Exact Histogram Specification for Digital Images Using a Variational Approach
Publication in refereed journal



摘要We consider the problem of exact histogram specification for digital (quantized) images. The goal is to transform the input digital image into an output (also digital) image that follows a prescribed histogram. Classical histogram modification methods are designed for real-valued images where all pixels have different values, so exact histogram specification is straightforward. Digital images typically have numerous pixels which share the same value. If one imposes the prescribed histogram to a digital image, usually there are numerous ways of assigning the prescribed values to the quantized values of the image. Therefore, exact histogram specification for digital images is an ill-posed problem. In order to guarantee that any prescribed histogram will be satisfied exactly, all pixels of the input digital image must be rearranged in a strictly ordered way. Further, the obtained strict ordering must faithfully account for the specific features of the input digital image. Such a task can be realized if we are able to extract additional representative information (called auxiliary attributes) from the input digital image. This is a real challenge in exact histogram specification for digital images. We propose a new method that efficiently provides a strict and faithful ordering for all pixel values. It is based on a well designed variational approach. Noticing that the input digital image contains quantization noise, we minimize a specialized objective function whose solution is a real-valued image with slightly reduced quantization noise, which remains very close to the input digital image. We show that all the pixels of this real-valued image can be ordered in a strict way with a very high probability. Then transforming the latter image into another digital image satisfying a specified histogram is an easy task. Numerical results show that our method outperforms by far the existing competing methods.
著者Nikolova M, Wen YW, Chan R
期刊名稱Journal of Mathematical Imaging and Vision
頁次309 - 325
關鍵詞Convex minimization; Exact histogram specification; Image processing; Minimizer analysis; Perturbation analysis; Restoration from quantization noise; Smooth nonlinear optimization; Strict-ordering; Variational methods
Web of Science 學科類別Computer Science; Computer Science, Artificial Intelligence; COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE; Computer Science, Software Engineering; COMPUTER SCIENCE, SOFTWARE ENGINEERING; Mathematics; Mathematics, Applied; MATHEMATICS, APPLIED

上次更新時間 2020-23-10 於 01:40