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Recovering Shape in the Presence of Interreflections: Algorithm and Model

This study presents an algorithm that explicitly models interreflections to improve shape-from-intensity estimations and reflectance on surfaces. By iteratively refining geometry and estimating reflectance, it converges to accurate solutions. The algorithm incorporates surface facets, albedo, and interreflectance kernels to recover shape and reflectance in Lambertian surfaces.

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Recovering Shape in the Presence of Interreflections: Algorithm and Model

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  1. Recovering Shape in the Presence of Interreflections Shree K. Nayar, Katsushi Ikeuchi, Takeo Kanade Presented by: Adam Smith

  2. Problem • All previous shape-from-intensity (and also shape-from-shading) algorithms assume there are no surface-to-surface reflections. • This is only true when imaging a single, convex surface. • These methods produce erroneous (psuedo) estimates of shape and reflectance.

  3. Example Failure Cases Psuedo shapes are always less concave than the actual shapes. Extra Light! Recovered shape is flatter

  4. Solution • Explicitly model interreflections and find the model that best fits the observations. • Start with the shape-from-intensity geometry • Iteratively calculate a better match and update geometry • Converges (after possibly infinite iterations) to a steady state solution for shape and reflectance

  5. Model • Surface is grid of infinitesimal facets. • Each facet has its own position, normal and reflectance. • Light observed from a facet is the sum of direct light and contribution from all other facets Li = observed light Lsi = radiance from direct illumination Rhoi = facet reflectance (albedo) Lj = radiance from facet j K = interreflectance kernel (based on geometry

  6. Teh Algorithmz0r

  7. Iterative Step F0 = Fp P0 = [0.95] Fk+1 = (I - PkKk)Fk Pk = P(Fk) Kk = K(Fk)

  8. Details Initialize: F0 = Fp P0 = [0.95] Update: Fk+1 = (I - PkKk)Fk Pk = P(Fk) Kk = K(Fk) F is facet matrix P is albedo matrix K is kernel matrix

  9. Results

  10. Conclusions • This method recovers shape and reflectance of Lambertian surface in the presence of

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