Photometric Stereo with Only Two Images: A Theoretical Study and Numerical Resolution

Yvain Quéau (1) , Roberto Mecca (2) , Jean-Denis Durou (1) , Xavier Descombes (3)

1 IRIT - Institut de recherche en informatique de Toulouse
2 Dipartimento di Mathematica, Università di Roma
3 MORPHEME - Morphologie et Images

The shape-from-shading problem, which aims at inferring the shape from a single image, is known to be ill-posed. Yet, scientists pursue the 3D-reconstruction of a shape from shading clues, considering the photometric stereo problem which enables the use of several images, acquired under different illuminations. Under standard assumptions such as diffuse reflection or uniform lighting, it is well-known that photometric stereo becomes well-posed using at least three images. In this work we consider the intermediate case with two images. Our contributions are twofold. We first analyze the arising ambiguities from a theoretical side. Based on this study, a reliable way to solve the ambiguities is put forward. We show that, when the surface albedo is known and integrability of the normals is imposed, the 3D-reconstruction problem can be reformulated as a binary labelling problem, efficiently solvable by resorting to the graph cut algorithm.

Mots clés: optimization; graph cut; 3D-reconstruction; shape-from-shading; photometric stereo; PDEs; numerical analysis

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]; Traitement des images [eess.IV]; Traitement du signal et de l'image [eess.SP]

Yvain Quéau, Roberto Mecca, Jean-Denis Durou, Xavier Descombes. Photometric Stereo with Only Two Images: A Theoretical Study and Numerical Resolution. 2016. ⟨hal-01334657v1⟩