Determining Surface Type from Surface Normals

Abstract

By exploiting the relationship which exists between the Gaussian image and gradient space, the two representations can be utilized in conjunction to facilitate the interpretation of a set of surface normals. The projection of the Gaussian image onto a plane can provide clear traces which quickly yield general knowledge of the underlying surface. I I ntroduct ion There are many methods in low-level machine vision which derive the 3-D surface orientation at each coordinate point in an image. Optical flow Cl 981, texture gradient c71, and photometric stereo [2,6] are all techniques used to generate these surface norma 1 vectors. Methods have been suggested for object recogni t i on [5] and segmentat ion [3] us i ng these normals. In general, however, the process of interpreting this local information to infer the underlying surface type is not well understood. This paw addresses the question: Given a collection of surface normals generated from a single, smooth surface, what can be determined about the surface? Using a variation of the gradient space, we present an approach for distinguishing simple surfaces. Our representation is purposely simple and limited as our object is to quickly obtain some basic knowledge of the surface. I I Representation If spatial information is ignored and all surface normals generated from an image are translated to a common origin, the gaussian image is formed [4,8]. This image can be seen as the locus of points formed by the intersection of the unit normals with a unit sphere called the Gaussian sphere. Any rotation in the scene causes a corresponding rotation of the Gaussian sphere about its origin. Histograming the X and Y components of the unit normals produces a 2-D approximation of the Gaussian image cal led the Gauss ian histogram [3]. At the present time, we do not utilize the cell counts of the histogram, Wayne State University