Research On Image Applications Under Wasserstein Distance

Optimal transport problem was first proposed by French mathematician Monge in the 1780 s,and the existence of its solution was proved by Russian mathematician Kantorovich.French mathematician Brenier established the intrinsic connection between optimal transport problem and convex functions.Optimal transfer mapping is the one that minimizes the transfer cost among all the measure-preserving maps.Wasserstein distance in optimal transmission theory is defined as the minimum cost required to transform the distribution P into the distribution Q,or the minimum value of the average moving distance.In recent years,the optimal transport theory has been widely used in computer science,statistics,medicine and other fields.On the basis of studying the relevant literatures,this paper applies Wasserstein distance of the optimal transfer theory into two aspects: 1)face image classification and thus recognition;2)color transfer among color images.The main innovations of this paper can be summarized as follows:1.A face image classification and thus recognition method based on Wasserstein distance is proposed.The normalized statistical histogram can be used as a discrete probability distribution,and the Wasserstein distance under optimal transport theory is an appropriate method to measure the difference between two probability distributions.Firstly,the normalized grayscale statistical histogram is extracted from the face image,secondly,the Wasserstein distance is used as the dissimilarity measure between different histograms,and finally the face image is classified and recognized by the nearest neighbor classifier.The experimental results show that compared with the traditional Euclidean distance and Manhattan distance,the recognition method based on Wasserstein distance in this paper is more accurate.2.A color transfer method among color images based on Wasserstein distance is proposed.In the field of image generation,how to better transfer the color distribution of the reference image to the target image is a research hotspot,and the mathematical theory of optimal transfer has been applied to this problem.Aiming at the problems of a large deviation of color distribution or the lack of color hierarchy between the reference image and the transferred image in the existing methods,a new method of color transfer is proposed in this paper.That is,firstly the reference image and the target image are segmented to obtain the foreground and background areas,secondly the optimal transfer theory are used to complete color transfer for the foreground and background areas respectively,finally the transferred areas of foreground and background are merged and enhanced to obtain the resulted image.The experimental results show that,compared with the two methods in the literatures,the proposed method can better transfer the color distribution of the reference image to the target image,and can better preserve the sense of color hierarchy,thereby obtaining better visual effect.