Introduction to numerical linear algebra and optimisation
Introduction to numerical linear algebra and optimisation
Digital image processing (2nd ed.)
Digital image processing (2nd ed.)
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
The image processing handbook (2nd ed.)
The image processing handbook (2nd ed.)
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
International Journal of Computer Vision
Matrix analysis and applied linear algebra
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A Parametric Texture Model Based on Joint Statistics of Complex Wavelet Coefficients
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Dynamic histogram warping of image pairs for constant image brightness
ICIP '95 Proceedings of the 1995 International Conference on Image Processing (Vol.2)-Volume 2 - Volume 2
Histogram modification via partial differential equations
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A Variational Approach to Remove Outliers and Impulse Noise
Journal of Mathematical Imaging and Vision
Journal of VLSI Signal Processing Systems
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Recursive sub-image histogram equalization applied to gray scale images
Pattern Recognition Letters
Almost Uniform Distributions for Computer Image Enhancement
IEEE Transactions on Computers
Local Histogram Based Segmentation Using the Wasserstein Distance
International Journal of Computer Vision
A histogram modification framework and its application for image contrast enhancement
IEEE Transactions on Image Processing
A variational approach for exact histogram specification
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Contrast enhancement using brightness preserving bi-histogram equalization
IEEE Transactions on Consumer Electronics
IEEE Transactions on Consumer Electronics
Brightness preserving histogram equalization with maximum entropy: a variational perspective
IEEE Transactions on Consumer Electronics
Contrast restoration of weather degraded images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Noise removal using smoothed normals and surface fitting
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Joint Exact Histogram Specification and Image Enhancement Through the Wavelet Transform
IEEE Transactions on Image Processing
Majorization–Minimization Algorithms for Wavelet-Based Image Restoration
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
An Energy-Based Model for the Image Edge-Histogram Specification Problem
IEEE Transactions on Image Processing
Fully Smoothed ℓ1-TV Models: Bounds for the Minimizers and Parameter Choice
Journal of Mathematical Imaging and Vision
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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.