Histogram preserving image transformations

Histograms are used to analyze and classify images. They have been found experimentally to have low sensitivity to certain types of image morphisms, for example, viewpoint changes and object deformations. However the precise effect of these image morphisms on the histogram has not been studied. In this work we derive the complete class of local transformations that preserve the histogram or simply scale its magnitude. To achieve this the transformations are represented as solutions to families of vector fields acting on the image. It is then shown that weak perspective projection and paraperspective projection belong to this class and simply scale the histogram. The results on weak perspective projection, together with the effect of illumination, are used to compute the histogram of the projection of 3D polyhedral objects. We verify the analytical results with several examples. Moreover we present and test a system that recognizes and approximates the poses of 3D polyhedral objects independent of viewpoint.