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Announcements

Announcements. Final exam Tuesday, March 13, 2:30-4:20, JHN 175 Closed book, closed notes Sample exams handed out today Prof’s office hours extra hour this week: Wednesday 4-5 next week: Monday 12:30-2pm. Photometric Stereo. Readings

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Announcements

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  1. Announcements • Final exam • Tuesday, March 13, 2:30-4:20, JHN 175 • Closed book, closed notes • Sample exams handed out today • Prof’s office hours • extra hour this week: Wednesday 4-5 • next week: Monday 12:30-2pm

  2. Photometric Stereo • Readings • Optional: Woodham’s original photometric stereo paper • http://www.cs.ubc.ca/~woodham/papers/Woodham80c.pdf 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. L1 L3 L2 Photometric stereo N V Can write this as a matrix equation:

  6. Solving the equations

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

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

  9. 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:

  10. Computing the light source direction • Can compute θ (and hence N) from this figure • Now just reflect V about N to obtain L Chrome sphere that has a highlight at position h in the image N h H rN θ c C sphere in 3D image plane

  11. 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 orthographic projection

  12. Results… Input (1 of 12) Normals Normals Shadedrendering Texturedrendering

  13. Results… from Athos Georghiades http://cvc.yale.edu/people/Athos.html

  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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