Histogram preserving image transformations

Histograms are used to analyze and index images. They have been found experimentally to have low sensitivity to certain types of image morphisms, for example, viewpoint changes and object deformations. The precise effect of these image morphisms on the histogram, however, has not been studied. In this work we derive the complete class of local transformations that preserve or scale the magnitude of the histogram of all images. We also derive a more general class of local transformations that preserve the histogram relative to a particular image. To achieve this, the transformations are represented as solutions to families of vector fields acting on the image. The local effect of fixed points of the fields on the histograms is also analyzed. The analytical results are verified with several examples. We also discuss several applications and the significance of these transformations for histogram indexing.