IsmailPeters

Back to Psych 221 Projects 2013

Background

Camera Basics

A digital camera captures color images by recording data in different channels of the visible spectrum (red, green, blue). Most cameras accomplish this by using a single type of CCD or CMOS sensor at each pixel. This sensor measures the intensity of light that is focused on it, but cannot distinguish between colors. Therefore, a color filter is placed over each sensor, and the sensor only records the intensity of a specific color at that pixel. The arrangement of these color filters over an image is known as a Color Filter Array. Figure 1 shows a very common CFA known as the Bayer Array.

Figure 1: Bayer Array

In the Bayer Array, green color filters are arranged in a checkerboard pattern, whereas the red and blue color filters are arranged by alternating rows. The original reasoning for using this distribution of colors was to mimic the physiology of the human eye. During daylight vision, the luminance perception of the retina uses both L and M cones, which are more sensitive to green light. The red and blue filters control the sensitivity of the eye to chrominance.

CFA Interpolation

Since each color channel is only tallied at specific coordinates, the remaining pixels in that channel must be estimated in some way. There are many interpolation schemes - a few simple examples are the bilinear,bicubic, and smooth hue transition interpolations shown below. Other interpolation schemes, such as median filter, gradient-based, and adaptive color plane, become increasingly complex. A wide survey of interpolation methods is available at (REFERENCE), along with an analysis of the advantages and disadvantages of each.

Bilinear/Bicubic

A linear combination of the nearest N neighbors in any direction for N = 1 (bilinear) or N = 3 (bicubic). INSERT BILINEAR/BICUBIC EQUATION HERE

Smooth Hue Transition

Operates on the assumption that the hue of a natural image (chrominance/luminance, or red/green and blue/green) changes smoothly in local regions INSERT SMOOTH HUE EQUATIONS

Detecting Forgeries

Regardless of the type of interpolation used in a given image, the estimated pixels should exhibit a strong correlation, or dependence, on their surrounding pixels. If one can categorize each pixel as either correlated or independent with respect to other pixels, one should see a periodic pattern that mimics the CFA used to construct the image. Even if an altered image does not have any visual cues that point to its forgery, inspecting the correlation of pixels to one another can potentially expose which parts of an image were altered. It is important to note that, even if an image has been altered, the mentioned correlations may still be kept intact. In this way, detecting forgeries through CFA interpolation is one tool out of many used to detect forgeries.

Methods

Measuring retinotopic maps

Retinotopic maps were obtained in 5 subjects using Population Receptive Field mapping methods Dumoulin and Wandell (2008). These data were collected for another research project in the Wandell lab. We re-analyzed the data for this project, as described below.

Subjects

Subjects were 5 healthy volunteers.

MR acquisition

Data were obtained on a GE scanner. Et cetera.

MR Analysis

The MR data was analyzed using mrVista software tools.

Pre-processing

All data were slice-time corrected, motion corrected, and repeated scans were averaged together to create a single average scan for each subject. Et cetera.

PRF model fits

PRF models were fit with a 2-gaussian model.

MNI space

After a pRF model was solved for each subject, the model was trasnformed into MNI template space. This was done by first aligning the high resolution t1-weighted anatomical scan from each subject to an MNI template. Since the pRF model was coregistered to the t1-anatomical scan, the same alignment matrix could then be applied to the pRF model.
Once each pRF model was aligned to MNI space, 4 model parameters - x, y, sigma, and r^2 - were averaged across each of the 6 subjects in each voxel.

Et cetera.

Results - What you found

Retinotopic models in native space

Some text. Some analysis. Some figures.

Retinotopic models in individual subjects transformed into MNI space

Some text. Some analysis. Some figures.

Retinotopic models in group-averaged data on the MNI template brain

Some text. Some analysis. Some figures. Maybe some equations.

Equations

If you want to use equations, you can use the same formats that are use on wikipedia.
See wikimedia help on formulas for help.
This example of equation use is copied and pasted from wikipedia's article on the DFT.

The sequence of N complex numbers x₀, ..., x_N−1 is transformed into the sequence of N complex numbers X₀, ..., X_N−1 by the DFT according to the formula:

$X_k=\sum _{n=0}^{N-1}{x}_n{e}^{-\frac{2\pi i}{N}kn}k=0,\dots ,N-1$

where i is the imaginary unit and $e^{\frac{2\pi i}{N}}$ is a primitive N'th root of unity. (This expression can also be written in terms of a DFT matrix; when scaled appropriately it becomes a unitary matrix and the X_k can thus be viewed as coefficients of x in an orthonormal basis.)

The transform is sometimes denoted by the symbol $ℱ$, as in $𝐗=ℱ\left\{𝐱\right\}$ or $ℱ\left(𝐱\right)$ or $ℱ𝐱$.

The inverse discrete Fourier transform (IDFT) is given by

$x_n=\frac{1}{N}\sum _{k=0}^{N-1}{X}_k{e}^{\frac{2\pi i}{N}kn}n=0,\dots ,N-1.$

Retinotopic models in group-averaged data projected back into native space

Some text. Some analysis. Some figures.

Conclusions

Here is where you say what your results mean.

References - Resources and related work

References

Software

Appendix I - Code and Data

Code

File:CodeFile.zip

Data

zip file with my data

Appendix II - Work partition (if a group project)

Brian and Bob gave the lectures. Jon mucked around on the wiki.