Multi-view Stereo Beyond Lambert Jin et al., CVPR ’03 Joshua Stough November 12, 2003

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.

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) <= 2. Cost function can be matrix discrepancy between model R(P) and observed R(P).

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 (?). Key

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 doesn’t matter. Now assume opposite. Maybe use lambertian on badly matching patches for agglomerated surfaces? I don’t understand their geometry model. They say they don’t need points or triangles. How would they transmit results (like above)? Results