Yongsheng Pan

Efficient Implementation of the Chan-Vese Models Without Solving PDEs

Efficient implementation methods are proposed for Chan-Vese models. The proposed methods do not require solutions of PDEs and are therefore fast. The advantages of level set methods, such as automatic handling of topological changes, are preserved. These methods utilize region information to guide the evolution of initial curves. Gaussian smoothing is applied to regularize the evolving curves. These algorithms are able to automatically and efficiently segment objects in complicated images. Experimental results show that the proposed methods work efficiently for images without strong noise. However, they still have initialization problems, as do the Chan-Vese models

A Fast Iterative Method for Solving the Eikonal Equation on Triangulated Surfaces

This paper presents an efficient, fine-grained parallel algorithm for solving the Eikonal equation on triangular meshes. The Eikonal equation, and the broader class of Hamilton-Jacobi equations to which it belongs, have a wide range of applications from geometric optics and seismology to biological modeling and analysis of geometry and images. The ability to solve such equations accurately and efficiently provides new capabilities for exploring and visualizing parameter spaces and for solving inverse problems that rely on such equations in the forward model. Efficient solvers on state-of-the-art, parallel architectures require new algorithms that are not, in many cases, optimal, but are better suited to synchronous updates of the solution. In previous work [W. K. Jeong and R. T. Whitaker, SIAM J. Sci. Comput., 30 (2008), pp. 2512-2534], the authors proposed the fast iterative method (FIM) to efficiently solve the Eikonal equation on regular grids. In this paper we extend the fast iterative method to solve Eikonal equations efficiently on triangulated domains on the CPU and on parallel architectures, including graphics processors. We propose a new local update scheme that provides solutions of first-order accuracy for both architectures. We also propose a novel triangle-based update scheme and its corresponding data structure for efficient irregular data mapping to parallel single-instruction multiple-data (SIMD) processors. We provide detailed descriptions of the implementations on a single CPU, a multicore CPU with shared memory, and SIMD architectures with comparative results against state-of-the-art Eikonal solvers.

Feasibility of GPU-assisted iterative image reconstruction for mobile C-arm CT

Computed tomography (CT) has been extensively studied and widely used for a variety of medical applications. The reconstruction of 3D images from a projection series is an important aspect of the modality. Reconstruction by filtered backprojection (FBP) is used by most manufacturers because of speed, ease of implementation, and relatively few parameters. Iterative reconstruction methods have a significant potential to provide superior performance with incomplete or noisy data, or with less than ideal geometries, such as cone-beam systems. However, iterative methods have a high computational cost, and regularization is usually required to reduce the effects of noise. The simultaneous algebraic reconstruction technique (SART) is studied in this paper, where the Feldkamp method (FDK) for filtered back projection is used as an initialization for iterative SART. Additionally, graphics hardware is utilized to increase the speed of SART implementation. Nvidia processors and compute unified device architecture (CUDA) form the platform for GPU computation. Total variation (TV) minimization is applied for the regularization of SART results. Preliminary results of SART on 3-D Shepp-Logan phantom using using TV regularization and GPU computation are presented in this paper. Potential improvements of the proposed framework are also discussed.

Preferential Image Segmentation Using Trees of Shapes

A novel preferential image segmentation method is proposed that performs image segmentation and object recognition using mathematical morphologies. The method preferentially segments objects that have intensities and boundaries similar to those of objects in a database of prior images. A tree of shapes is utilized to represent the content distributions in images, and curve matching is applied to compare the boundaries. The algorithm is invariant to contrast change and similarity transformations of translation, rotation and scale. A performance evaluation of the proposed method using a large image dataset is provided. Experimental results show that the proposed approach is promising for applications such as object segmentation and video tracking with cluttered backgrounds.

TV-regularized iterative image reconstruction on a mobile C-ARM CT

3D computed tomography has been extensively studied and widely used in modern society. Although most manufacturers choose the filtered backprojection algorithm (FBP) for its accuracy and efficiency, iterative reconstruction methods have a significant potential to provide superior performance for incomplete, noisy projection data. However, iterative methods have a high computational cost, which hinders their practical use. Furthermore, regularization is usually required to reduce the effects of noise. In this paper, we analyze the use of the Simultaneous Algebraic Reconstruction Technique (SART) with total variation (TV) regularization. Additionally, graphics hardware is utilized to increase the speed of SART. NVIDIAs GPU and Compute Unified Device Architecture (CUDA) comprise the core of our computational platform. GPU implementation details, including ray-based forward projection and voxel-based backprojection are illustrated. Experimental results for high-resolution synthetic and real data are provided to demonstrate the accuracy and efficiency of the proposed framework.

An Efficient Bottom-Up Image Segmentation Method Based on Region Growing, Region Competition and the Mumford Shah Functional

Curve evolution implementations of the Mumford-Shah functional are of broad interest in image segmentation. These implementations, however, have initialization problems. A mathematical analysis of the initialization problem for the bi-modal Chan-Vese model is provided in this paper. The initialization problem is a result of the non-convexity of the Mumford-Shah functional and the top-down hierarchy of the models use of global region information in the image. An efficient image segmentation method is proposed that alleviates the initialization problem, based on region growing, region competition and the Mumford Shah functional. This algorithm is able to automatically and efficiently segment objects in complicated images. Using a bottom-up hierarchy, the method avoids the initialization problem in the Chan-Vese model and works for images with multiple junctions and color images. It can be extended to textured images. Experimental results show that the proposed method is robust to the effects of noise

Bottom-Up Hierarchical Image Segmentation Using Region Competition and the Mumford-Shah Functional

This paper generalizes the methods in a previous paper in Pan, Y. et al, (2006) in two ways. First, a more comprehensive analysis of the initialization problem of the Chan-Vese models is given. Second, the image segmentation method proposed in Pan, Y. et al. (2006) is improved by applying bimodal curve evolution with region competition. The improved method maintains the advantages of the previous method. It is efficient, stable in the presence of strong noise and able to handle complicated images. It outperforms the previous method for images with weak edges. Experimental results in this paper demonstrate these improvements

Efficient Bottom-Up Image Segmentation Using Region Competition and the Mumford-Shah Model for Color and Textured Images

Curve evolution implementations of the Mumford-Shah functional are of broad interest in image segmentation. These implementations, however, have initialization problems. A mathematical analysis of the initialization problem for the Chan-Vese implementation is provided in this paper. The initialization problem is a result of the non-convexity of the MumfordShah functional and the top-down hierarchy of the models use of global region information in the image. Based on the analysis, efficient implementation methods are proposed for the Chan-Vese models. The proposed methods do not have to solve PDEs and thus work fast. The advantages of level set methods, such as automatic handling of topological changes, are preserved. These methods work well for images without strong noise. Initialization problems, however, still exist. A bottom-up image segmentation method is proposed that alleviates the initialization problem, based on region competition and the Mumford Shah functional. This algorithm extends the method in Jean Michel Morel, et al., (1995) and is able to automatically and efficiently segment objects in complicated images. Using a bottom-up hierarchy, the method avoids the initialization problem in the Chan-Vese model and works for images with multiple junctions and color images. It is then extended to textured images using Gabor filters and fractal methods. Experimental results show that the proposed method works well and is robust to the effects of noise

Top-down image segmentation using the Mumford-Shah functional and level set image representation

A top-down image segmentation method is proposed in this paper, utilizing level set image representation and the piecewise-constant Mumford-Shah functional. The method achieves top-down hierarchical segmentation by taking advantage of the tree structure provided by level set image representation. The piecewise-constant Mumford-Shah functional is utilized in the proposed method to determine if each node in the tree segments the image. Experimental results show that this method is able to segment complicated real images.

Image Segmentation Using Curve Evolution and Anisotropic Diffusion: An Integrated Approach

In this paper, a new model is proposed for image segmentation that integrates the curve evolution and anisotropic diffusion methods. The curve evolution method, utilizing both gradient and region information, segments an image into multiple regions. During the evolution of the curve, anisotropic diffusion is adaptively applied to the image to remove noise while preserving boundary information. Coupled partial differential equations (PDEs) are used to implement the method. Experimental results show that the proposed model is successful for complex images with high noise