Ling Pi

Variable exponent functionals in image restoration

Abstract We study a functional with variable exponent, 1 p ( x ) ⩽ 2 , which provides a model for image denoising and restoration. Here p ( x ) is defined by the gradient information in the observed image. The diffusion derived from the proposed model is between total variation based regularization and Gaussian smoothing. The diffusion speed of the corresponding heat equation is tuned by the variable exponent p ( x ) . The minimization problem and its associated flow in a weakened formulation are discussed. The existence, uniqueness, stability and long-time behavior of the proposed model are established in the variable exponent functional space W 1 , p ( x ) . Experimental results illustrate the effectiveness of the model in image restoration.

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 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.

Delineating lakes and enclosed islands in satellite imagery by geodesic active contour model

The objective of the present paper is to develop a new method for delineating lakes and enclosed islands from shuttle radar topography mission (SRTM) digital elevation model (DEM). The Thousand‐Island Lake in China is chosen as the study site. DEM may have missing values or be inaccurate over water bodies. Thus, it is not trivial to delineate the shorelines of lake directly from DEM. We achieve this objective by overlaying the boundary derived from the Landsat image of the same area. Unlike traditional water body delineation techniques, e.g. the band ratio method, which make use of physical quantities, we only use the colour information from Landsat ETM+ band 7, 4 and 2. The main reason is that the colour information is the only resource available for most publicly available satellite data such as the maps from Google Earth. Thus, it is necessary to develop a method depending on only colour information. In the Landsat image, a discrimination function to determine whether a pixel belongs to the lake area is obtained by studying sample pixels chosen from the lake area. The delineation of shorelines is an evolutionary process. The evolution equation is derived according to the active contour model and the discrimination function. The initial contour is inside the lake and expands according to the evolution equation. The evolving curve converges to the boundaries of the lake efficiently with a satisfactory result. Finally, the shorelines are overlaid on the DEM according to latitude and longitude. Our geodesic active contour method is a general one, and could be used to delineate objects of interest such as oil slicks and burn scars in satellite images.

Explicit Coherence Enhancing Filter With Spatial Adaptive Elliptical Kernel

The goal of this letter is to provide an elliptical filter to improve image coherence for the task of image smoothing and inpainting. The kernel of this filter is adaptively weighted and its shape is determined by local coherence estimation. The long axis of its ellipse is the same as the coherence direction and we put more weight there to enhance coherence. Compared with the related anisotropic partial differential equations (PDEs) or wavelet shrinkage methods, the proposed filter is extremely simple, instinctive and easy to code. Numerical examples and comparisons illustrate clearly the good performance of the proposed filter.

Object(s)-of-interest segmentation for images with inhomogeneous intensities based on curve evolution

In this paper, we propose an object(s)-of-interest (OOI) segmentation method for images with inhomogeneous intensities. First, we define a discrimination function for each pixel, labelling whether the pixel belongs to OOI based on the characteristics of OOI. This function is then integrated with image gradient to construct a stopping function in an energy functional. Finally, this energy functional is minimized by means of level set evolution, which guides the motion of the zero level set toward object boundaries. The results demonstrate that our model is effective.

A semi-automatic method for burn scar delineation using a modified Chan-Vese model

We propose a novel semi-automatic method for burn scar delineation from Landsat imagery using a modified Chan-Vese model. Burn scars appear reddish-brown in band 742 false-colour composite of Landsat 7 images. This property is used in our algorithm to delineate burn scars. Firstly, we visually choose sample pixels from the burn scar. From these pixels, a discrimination function for burn scars is determined by the principal component analysis and interval estimation. Then we define a modified Chan-Vese functional. The minimizer of the functional corresponds to the boundary of the burn scar. In order to minimize this functional, the corresponding contour evolution equation is given. We use the discrimination function to locate an initial contour that is near the boundary of the burn scar. The evolving curve then efficiently converges to the desired boundary. A Landsat image over Russia is used to examine our algorithm. The result shows that the algorithm is effective.

A spatially variant total variational model for chromatic aberration correction

Abstract In this paper, we propose a spatially variant total variational model to correct chromatic aberration (CA) that causes false color artifacts near edges in captured images. In general, it may be very difficult to determine suitably CA regions in captured images. Instead of using local image processing methods, our idea is to make use of spatially variant model to control the gradient and intensity matching between the red and blue color channels and the green color channel at the edges. The total variation regularization is also employed to constraint the change of the intensity of red and blue color channels during the gradient and intensity matching. We present both theoretical results and algorithms for the proposed model. Experimental results are given to illustrate the effectiveness of the proposed model and algorithm and show that their corrected images are visually better than those corrected by the other testing methods.

Variational-based speckle noise removal of SAR imagery

In this paper we present a variational method for synthetic aperture radar (SAR) speckle removal. Variational method is a newly developed technique for the removal of SARs multiplicative noise. For an image, we could define an energy functional. The energy evolves as the original image changes, and the minimum energy corresponds to the speckle reduced result. Partial differential equation (PDE) technique is used to get the minimal solution. Our energy functional makes use of the statistical information of the multiplicative noise since it follows a Gamma law with mean mu = 1 and variance sigma2 = 1/M for M-look SAR. Our energy is a regularization term with two constraints. The regularization term is the integral for the norm of image gradient; two constraints are the mean of noise should be 1 and the variance of noise should be 1/M. We use the method of Lagrange multipliers, Euler-Lagrange equation and heat flow method to obtain the minimizer of the energy. ERS Precision Image (PRI) data are to demonstrate our algorithm. Numerical result shows that the speckle reduced image preserves edges and point targets while smoothes homogenous regions in the original image. The algorithm is computationally efficient and easy to implement.