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Announcements

Announcements. Project 2 due today Project 3 out today demo session at the end of class. Photometric Stereo. Readings Forsyth and Ponce, section 5.4. Merle Norman Cosmetics, Los Angeles. image intensity of P. Diffuse reflection. Simplifying assumptions

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Announcements

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Presentation Transcript

  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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