Text Box: Computer  Vision

Text Box: Take Home Mid-term Exam.

Text Box: Exam Paper

Text Box: 1. Consider the problem of image formation, ie, mapping of the 3D world into a 2D plane. This problem was discussed in great details in the class. Now consider that the points are not projected on a planar surface, but they are projected on a spherical surface (a simple approximation of how it happens on our retina). To simplify, assume that the optical center (pin-hole) is at the center of the sphere. Derive: · The geometric relationship between a point in the scene and its image. · The photometric relationship in terms of the scene radiance and the image irradiance.                                           [7 Marks] 2. For the variational approach to shape from shading (like Ikeuchi & Horn), we have used the smoothness of the surface normal through p & q or f & g parameterization. One may use first or second order smoothness while solving the problem. Meanwhile you may notice that one can also solve the problem using the depth z=z(x,y) itself as the parameterization which will automatically take care of the integrability  constraint. Instead we want the estimated surface to have a smooth curvature! · Find out how one defines the curvature of a surface z=z(x,y). What does it physically mean? · Use the smoothness of the curvature as the constraint while solving the shape from shading.  (Feel free to use any suitable reflectance map to solve the problem).                              [9 Marks] 3. Consider the problem of depth recovery using binocular stereo. · What all physical constraints can you use to restrict the search space while setting up the feature correspondence? · You may be aware that human visual system has non-uniform density of photo-receptors (rod-cells) in the retina. Our stereo vision system is a simple one with epipolar lines along the x-axis (like the one discussed in the class). However, the CCD elements on the image plane are not uniformly placed. Rather its density goes down in a radially symmetric fashion as the inverse of the distance from the optical axis. Explain what kind of depth perception can you achieve with this kind of stereo set-up? Assume both the camera systems to be identical.                                                         [7 Marks] 4. From stereo vision we move to analyze a scene with a hand-held camera undergoing an arbitrary motion. Prove that · Translation can be estimated up to a scale factor only, and · Depth in the scene also can be obtained up to a scale factor. · What are the properties of the essential/fundamental matrix?                                                                                   [6 Marks] 5. (Use this to relax yourself — has nothing to do with CV) Choose some values of the integer variables ‘a’ and ‘b’. Find the ratio a/b. Now replace a <- (a + Nb) and b <- (a+b) where N=2. Keep repeating the operation and find the value of a/b. What happens if N is –ve?                                                                                    [1 Mark] NOTE: The solution must reach me by 8:30 am IST on 28/2/05 Late submission will invite –4 marks/hour penalty. The emphasis is more on bringing out the concept rather than the solution itself. It is an open-book, open-internet, take-home exam. Discussion with friends and foes are NOT allowed. The answers should be concise — there is a page limit for answering each question. It is a HARD 2 page (A-4) limit! You are free to meet me on 25/2 to clarify any doubt regarding the question paper.           THE PAPER ENDS HERE ….   Your story begins!

Text Box: Subhasis Chaudhuri#