MONT 104S Perception and VR
College of the Holy Cross, Fall 2008
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Assignment 4Due: Wednesday, October 8, in class
Problem 1: Trichromacy in color vision a) Computer monitors and televisions use only 3 colors (red, green and blue) to generate all the colors you see on the screen. Explain why this is possible in terms of your understanding of how human color vision works. b) Based on the organization of retinal ganglion cells' receptive fields in terms of their responses to color, explain why there appear to be pairs of complementary colors (red/green, blue/yellow and white/black).
Problem 2: Critical Periods in Development a) What is the "critical period" in visual development? b) Name two visual abilities that are affected by the critical period. c) What does the critical period tell us about the importance of visual experience for brain development?
Problem 3: Binocular Stereo Binocular stereo makes use of the fact that our two eyes are in different positions, which results in the image positions being in different places on each retina. In this problem, we will compute image positions for some points in the world when projected onto two image planes that are separated horizontally to see how this difference in image position, or "disparity", is generated. Consider the image of a point projecting onto two image planes below. For simplicity, the two eyes are looking straight off in the distance, so the plane of fixation is at infinity.
The centers of projection for the right eye and the left eye image planes are separated horizontally by a distance of 8 cm. We will give each eye its own coordinate system, so that a point in space will have one position relative to the left eye and a different position relative to the right eye. In particular, for every point in space, the horizontal position relative to the right eye is 8 cm less than its horizontal position relative to the left eye. The point shown is at poisition (4, 0, 10) with respect to the left eye (its horizontal position is +4 cm from the left eye's center of projection), and is at position (-4, 0, 10) for the right eye (its horizontal position is -4 cm from right eye's center of projection). Because of this difference, the point will project to different locations on the two retinas. a) Compute the image position on each retina for the following points. For each point, the image position is given for both the right eye and the left eye.
b) For each point in part a, calculate the horizontal disparity in the position on the right image plane and the position on the left image plane. That is, the disparity equals the right eye horizontal image position minus the left eye horizontal image position. c) How does the distance (Z value) of the point affect the horizontal disparity? How do disparities for points at the same distance (Z value) compare to one another? How do disparities for points at different distances compare? When the distance (Z value) is doubled, how does the disparity change (be specific)? d) There is no vertical disparity (difference in y image position) in this example. Why is there horizontal disparity, but no vertical disparity?
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Constance Royden--croyden@mathcs.holycross.edu
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