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Announcements

Learn about the concepts of shape from shading and color images in Photometric Stereo. Explore the limitations and tricks for handling shadows in this project. Read Forsyth and Ponce, section 5.4 for more information.

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Announcements

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  1. Announcements • Project 2 due today • Project 3 out today • demo session at the end of class

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

  3. image intensity of P Diffuse reflection • Simplifying assumptions • I = Re: 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 • Ri = 1: light source intensity is 1 • can achieve this by dividing each pixel in the image by Ri

  4. 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?

  5. L3 L2 L1 Photometric stereo N V • Can write this as a matrix equation:

  6. Solving the equations

  7. Least squares solution: • Solve for N, kd as before What’s the size of LTL? More than three lights • Get better results by using more lights

  8. call this J 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 kd s:

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

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

  11. 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 Chrome sphere that has a highlight at position h in the image N h H rN c C sphere in 3D image plane

  12. V2 V1 N Depth from normals • Get a similar equation for V2 • Each normal gives us two linear constraints on z • compute z values by solving a matrix equation (project 3)

  13. Project 3

  14. 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

  15. Trick for handling shadows • Weight each equation by the pixel brightness: • Gives weighted least-squares matrix equation: • Solve for N, kd as before

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