You will use your student ID parameter X,Y in this question] H 4 8 10 12...

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You will use your student ID parameter X,Y in this question] H 4 8 10 12 13 6 8 8 11 9 6 5 X 96 6 3 7 10 9 3 5 6 8 12 5 9 10 11 12 6 8799 76 Y 86 8 5 8 10 9 2 5 6 8 11 For the images given above, we would like to estimate the motion vector at the center position from image H to image /. Do the following steps: (a) Calculate the horizontal and vertical derivatives (in image /) for the shaded pixels using filter (-1,0,1] and its transpose, respectively. (Denote these derivates as lx and ly.) (b) Calculate / for the center pixel and write the optical flow equation for the center pixel. (c) Write the gradient vector at the center position. (d) If possible, solve for the optical flow component along the gradient vector. If not, explain. (e) Assume the motion vector is constant in the 3x3 region around the center position. Write the linear set of equations in matrix-vector form to solve for the motion vector. (You do not need to calculate.) (f) Write the formula for the least squares solution of equation Ad = b, where A and b are given; A is a Nx2 matrix and b is Nx1 vector, and N is an integer greater than or equal to 2. You will use your student ID parameter X,Y in this question] H 4 8 10 12 13 6 8 8 11 9 6 5 X 96 6 3 7 10 9 3 5 6 8 12 5 9 10 11 12 6 8799 76 Y 86 8 5 8 10 9 2 5 6 8 11 For the images given above, we would like to estimate the motion vector at the center position from image H to image /. Do the following steps: (a) Calculate the horizontal and vertical derivatives (in image /) for the shaded pixels using filter (-1,0,1] and its transpose, respectively. (Denote these derivates as lx and ly.) (b) Calculate / for the center pixel and write the optical flow equation for the center pixel. (c) Write the gradient vector at the center position. (d) If possible, solve for the optical flow component along the gradient vector. If not, explain. (e) Assume the motion vector is constant in the 3x3 region around the center position. Write the linear set of equations in matrix-vector form to solve for the motion vector. (You do not need to calculate.) (f) Write the formula for the least squares solution of equation Ad = b, where A and b are given; A is a Nx2 matrix and b is Nx1 vector, and N is an integer greater than or equal to 2.

Answer rating: 100% (QA)

a To calculate the horizontal and vertical derivatives for the shaded pixels using the filter 1 0 1 and its transpose we apply the filters to each pix... View the full answer