less than 0.6 meters, but as the depth increases past 0.8 meters, the object's resolution dramatically decreases. The depth data for calibration tool at farther depths shows more noise and spread than the depths closer to the camera.
			As depicted in Figure 12, the point cloud reconstruction quality dramatically decreases. The data becomes noisier, the alignment between the cameras worsens, and it becomes difficult to distinguish finer details in the calibration tool. The rapid increase in measurement noise that occurs as distance increases—a phenomenon characterized above for a single camera—is a significant drawback of the RealSense d435, limiting its ability to perform 3d reconstruction outside of close range measurements.
	[[File:Point creation.png\|300px\|thumb\|right\|alt text\| Figure 10: 3D Point cloud reconstruction at a depth of 0.2 meters]]		[[File:Point creation.png\|300px\|thumb\|right\|alt text\| Figure 10: 3D Point cloud reconstruction at a depth of 0.2 meters]]
	[[File:Pointclouds.png\|300px\|thumb\|left\|alt text\| Figure 11: 3D Point cloud reconstruction at depths of 0.4, 0.6, 0.8, and 1 meter]]		[[File:Pointclouds.png\|300px\|thumb\|left\|alt text\| Figure 12: 3D Point cloud reconstruction at depths of 0.4, 0.6, 0.8, and 1 meter]]
	[[File:Image1016.png\|300px\|thumb\|center\|alt text\| Figure 12: Heatmap of depth images from two cameras at depths of 0.4, 0.6, 0.8, and 1 meter]]		[[File:Image1016.png\|300px\|thumb\|center\|alt text\| Figure 11: Heatmap of depth images from two cameras at depths of 0.4, 0.6, 0.8, and 1 meter]]

	== Conclusions ==		== Conclusions ==