Computing Reeectance Ratios from an Image

This paper presents a photometric invariant called reeectance ratio that can be computed from a single brightness image of a scene. The brightness variation in an image of a surface depends on several factors; the three-dimensional shape of the surface, its reeectance properties, and the illumination conditions. Since neighboring points on a smoothly curved surface have similar surface orientations, their brightness values can be used to compute the ratio of their reeectance coeecients. Based on this observation, we develop an algorithm that estimates a reeectance ratio for each region in the image with respect to its background. The algorithm is computationally eecient as it computes ratios for all image regions in just two raster scans. In the rst scan, the image is segmented into regions using a sequential labeling algorithm. During labeling, the reeectance ratio between adjacent pixels is used as a measure of connectivity. In the second scan, a reeectance ratio is computed for each image region as an average of the ratios computed for all points that lie on its boundary. The region reeectance ratio is also a photometric invariant; it represents a physical property of the region and is invariant to the illumination conditions. Several experimental results are included to demonstrate the invariance of reeectance ratios to imaging and illumination parameters. We conclude with a brief discussion on the application of reeectance ratios to the problems of object recognition and visual inspection.