Multiview Stereo Beyond Lambert

1
Multi-view Stereo Beyond Lambert

• Jin et al., CVPR 03
• Joshua Stough
• November 12, 2003

2
Basics

• Reconstruct 3D shape from calibrated set of
  views. (uncalibrated possible).
• Assume Non-Lambertian
• Establish Correspondence from model to image, NOT
  image to image
• Constraint on the radiance tensor field.

3
Radiance Tensor Field

• Given point P on surface, g1,,gn camera
  reference frames, and v1,,vm vectors along
  tangent plane to P to tesselation around P.
• For Lambertian, rank is 1.
• For any diffuse specular reflection model,
  rank 2.
• More specifically, any reasonably lit and viewed
  surface patch obeying the BRDF model has R(P) lt
  2.
• Cost function can be matrix discrepancy between
  model R(P) and observed R(P).

4
Key

• Discrepancy between their model and the observed
  drives a flow towards the correct shape.
• They prove that the Frobenius norm of the tensor
  discrepancy is optimizable.
• F norm the obvious one (root of sum of squares
  of elements), as opposed to the square root of
  the max eigenvalue of the adjoint matrix (?).

5
Results

• Kind of weird that they show that how nothing is
  practically like their model is a good thing
  (drives the optimization).
• Before, a weakness was this odd assumption that
  viewpoint doesnt matter. Now assume opposite.
  Maybe use lambertian on badly matching patches
  for agglomerated surfaces?
• I dont understand their geometry model. They
  say they dont need points or triangles. How
  would they transmit results (like above)?