# Computing reflectance ratios from an image

## Abstract

A photometric invariant called reflectance ratio is presented 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 reflectance 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 reflectance coefficients. Based on this observation, an algorithm is developed that estimates a reflectance ratio for each region in the image with respect to its background. The algorithm is computationally efficient as it computes ratios for all image regions in just two raster scans. In the first scan, the image is segmented into regions using a sequential labeling algorithm. During labeling, the reflectance ratio between adjacent pixels is used as a measure of connectivity. In the second scan, a reflectance ratio is computed for each image region as an average of the ratios computed for all points that lie on its boundary. The region reflectance 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 reflectance ratios to imaging and illumination parameters. A brief discussion on the application of reflectance ratios to the problems of object recognition and visual inspection is also given. © 1993.