Shape, surface reflectance, illuminant direction and illuminant intensity from images with shading

Abstract

AbstractA method is proposed for estimating shape, surface reflectance, illuminant direction and illuminant intensity from images with shading. First, an n x m image data matrix I is constructed from n pixel image inten‐sity data through m frames by moving a light source arbitrarily. Using the Lambertian assumption, the image data matrix I can be written as the product of two matrices N and S; N represents the surface normal and surface reflectance, and S represents the illuminant direction and illuminant intensity. Based on this for‐mulation, a singular value decomposition technique is employed and one of the following two constraints is used to factorize the image data matrix.One is the constraint of surface reflectance which can be used when there are at least 6 pixels in the images, where the surface reflectance is constant. The other is the constraint of illuminant intensity which can be used when there are at least 6 frames among the images, where the illuminant intensity is constant.As the number of images with shading increases, the estimation errors become smaller even if the images are taken in a noisy environment. The proposed method can also treat self shadows and cast shadows without assumptions. The effectiveness of the proposed method is demonstrated through computer simulation, performance analysis and laboratory experiment.