Regularizing Image Intensity Transformations Using the Wasserstein Metric

In this paper we direct our attention to the problem of discretization effects in intensity transformations of images. We propose to use the Wasserstein metric (also known as the Earth mover distance) to bootstrap the transformation process. The Wasserstein metric gives a mapping between gray levels that we use to direct our image mapping. In order to spatially regularize the image mapping we apply anisotropic filtering and use this to steer our mapping. We describe a general framework for intensity transformation, and investigate the application of our method on a number of special problems, namely histogram equalization, color transfer and bit depth expansion. We have tested our algorithms on real images, and we show that we get state-of-the-art results.