Chaomin Shen

Image restoration combining a total variational filter and a fourth-order filter

In this paper, a noise removal algorithm based on variational method and partial differential equations (PDEs) is proposed. It combines a total variational filter (ROF filter) with a fourth-order PDE filter (LLT filter). The combined algorithm takes the advantage of both filters since it is able to preserve edges while avoiding the staircase effect in smooth regions. The existence and uniqueness of a solution to the minimization problem is established. Experimental results illustrate the effectiveness of the model in image restoration.

Multiplicative Noise Removal with Spatially Varying Regularization Parameters

The Aubert-Aujol (AA) model is a variational method for multiplicative noise removal. In this paper, we study some basic properties of the regularization parameter in the AA model. We develop a method for automatically choosing the regularization parameter in the multiplicative noise removal process. In particular, we employ spatially varying regularization parameters in the AA model in order to restore more texture details of the denoised image. Experimental results are presented to demonstrate that the spatially varying regularization parameters method can obtain better denoised images than the other tested multiplicative noise removal methods.

Multiphase Soft Segmentation with Total Variation and H1 Regularization

In this paper, we propose a variational soft segmentation framework inspired by the level set formulation of multiphase Chan-Vese model. We use soft membership functions valued in [0,1] to replace the Heaviside functions of level sets (or characteristic functions) such that we get a representation of regions by soft membership functions which automatically satisfies the sum to one constraint. We give general formulas for arbitrary N-phase segmentation, in contrast to Chan-Vese’s level set method only 2m-phase are studied. To ensure smoothness on membership functions, both total variation (TV) regularization and H1 regularization used as two choices for the definition of regularization term. TV regularization has geometric meaning which requires that the segmentation curve length as short as possible, while H1 regularization has no explicit geometric meaning but is easier to implement with less parameters and has higher tolerance to noise. Fast numerical schemes are designed for both of the regularization methods. By changing the distance function, the proposed segmentation framework can be easily extended to the segmentation of other types of images. Numerical results on cartoon images, piecewise smooth images and texture images demonstrate that our methods are effective in multiphase image segmentation.

A variational formulation for segmenting desired objects in color images

This paper presents a new variational formulation for detecting interior and exterior boundaries of desired object(s) in color images. The classical level set methods can handle changes in topology, but can not detect interior boundaries. The Chan-Vese model can detect the interior and exterior boundaries of all objects, but cannot detect the boundaries of desired object(s) only. Our method combines the advantages of both methods. In our algorithm, a discrimination function on whether a pixel belongs to the desired object(s) is given. We define a modified Chan-Vese functional and give the corresponding evolution equation. Our method also improves the classical level set method by adding a penalizing term in the energy functional so that the calculation of the signed distance function and re-initialization can be avoided. The initial curve and the stopping function are constructed based on that discrimination function. The initial curve locates near the boundaries of the desired object(s), and converges to the boundaries efficiently. In addition, our algorithm can be implemented by using only simple central difference scheme, and no upwind scheme is needed. This algorithm has been applied to real images with a fast and accurate result. The existence of the minimizer to the energy functional is proved in the Appendix A.

Color Image Segmentation for Objects of Interest with Modified Geodesic Active Contour Method

In this paper, we propose a novel variational method for color image segmentation using modified geodesic active contour method. Our goal is to detect Object(s) of Interest (OOI) from a given color image, regardless of other objects. The main novelty of our method is that we modify the stopping function in the functional of usual geodesic active contour method so that the new stopping function is coupled by a discrimination function of OOI. By minimizing the functional, the OOI is segmented. Firstly, we study the pixel properties of the OOI by sample pixels visually chosen from OOI. From these sample pixels, by the principal component analysis and interval estimation, the discrimination function of whether a pixel is in the OOI is obtained probabilistically. Then we propose the energy functional for the segmentation of OOI with new stopping function. Unlike usual stopping functions defined by the image gradient, our improved stopping function depends on not only the image gradient but also the discrimination function derived from the color information of OOI. As a result, better than usual active contour methods which detect all objects in the image, our modified active contour method can detect OOI but without unwanted objects. Experiments are conducted in both synthetic and natural images. The result shows that our algorithm is very efficient for detecting OOI even the background is complicated.

A Variational Approach for Pan-Sharpening

Pan-sharpening is a process of acquiring a high resolution multispectral (MS) image by combining a low resolution MS image with a corresponding high resolution panchromatic (PAN) image. In this paper, we propose a new variational pan-sharpening method based on three basic assumptions: 1) the gradient of PAN image could be a linear combination of those of the pan-sharpened image bands; 2) the upsampled low resolution MS image could be a degraded form of the pan-sharpened image; and 3) the gradient in the spectrum direction of pan-sharpened image should be approximated to those of the upsampled low resolution MS image. An energy functional, whose minimizer is related to the best pan-sharpened result, is built based on these assumptions. We discuss the existence of minimizer of our energy and describe the numerical procedure based on the split Bregman algorithm. To verify the effectiveness of our method, we qualitatively and quantitatively compare it with some state-of-the-art schemes using QuickBird and IKONOS data. Particularly, we classify the existing quantitative measures into four categories and choose two representatives in each category for more reasonable quantitative evaluation. The results demonstrate the effectiveness and stability of our method in terms of the related evaluation benchmarks. Besides, the computation efficiency comparison with other variational methods also shows that our method is remarkable.

A New Diffusion-Based Variational Model for Image Denoising and Segmentation

In this paper we propose a new variational model for image denoising and segmentation of both gray and color images. This method is inspired by the complex Ginzburg–Landau model and the weighted bounded variation model. Compared with active contour methods, our new algorithm can detect non-closed edges as well as quadruple junctions, and the initialization is completely automatic. The existence of the minimizer for our energy functional is proved. Numerical results show the effectiveness of our proposed model in image denoising and segmentation.

A variational method for multisource remote-sensing image fusion

With the increasing availability of multisource image data from Earth observation satellites, image fusion, a technique that produces a single image which preserves major salient features from a set of different inputs, has become an important tool in the field of remote sensing since usually the complete information cannot be obtained by a single sensor. In this article, we develop a new pixel-based variational model for image fusion using gradient features. The basic assumption is that the fused image should have a gradient that is close to the most salient gradient in the multisource inputs. Meanwhile, we integrate the inputs with the average quadratic local dispersion measure for the purpose of uniform and natural perception. Furthermore, we introduce a split Bregman algorithm to implement the proposed functional more effectively. To verify the effect of the proposed method, we visually and quantitatively compare it with the conventional image fusion schemes, such as the Laplacian pyramid, morphological pyramid, and geometry-based enhancement fusion methods. The results demonstrate the effectiveness and stability of the proposed method in terms of the related fusion evaluation benchmarks. In particular, the computation efficiency of the proposed method compared with other variational methods also shows that our method is remarkable.

Variational denoising of partly textured images

The Rudin-Osher-Fatemi model is a widely used variational denoising algorithm which favors piecewise constant solutions. Although edge sharpness and location are well preserved, some local features such as textures and small details are often diminished with noise simultaneously. This paper aims to better preserve these local features using a similar variational framework. We introduce a texture detecting function according to the derivatives of the noisy textured image. Then this function is used to construct a spatially adaptive fidelity term, which adjusts the denoising extent in terms of the local features. Numerical results show that our method is superior to the Rudin-Osher-Fatemi model in both signal-to-noise ratio and visual quality. Moreover, part of our results are also compared with other state-of-the-art methods including a variational method and a non local means filter. The comparison shows that our method is competitive with these two methods in restoration quality but is much faster.

Framelet based pan-sharpening via a variational method

Pan-sharpening is a process of combining a low resolution multi-spectral (MS) image and a high resolution panchromatic (PAN) image to obtain a single high resolution MS image. In this paper, we propose two pan-sharpening methods based on the framelet framework. The first method, as a basic work, is called a framelet-based pan-sharpening (FP) method. In the FP method, we first decompose the MS and PAN images into framelet coefficients, then obtain a new set of coefficients by choosing the approximation coefficients in MS and detail coefficients in PAN, and finally construct the pan-sharpened image from the new set of coefficients. To overcome the inflexibility of FP, in the second method, by combining FP and other three fusion requirements, i.e., geometry keeping, spectral preserving and the sparsity of the image in the framelet domain, four assumptions are established. Based on these assumptions, a framelet based variational energy functional, whose minimizer is related to the final pan-sharpened result, is then formulated. To improve the numerical efficiency, the split Bregman iteration is further introduced, and the result of FP method is set as an initial value. We refer this method as the variational framelet pan-sharpening (VFP) method. To verify the effectiveness of our methods, we present the results of the two methods on the QuickBird and IKONOS images, compare them with five existing methods qualitatively and quantitatively, analyze the influence of parameters of VFP, and extend the VFP to hyperspectral data as well as comparison study. The experimental results demonstrate the superiority of our methods.