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assignment105

# assignment105 - UNIVERSITY OF MINNESOTA DEPARTMENT OF...

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UNIVERSITY OF MINNESOTA DEPARTMENT OF COMPUTER SCIENCE 5561 COMPUTER VISION Spring 2010 Homework 2 (100 Points) Assigned: 04/22/10 Due: 05/6/10 Problem 1 (20 points) A rigid body rotates about an axis through the origin. The axis of rotation is parallel to the vector w , while the angular velocity is given by the magnitude of this vector. The velocity of a point r is the cross-product w × r . Define r = ( x, y, z ) T and w = ( a, b, c ) T . Show that the smoothness of the optical flow is related to the smoothness of the rotating body. What happens on the silhouette? Assume orthographic projection. Hint: Show that 2 u and 2 v are related to 2 z . Problem 2 (30 points) This problem examines the relationship between distance and disparity. Let the length of the baseline, the line connecting two camera stations, be 2 d . Suppose that an object can be seen from both station points and that the lines of the left and right cameras to the object make angles θ r and θ l , respectively, with the baseline. Show that the perpendicular distance to the object from the

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assignment105 - UNIVERSITY OF MINNESOTA DEPARTMENT OF...

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