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.
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. A novel color image histogram equalization approach is proposed that exploits the correlation between color components and it is enhanced by a multi-level smoothing technique borrowed from statistical language engineering. Multi-level smoothing aims at dealing efficiently with the problem of unseen color values, either considered independently or in combination with others. It is applied here to the HSI color space for the probability of intensity and the probability of saturation given the intensity, while the hue is left unchanged. Moreover, the proposed approach is extended by an empirical technique, which is based on a hue preserving non-linear transformation, in order to eliminate the gamut problem. This is the second method proposed in the paper. The equalized images by the two methods are compared to those produced by other well-known methods. The better quality of the images equalized by the proposed methods is judged in terms of their visual appeal and objective figures of merit, such as the entropy and the Kullback-Leibler divergence estimates between the resulting color histogram and the multivariate uniform probability density function. Conventional contrast enhancement techniques often fail to produce satisfactory results for low-contrast images, and cannot be automatically applied to different images because their processing parameters must be specified manually to produce a satisfactory result for a given image. This work presents a colour-preserving contrast enhancement (CPCE) algorithm for images. Modification to images was performed in the HSV colour-space. The Hue component is preserved (unchanged), luminance modified using Contrast Limited Adaptive Histogram Equalization (CLAHE), while Saturation components were up-scaled using a derived mapping function on the approximate components of its discrete wavelet transform. Implementation was done in MATLAB and compared with CLAHE and Histogram Equalization (HE) algorithms in the RGB colour space. Subjective (visual quality inspection) and objective parameters (Peak-signal-to-noise ratio (PSNR), Absolute Mean Brightness Error (AMBE) and Mean squared error (MSE)) were used for performance evaluation. The method produced images with the lowest MSE, AMBE, and highest PSNR when tested, yet preserved the visual quality of the image. In this paper, we present a color consistency technique in order to make images in the same collection share the same color style and to avoid gamut problems. Some previous methods define simple global parameter-based models and use optimizing algorithms to obtain the unknown parameters, which usually cause gamut problems in bright and dark regions. Our method is based on the range-preserving histogram specification and can enforce images to share the same color style, without resulting in gamut problems. We divide the input images into two sets having respectively high visual quality and low visual quality. The high visual quality images are used to make color balance. And then the low visual quality images are color transferred using the previous corrected high quality images. Our experiments indicate that such histogram-based color correction method is better than the compared algorithm. Color image enhancement is a complex and challenging task in digital imaging with abundant applications. Preserving the hue of the input image is crucial in a wide range of situations. We propose simple image enhancement algorithms, which conserve the hue and preserve the range (gamut) of the R, G, B channels in an optimal way. In our setup, the intensity input image is transformed into a target intensity image whose histogram matches a specified, well-behaved histogram. We derive a new color assignment methodology where the resulting enhanced image fits the target intensity image. We analyze the obtained algorithms in terms of chromaticity improvement and compare them with the unique and quite popular histogram-based hue and range preserving algorithm of Naik and Murthy. Numerical tests confirm our theoretical results and show that our algorithms perform much better than the Naik-Murthy algorithm. In spite of their simplicity, they compete with well-established alternative methods for images where hue-preservation is desired. 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.