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Announcements Project 2 due today Project 3 out today –demo session at the end of class

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Photometric Stereo Readings Forsyth and Ponce, section 5.4 Merle Norman Cosmetics, Los Angeles

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Diffuse reflection Simplifying assumptions I = R e : camera response function f is the identity function: –can always achieve this in practice by solving for f and applying f -1 to each pixel in the image R i = 1: light source intensity is 1 –can achieve this by dividing each pixel in the image by R i image intensity of P

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Shape from shading Suppose You can directly measure angle between normal and light source Not quite enough information to compute surface shape But can be if you add some additional info, for example –assume a few of the normals are known (e.g., along silhouette) –constraints on neighboring normals—“integrability” –smoothness Hard to get it to work well in practice –plus, how many real objects have constant albedo?

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Photometric stereo N L1L1 L2L2 V L3L3 Can write this as a matrix equation:

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Solving the equations

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More than three lights Get better results by using more lights What’s the size of L T L? Least squares solution: Solve for N, k d as before

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Color images The case of RGB images get three sets of equations, one per color channel: Simple solution: first solve for N using one channel Then substitute known N into above equations to get k d s: call this J

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Computing light source directions Trick: place a chrome sphere in the scene the location of the highlight tells you where the light source is

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For a perfect mirror, light is reflected about N Recall the rule for specular reflection We see a highlight when V = R then L is given as follows:

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Computing the light source direction Can compute N by studying this figure Hints: –use this equation: –can measure c, h, and r in the image N rNrN C H c h Chrome sphere that has a highlight at position h in the image image plane sphere in 3D

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Depth from normals Get a similar equation for V 2 Each normal gives us two linear constraints on z compute z values by solving a matrix equation (project 3) V1V1 V2V2 N

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Project 3

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Limitations Big problems doesn’t work for shiny things, semi-translucent things shadows, inter-reflections Smaller problems camera and lights have to be distant calibration requirements –measure light source directions, intensities –camera response function

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Trick for handling shadows Weight each equation by the pixel brightness: Gives weighted least-squares matrix equation: Solve for N, k d as before

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Lecture 20: Light, reflectance and photometric stereo

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