Transcript Lecture 26
Computational Vision CSCI 363, Fall 2012 Lecture 26 Review for Exam 2 1 Intersection of Constraints 1. Consider the plaid grating drawn below. The velocity vector associated with one component is v1 = (-1, 1). The velocity vector associated with the second component is v2 = (2, 0). What is the velocity of the coherent plaid grating formed by summing the two gratings? + =? 2 Motion Essay questions What is the aperture problem? How does it affect how we see motion? Describe how component cells and pattern cells respond to plaid stimuli. Where is each type of cell found in the visual system? What is the motion after-affect? What does it tell us about the motion processing performed by the brain? Explain why the stripes on a barberpole appear to move upward as the pole spins. 3 The Gradient Method Consider the following two images taken at two different times, t0 and t1. Assume that each image has been convolved with a Laplacian of a Gaussian filter. 5 -5 -9 -10 9 5 -5 -9 10 9 5 -5 11 10 9 5 Image 1 -5 5 9 10 -9 -10 -11 -5 -9 -10 5 -5 -9 9 5 -5 dC dt vp 2 nx ny2 Image 2 Use the gradient method to compute the magnitude and direction of the perpendicular velocity vector atthe edge. Assume x=1, y=1 is at the lower left corner. Compute your value starting at position (3, 2) of the 2nd image. 4 Binocular Disparity Assume an observer is fixating on the square. Sketch the projection of the square and the triangle on the retina. In the rectangles below sketch the approximate positions of each image on the rectangular slice of the retina. Center of projection Left Right Does the triangle have crossed or uncrossed disparity? 5 Binocular Disparity II Assume an observer is fixating on the square. Sketch the projection of the square and the triangle on the retina. In the rectangles below sketch the approximate positions of each image on the rectangular slice of the retina. Center of projection Left Right Does the triangle have crossed or uncrossed disparity? 6 Stereo Essay Questions What is the correspondence problem? Name 4 constraints that can be used to help solve the correspondence problem. Briefly describe each one. Briefly describe the Marr-Poggio algorithm for solving the stereo correspondence problem. Briefly describe the Marr-Poggio-Grimson algorithm for determining stereo disparity from two images. Describe the four types of cells that are tuned to disparity in V1. Sketch their responses with respect to disparity. How might these cells be used to compute disparity of a feature in the visual scene? 7 Fourier Spectra fft Image 1 Image 2 Fourier spectrum 1 Fourier spectrum 2 Sketch the resulting image and its Fourier spectrum after convolving Image 1 with image 2. 8 Spatial Frequency Essay Questions What is the psychophysical evidence that the human visual system processes images in terms of spatial frequencies? What evidence is the evidence that V1 cells respond specifically to spatial frequencies as opposed to edges and bars? Describe ways in which neurons are non-linear. Describe how simple and complex neurons can be classified in terms of their responses to drifting sine-wave gratings. 9 Temporal Frequency vs. Speed A V1 cell is shown a drifting sinewave grating with spatial frequency of 2 cycles/deg. It gives a maximal response when this grating's speed is v=4deg/sec. What speed will the V1 cell give its maximal response for a spatial frequency of 4 cycles/deg? Answer the same question for an MT cell that is tuned to speed. 10 More Motion Questions Describe the three types of motion detection techniques we learned in class. What is a motion energy filter? How does it detect motion? How can true velocity be computed from multiple measurements of the perpendicular velocities at different locations on an object? How can one deal with noise in the measurements? How do MT cells respond to motion? Specifically, what types of tuning to they exhibit? What is the spatial structure of their receptive fields? 11