Multi-exposure image fusion (MEF) is the main method to obtain High Dynamic Range (HDR) images by fusing multiple images taken under various exposure values. In this paper, we propose and develop a novel variational model based on detail-base decomposition for MEF. The main idea is to incorporate the decomposition procedure and the reconstruction procedure into a unified framework, and to interact the detail information and the base information at the same time. Specifically, we make use of Tikhonov regularization to model the base layer, and we present an efficient design to obtain the detail layer, which is able to capture more detailed information effectively. Meanwhile, we incorporate multi-scale techniques to remove halo artifacts. Numerically, we apply alternating direction method of multipliers (ADMM) to solve the proposed minimization problem. Theoretically, we study the existence of the solution of the proposed model and the convergence of the proposed ADMM algorithm. Experimental examples are presented to demonstrate that the performance of the proposed model is better than that by using other testing methods in terms of visual quality and some criteria, e. g., the proposed model gives the best Natural image quality evaluator (NIQE) values with 1% - 10% improvement for real image fusion experiments and gives the best PSNR values with 13% - 20% improvement for the synthetic image fusion experiment.

Color image enhancement is one of the most important tasks in image processing. In this paper, we focus on the red and/or blue attenuation problem that arises in underwater image enhancement. We propose and develop a novel spatial color compensation model based on saturation-value total variation (SV-TV). In the proposed model, the compensation of the red and/or blue attenuation is achieved by adding a fraction of the green channel to the red and/or blue channel. The fraction is determined by a spatially varying function, which is controlled by the TV regularization. In order to avoid overcompensation and too many color artifacts, we make use of the SV-TV to regularize the objective compensation result. We numerically apply the proximal alternating linearized minimization to solve the proposed minimization problem, and we give the convergence analysis of the proposed algorithm. Numerical examples are presented to demonstrate that the performance of the proposed color compensation model is better than that of other testing methods in terms of visual quality and certain criteria, such as peak signal-to-noise ratio (PSNR), structure similarity (SSIM), and CIEde2000 color difference.

Color image restoration is one of the important tasks in color image processing. Covariant differentiation has been applied to handle vector bundles arising from color images in the red, green, blue (RGB) color space. However, there are strong correlations among these three channels, and color image regularization in RGB color space may not be effective enough. The main aim of this paper is to study vector bundles of color images in saturation-value color space and to develop color image regularization models based on vector bundles in saturation-value color space. We develop the saturation-value metric of a vector bundle of $\mathbb{R}^5$-valued functions, and we generalize the vectorial total variation and the vector bundle-valued total variation in saturation-value color space based on the saturation-value metric via the transformation between RGB color space and saturation-value color space. We then develop a saturation-value total variation regularization on vector bundles. We study color image restoration models by using such total variation, and show numerical examples that the proposed color image restoration model outperforms existing methods in terms of visual quality, peak signal-to-noise ratio, and structural similarity.

Color image restoration is one of the important tasks in color image processing. Total variation regularizaton was proposed and employed for the recovery of edges in a grayscale image. In the literature, there are several methods for extension of total variation regularization for color images, for example, based on color channel coupling and tensor regularization. The main contribution of this paper is to propose and develop a new saturation-value (SV) color total variation regularization in the hue, saturation, amd value color space instead of in the original red, green, and blue color space. The development of this SV total variation can be studied via the representation of color images in the quaternion framework for color edge detection. We will investigate the properties of the SV total variation regularization and the resulting optimization model for color image restoration. Numerical examples are presented to demonstrate that the performance of the new SV total variation is better than that of existing color image total variation methods in terms of some criteria such as PSNR, SSIM, and S-CIELAB error.

In this paper, we propose and develop a novel nonlocal variational technique based on structural similarity (SS) information for image restoration problems. In the literature, patches extracted from images are compared according to their pixel values, and then nonlocal filtering can be employed for image restoration. The disadvantage of this approach is that intensity-based patch distance may not be effective in image restoration, especially for images containing texture or structural information. The main aim of this paper is to propose using SS between image patches to develop nonlocal regularization models. In particular, two types of nonlocal regularizing functions are studied: an SS-based nonlocal quadratic function (SS-NLH1) and an SS-based nonlocal total variation function (SS-NLTV) for regularization of image restoration problems. Moreover, we employ iterative algorithms to solve these SS-NLH1 and SS-NLTV variational models numerically and discuss the convergence of these algorithms. The experimental results are presented to demonstrate the effectiveness of the proposed models.

In [W. Wang and M. K. Ng, SIAM J. Imaging Sci., 6 (2013), pp. 1318--1344], we proposed and developed an image stitching algorithm by studying a variational model for automatically computing weighting mask functions on input images and stitching them together. The main aim of this paper is to further develop an image stitching algorithm using the gradients of input images. Our idea is to study a variational method for computing a stitched image by using an energy functional containing the data-fitting term based on the difference between the gradients of the stitched image and the input images, and the Laplacian regularization term based on the smoothness of weighting mask functions. The use of image gradient information allows us to automatically adjust the stitched image to handle color inconsistency across input images. In the model, we incorporate both boundary conditions of the stitched image and the weighting mask functions. The existence of a solution of the proposed energy functional is shown. We also present an alternating minimizing algorithm for solving the variational model numerically, and we show the convergence of this algorithm. Experimental results show that the performance of the proposed method is better than the other testing methods proposed in the literature for input images with color inconsistency.

The main aim of this paper is to develop an algorithm for image stitching. Our idea is to propose a variational approach containing an energy functional to determine both a weighting mask function and a stitched image together. The existence of a solution of the proposed energy functional is shown. We present an alternating minimizing algorithm to solve the proposed model numerically, and we show the convergence of the algorithm. Experimental results show that the proposed model works very well. We also consider a novel color correction procedure to enhance the visual quality of stitched images where source images have different lighting conditions.

The main aim of this paper is to develop a histogram equalization algorithm for image contrast enhancement. Our idea is to propose a variational approach containing an energy functional to determine a local transformation such that the histogram can be redistributed locally, and the brightness of the transformed image can be preserved. In order to minimize the differences among the local transformation at the nearby pixel locations, the spatial regularization of the transformation is also incorporated into the functional for the equalization process. In the variational problem, we consider both $H_1$-norm regularization and total variation regularization of the transformation in the model. The existence and uniqueness of the minimizers of the two proposed models are studied and analyzed. Experimental results are reported to show that the performance of the proposed models are competitive with the other compared methods for several testing images.

The main aim of this paper is to develop an algorithm for blending of multiple images in the image-stitching process. Our idea is to propose a variational method containing an energy functional to determine both a stitched image and weighting mask functions of multiple input images for image blending. The existence of the solution of the proposed energy functional is shown. We also present an alternative minimizing algorithm to solve the proposed model numerically and show the convergence of this algorithm. Experimental results show that the proposed model works effectively and efficiently and that the proposed method is competitive with the tested existing methods under noisy conditions.

Human vision has the ability to recognize color under varying illumination conditions. Retinex theory is introduced to explain how the human visual system perceives color. The main aim of this paper is to present a total variation model for Retinex. Different from the existing methods, we consider and study two important elements which include illumination and reflection. We assume spatial smoothness of the illumination and piecewise continuity of the reflection, where the total variation term is employed in the model. The existence of the solution of the model is shown in the paper. We employ a fast computation method to solve the proposed minimization problem. Numerical examples are presented to illustrate the effectiveness of the proposed model.