Sign of Gaussian curvature from eigen plane using principal components analysis

Abstract

Describes a method to recover the sign of the local Gaussian curvature at each point on the visible surface of a 3-D object. Multiple (p>3) shaded images are acquired under different conditions of illumination. The required information is extracted from a 2-D subspace obtained by applying principal components analysis (PCA) to the p-dimensional space of normalized irradiance measurements. The number of dimensions is reduced from p to 2 by considering only the first two principal components. The sign of the Gaussian curvature is recovered based on the relative orientation of measurements obtained on a local five point test pattern to those in the 2-D subspace, called the eigen plane. The method does assume generic diffuse reflectance. The method recovers the sign of Gaussian curvature without assumptions about the light source directions or about the specific functional form of the diffuse surface reflectance. Multiple (p>3) light sources minimize the effect of shadows by allowing a larger area of visible surface to be analyzed. Results are demonstrated by experiments on synthetic and real data. The results are more accurate and more robust compared to previous approaches.