The Lawn-Mowing Algorithm for Noisy Gradient Vector Fields

In this paper we analyze a specific problem within the context of recovering the geometric shape of an unknown surface from multiple noisy shading patterns generated by consecutive parallel illuminations by different light-sources. Shading-based single-view shape recovery in computer vision often leads to vector fields (i.e. estimated surface normals) which have to be integrated for calculations of height or depth maps. We present an algorithm for enforcing the integrability condition of a given non-integrable vector field which ensures a global suboptimal solution by local optimizations. The scheme in question relies neither on a priori knowledge of boundary conditions nor on other global constraints imposed on the sofar derived noise contaminated gradient integration techniques. The discussion is supplemented by examples illustrating algorithm performance. 1 Department of Mathematics 2Department of Computer Science The University of Western Australia, Nedlands, WA 6907, Australia 3 The University of Auckland, Computer Science Department, CITR, Tamaki Campus (Building 731), Glen Innes, Auckland, New Zealand The Lawn-Mowing Algorithm for Noisy Gradient Vector Fields Lyle Noakes, Ryszard Kozera, and Reinhard Klette Department of Mathematics Department of Computer Science The University of Western Australia, Nedlands, WA 6907, Australia CITR Tamaki, University of Auckland Tamaki Campus, Building 731, Auckland, New Zealand ABSTRACT In this paper we analyze a speci c problem within the context of recovering the geometric shape of an unknown surface frommultiple noisy shading patterns generated by consecutive parallel illuminations by di erent light-sources. Shading-based single-view shape recovery in computer vision often leads to vector elds (i.e. estimated surface normals) which have to be integrated for calculations of height or depth maps. We present an algorithm for enforcing the integrability condition of a given non-integrable vector eld which ensures a global suboptimal solution by local optimizations. The scheme in question relies neither on a priori knowledge of boundary conditions nor on other global constraints imposed on the so-far derived noise contaminated gradient integration techniques. The discussion is supplemented by examples illustrating algorithm performance.