quiz_one_04

# quiz_one_04 - Massachusetts Institute of Technology...

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Institute of Technology Department of Computer Science and Electrical Engineering 6.801/6.866 Machine Vision Quiz I Handed out: 2004 Oct. 21st Due on: 2003 Oct. 28th Problem 1: Uniform reﬂecting properties are a prerequisite for the usual shape from shading methods. Consider now a surface covered by a material of spatially varying reﬂectance. Suppose that the brightness can be treated as the product of a spatially varying ‘reﬂectance’ or ‘albedo’ ρ(x, y) , and a ‘geometric factor’ R(p, q) that depends only on surface orientation. There are two unknowns— z(x, y) and ρ(x, y) —at every position on the surface, so a single image will not provide enough information to recover both (consider, for example, a photographic print of a rounded object where the bright- ness variations could either be from a rounded object of uniform albedo or from a ﬂat object of varying albedo). Now suppose we take two images under different lighting conditions. (a) Combine the two resulting image irradiance equations in such a way as to eliminate ρ(x, y) . Suppose the new—now ρ -free’—equation can be written in the form E (x, y) = R (p, q). (b) Show that if the underlying surface actually is a Lambertian reﬂector. then the isophotes in gradient space are straight lines. When will they be parallel straight lines? (c) Show that the isophotes all go through a common point in gradient space in the case that they are not parallel. Where in gradient space would you expect the highest accuracy in recovering surface orientation? That is, where is ‘brightness’ (in the ρ -free equation) most affected by small changes in surface orientation? Relate this back to the original imaging situation. How should the lighting be arranged to obtain high accuracy? Problem 2: An edge detection method starts by ﬁnding the brightness gradient (E x ,E y ) at each picture cell using some local estimator of the partial deriva- tives of image brightness E(x, y) . The magnitude of the brightness gradient is then computed. Next, “non-maximum suppression’’ keeps for further consider- ation only pixels where the magnitude of the gradient

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## This note was uploaded on 10/06/2009 for the course ECE Vision taught by Professor Bertholdhorn during the Spring '04 term at MIT.

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quiz_one_04 - Massachusetts Institute of Technology...

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