A Lighting-Invariant Point Processor for Shading

Under the conventional diffuse shading model with unknown directional lighting, the set of quadratic surface shapes that are consistent with the spatial derivatives of intensity at a single image point is a two-dimensional algebraic variety embedded in the five-dimensional space of quadratic shapes. We describe the geometry of this variety, and we introduce a concise feedforward model that computes an explicit, differentiable approximation of the variety from the intensity and its derivatives at any single image point. The result is a parallelizable processor that operates at each image point and produces a lighting-invariant descriptor of the continuous set of compatible surface shapes at the point. We describe two applications of this processor: two-shot uncalibrated photometric stereo and quadratic-surface shape from shading.

[1]  P. Cavanagh.  The artist as neuroscientist , 2005, Nature.

[2]  Ronen Basri,et al.  Lambertian reflectance and linear subspaces , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[3]  Rob Fergus,et al.  Depth Map Prediction from a Single Image using a Multi-Scale Deep Network , 2014, NIPS.

[4]  Stefan Roth,et al.  Discriminative shape from shading in uncalibrated illumination , 2015, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[5]  David J. Kriegman,et al.  The Bas-Relief Ambiguity , 2004, International Journal of Computer Vision.

[6]  Lawrence B. Wolff,et al.  Surface Curvature and Shape Reconstruction from Unknown Multiple Illumination and Integrability , 1997, Comput. Vis. Image Underst..

[7]  Bill Freeman,et al.  Shape and Illumination from Shading using the Generic Viewpoint Assumption , 2014, NIPS.

[8]  J. Koenderink,et al.  Representation of local geometry in the visual system , 1987, Biological Cybernetics.

[9]  Andrew W. Fitzgibbon,et al.  Efficient Intersection of Three Quadrics and Applications in Computer Vision , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[10]  Pat Hanrahan,et al.  An efficient representation for irradiance environment maps , 2001, SIGGRAPH.

[11]  Ron Goldman,et al.  Using multivariate resultants to find the intersection of three quadric surfaces , 1991, TOGS.

[12]  Steven W. Zucker,et al.  How Shading Constrains Surface Patches without Knowledge of Light Sources , 2014, SIAM J. Imaging Sci..

[13]  J T Todd,et al.  Ambiguity and the ‘Mental Eye’ in Pictorial Relief , 2001, Perception.

[14]  Daniel Snow,et al.  Shape and albedo from multiple images using integrability , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[15]  David A. Forsyth,et al.  Variable-Source Shading Analysis , 2011, International Journal of Computer Vision.

[16]  Ronen Basri,et al.  From Shading to Local Shape , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Jitendra Malik,et al.  Shape, Illumination, and Reflectance from Shading , 2015, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  Berthold K. P. Horn.  SHAPE FROM SHADING: A METHOD FOR OBTAINING THE SHAPE OF A SMOOTH OPAQUE OBJECT FROM ONE VIEW , 1970 .

[19]  Hideki Hayakawa.  Photometric stereo under a light source with arbitrary motion , 1994 .