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3D Modeling from a photograph

3D Modeling from a photograph. https://research.microsoft.com/vision/cambridge/3d/3dart.htm. A different way of modeling. http://mit.edu/jxiao/museum/. Last topic. Single View Modeling. Vermeer ’ s Music Lesson. Reconstructions by Criminisi et al. Next. Photometric Stereo

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3D Modeling from a photograph

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  1. 3D Modeling from a photograph https://research.microsoft.com/vision/cambridge/3d/3dart.htm

  2. A different way of modeling • http://mit.edu/jxiao/museum/

  3. Last topic • Single View Modeling Vermeer’s Music Lesson Reconstructions by Criminisi et al.

  4. Next • Photometric Stereo • Separate Global and Direct Illumination

  5. Photometric Stereo

  6. Photometric Stereo Readings • R. Woodham, Photometric Method for Determining Surface Orientation from Multiple Images. Optical Engineering 19(1)139-144 (1980). (PDF) Merle Norman Cosmetics, Los Angeles

  7. 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

  8. 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) • smoothness • Hard to get it to work well in practice • plus, how many real objects have constant albedo?

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

  10. Solving the equations

  11. 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

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

  13. 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:

  14. 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

  15. Example

  16. What if we don’t have mirror ball? • Hayakawa, Journal of the Optical Society of America, 1994, Photometric stereo under a light source with arbitrary motion.

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