A Variational Approach for Exact Histogram Specification

Chan, Raymond H.; Nikolova, Mila; Wen, You-Wei

doi:10.1007/978-3-642-24785-9_8

Cited by 2 publications

(3 citation statements)

References 20 publications

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“…A problem of histogram techniques is the meaningful strict ordering of the pixel values. If such ordering is available, the HS can be done in a straightforward way, see, e.g., [15]. Several methods to obtain a meaningful ordering were developed as the local mean ordering [17], the wavelet based ordering [55], and the variational approach based on the minimization of a fully smoothed 1 -TV functional [15,38] together with its fast version [37].…”

Section: Histogram Methodsmentioning

confidence: 99%

Variational Contrast Enhancement of Gray-Scale and RGB Images

et al. 2016

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The aim of this paper is twofold. First, we propose a new method for enhancing the contrast of gray-value images. We use the difference of the average local contrast measures between the original and the enhanced images within a variational framework. This enables the user to control the contrast level and the scale of the enhanced details intuitively. Moreover, our model avoids large modifications of the original image histogram. Thereby it preserves the global illumination of the scene and can cope with large areas having similar gray values. The minimizer of the proposed functional is computed by a gradient descent algorithm in connection with a polynomial approximation of the average local contrast measure. The polynomial approximation is done via Bernstein polynomials and leads to to a speed up of the algorithm by applying fast Fourier transforms. In the second part, the approach is extended to a variational enhancement method for color images. The model approximately preserves the hue of the original image and includes additionally a total variation term to correct possible noise. The method requires no post-or pre-processing. The minimization problem is solved with a hybrid primal-dual algorithm. Numerical experiments demonstrate the efficiency and the flexibility of the proposed approaches in comparison with state-of-the-art methods.

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Section: Histogram Methodsmentioning

confidence: 99%

Variational Contrast Enhancement of Gray-Scale and RGB Images

et al. 2016

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“…A sketch of our approach was given in a conference paper [11]. Here we provide a theoretical analysis of our variational method and show that the pixels of the images that it yields can be ordered in a strict way with a high probability.…”

Section: −1 Tmentioning

confidence: 96%

“…These parameters can slightly be changed so that f remains close enough to u-rigorous tools for such modifications are provided in subsection III-C. Also, instead of the four adjacent neighbors, on may consider the 8 nearest neighbors. Any such change modifies the possible intersections of K G and K I in Theorem 1 with the set S n P in (11). These questions are not considered here as they would lead to a trickier algorithm.…”

Section: Some Practical Limitationsmentioning

confidence: 99%

Exact Histogram Specification for Digital Images Using a Variational Approach

2012

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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.

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A Variational Approach for Exact Histogram Specification

Cited by 2 publications

References 20 publications

Variational Contrast Enhancement of Gray-Scale and RGB Images

Variational Contrast Enhancement of Gray-Scale and RGB Images

Exact Histogram Specification for Digital Images Using a Variational Approach

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