Fast Ordering Algorithm for Exact Histogram Specification

Mila Nikolova, Gabriele Steidl
2014 IEEE Transactions on Image Processing  
This paper provides a fast algorithm to order in a meaningful, strict way the integer gray values in digital (quantized) images. It can be used in any exact histogram specification based application. Our algorithm is based on the ordering procedure relying on the specialized variational approach proposed in [1]. This variational method was shown to be superior to all other state-of-the art ordering algorithms in terms of faithful total strict ordering but not in speed. Indeed, the relevant
more » ... , the relevant functionals are in general difficult to minimize because their gradient is nearly flat over vast regions. In this paper we propose a simple and fast fixed point algorithm to minimize these functionals. The fast convergence of our algorithm results from known analytical properties of the model. In particular the original image is a pertinent starting point for the iterations and all functions involved in the algorithm were shown to admit a simple explicit form which is quite exceptional. Only few iteration steps of this algorithm provide images whose pixels can be ordered in a strict and faithful way. Equivalently, our algorithm can be seen as iterative nonlinear filtering. Numerical experiments confirm that our algorithm outperforms by far its main competitors. Our minimization algorithm and ordering approach provide the background for any exact histogram specification based application.
doi:10.1109/tip.2014.2364119 pmid:25347881 fatcat:ykxpcryv3zhk7cxbjlquhvli3a