Backward diffusion processes appear naturally in image enhancement and deblurring applications. However, the inverse problem of backward diffusion is known to be ill-posed and straightforward numerical algorithms are unstable. So far, existing stabilisation strategies in the literature require sophisticated numerics to solve the underlying initial value problem. Therefore, it is desirable to establish a backward diffusion model which implements a smart stabilisation approach that can be used in combination with a simple numerical scheme. We derive a class of space-discrete one-dimensional backward diffusion as gradient descent of energies where we gain stability by imposing range constraints. Interestingly, these energies are even convex. Furthermore, we establish a comprehensive theory for the time-continuous evolution and we show that stability carries over to a simple explicit time discretisation of our model. Finally, we confirm the stability and usefulness of our technique in experiments in which we enhance the contrast of digital greyscale and colour images.
Another related research topic is the rich field of colour image enhancement which we broach in sec:app:colour . A short review of existing methods -- as well as two new ideas -- is presented in @cite_28 . Therein, Bassiou and Kotropoulus also mention the colour gamut problem for methods which perform contrast enhancement in a different colour space and transform colour coordinates to RGB afterwards. Of particular interest are the publications by Naik and Murthy @cite_12 and Nikolova and Steidl @cite_13 whose ideas are used in sec:app:colour . Both of them suggest -- based on an affine colour transform -- strategies to overcome the colour gamut problem while avoiding colour artefacts in the resulting image. A recent approach which also makes use of these ideas is presented by Tian and Cohen @cite_45 . @cite_6 make use of the HSV colour space to avoid the colour gamut problem when enhancing the contrast of colour images. A variational approach for contrast enhancement which tries to approximate the hue of the input image was recently published by @cite_7 .
@cite_7 @cite_28 @cite_6 @cite_45 @cite_13 @cite_12
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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 intuitively control the contrast level and the scale of the enhanced details. Moreover, our model avoids large modifications of the original image histogram. Thereby it preserves the global illumination of the scene and it 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 computed via Bernstein polynomials. 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 additionally includes a total variation term to correct the possible noise. The method requires no post- or preprocessing. The minimization problem is solved with a hybrid primal---dual algorithm. Experiments demonstrate the efficiency and the flexibility of the proposed approaches in comparison with state-of-the-art methods. The first step in many techniques for processing intensity and saturation in color images keeping hue unaltered is the transformation of the image data from RGB space to other color spaces such as LHS, HSI, YIQ, HSV, etc. Transforming from one space to another and processing in these spaces usually generate a gamut problem, i.e., the values of the variables may not be in their respective intervals. We study enhancement techniques for color images theoretically in a generalized setup. A principle is suggested to make the transformations gamut-problem free. Using the same principle, a class of hue-preserving, contrast-enhancing transformations is proposed; they generalize existing grey scale contrast intensification techniques to color images. These transformations are also seen to bypass the above mentioned color coordinate transformations for image enhancement. The developed principle is used to generalize the histogram equalization scheme for grey scale images to color images. Abstract Conventional enhancements for the color display of multispectral images are based on independent contrast modifications or “stretches” of three input images. This approach is not effective if the image channels are highly correlated or if the image histograms are strongly bimodal or more complex. Any of several procedures that tend to “stretch” color saturation while leaving hue unchanged may better utilize the full range of colors for the display of image information. Two conceptually different enhancements are discussed: the “decorrelation stretch”, based on principal-component (PC) analysis, and the “stretch” of “hue”-“saturation”-intensity (HSI) transformed data. The PC transformation is scene-dependent, but the HSI transformation is invariant. Examples of images enhanced by conventional linear stretches, decorrelation stretch, and by stretches of HSI transformed data are compared. Schematic variation diagrams or two- and three-dimensional histograms are used to illustrate the “decorrelation stretch” method and the effect of the different enhancements. A novel architecture for performing hue-saturation-value (HSV) domain enhancement of digital color images with non-uniform lighting conditions is proposed in this paper for video streaming applications. The approach promotes log-domain computation to eliminate all multiplications, divisions and exponentiations utilizing the effective logarithmic estimation modules. An optimized quadrant symmetric architecture is incorporated into the design of homomorphic filter for the enhancement of intensity value. Efficient modules are also presented for conversion between RGB and HSV color spaces. The design is able to bring out details hidden in shadow regions of the image. It is capable of producing 187.86 million outputs per second (MOPs) on Xilinx's Virtex II XC2V2000-4ff896 field programmable gate array (FPGA) at a clock frequency of 187.86 MHz. It can process over 179.1 (1024 X 1024) frames per second and consumes approximately 70.7 and 76.8 less hardware resource with 127 and 280 performance boost when compared to the designs with machine learning algorithm [10], and with separated dynamic and contrast enhancements [11], respectively.