Extended photometric stereo for an object with unknown reflectance property

Abstract

AbstractConventional Photometric Stereo can obtain the surface gradients of an object when its reflectance property is known. This paper proposes a new method of accurately obtaining the surface gradients with three light source directions under the assumption that the reflectance property of the surface is unknown. Assuming that the reflectance property is uniform over the entire surface, surface gradients can be obtained by the following two steps: (1) reflectance property parameters and the gradients of the suitable surface elements that characterize the reflectance property by solving the nonlinear simultaneous equations for them, so that a pseudo‐reflectance map is obtained; and (2) the gradient of each surface element is determined by using parameters obtained by (1). The reliability for the values of the reflectance property parameters (i. e., those for the pseudo‐reflectance map) can be improved by applying the method of selecting the surface elements that are sensitive to the reflectance property; this is called the characterized surface elements selection method. In computer experiment with 8‐bits shading resolution using three parallel light sources, the values of the reflectance property parameters can be obtained in optimum, and the accurate surface gradients for a glossy object can be determined.A mean square error in a depth measurement becomes an order of 10−2, confirming the usefulness of the proposed method.