Molnár, József and Csetverikov, Dmitrij (2014) Quadratic Transformation for Planar Mapping of Implicit Surfaces. JOURNAL OF MATHEMATICAL IMAGING AND VISION, 48 (1). pp. 176-184. ISSN 0924-9907 10.1007/s10851-012-0407-2

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Abstract

Level Set methods use a non-parametric, implicit representation of surfaces such as the signed distance function. These methods are applied to multiview 3D reconstruction and other machine vision problems that need correspondences between views of a surface. Correspondences can be found by matching surface texture patches of the size sufficient for their identification. Good matching requires precise mapping of a patch across the two image planes. Affine mapping is often used for this purpose assuming that the patches are small and nearly flat. However, this assumption is violated in locations of high surface curvature and/or when the surface is poorly textured and large windows are needed to provide enough information. Using second-order surface approximation, we derive a more precise, quadratic transformation for planar mapping of implicit surfaces. To validate this theoretical result, we apply it to correlation based, variational multiview 3D reconstruction using Level Sets. It is shown that a more detailed reconstruction can be achieved compared to the traditional affine mapping.

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