Yunmei Chen

Variable Exponent, Linear Growth Functionals in Image Restoration

We study a functional with variable exponent,

Using Prior Shapes in Geometric Active Contours in a Variational Framework

1\leq p(x)\leq 2

Cumulative residual entropy: a new measure of information

, which provides a model for image denoising, enhancement, and restoration. The diffusion resulting from the proposed model is a combination of total variation (TV)-based regularization and Gaussian smoothing. The existence, uniqueness, and long-time behavior of the proposed model are established. Experimental results illustrate the effectiveness of the model in image restoration.

A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from complex DWI

In this paper, we report an active contour algorithm that is capable of using prior shapes. The energy functional of the contour is modified so that the energy depends on the image gradient as well as the prior shape. The model provides the segmentation and the transformation that maps the segmented contour to the prior shape. The active contour is able to find boundaries that are similar in shape to the prior, even when the entire boundary is not visible in the image (i.e., when the boundary has gaps). A level set formulation of the active contour is presented. The existence of the solution to the energy minimization is also established.We also report experimental results of the use of this contour on 2d synthetic images, ultrasound images and fMRI images. Classical active contours cannot be used in many of these images.

On the incorporation of shape priors into geometric active contours

In this paper, we use the cumulative distribution of a random variable to define its information content and thereby develop an alternative measure of uncertainty that extends Shannon entropy to random variables with continuous distributions. We call this measure cumulative residual entropy (CRE). The salient features of CRE are as follows: 1) it is more general than the Shannon entropy in that its definition is valid in the continuous and discrete domains, 2) it possesses more general mathematical properties than the Shannon entropy, and 3) it can be easily computed from sample data and these computations asymptotically converge to the true values. The properties of CRE and a precise formula relating CRE and Shannon entropy are given in the paper. Finally, we present some applications of CRE to reliability engineering and computer vision.

Fiber tract mapping from diffusion tensor MRI

In this paper, we present a novel constrained variational principle for simultaneous smoothing and estimation of the diffusion tensor field from complex valued diffusion-weighted images (DWI). The constrained variational principle involves the minimization of a regularization term of L/sup p/ norms, subject to a nonlinear inequality constraint on the data. The data term we employ is the original Stejskal-Tanner equation instead of the linearized version usually employed in literature. The complex valued nonlinear form leads to a more accurate (when compared to the linearized version) estimate of the tensor field. The inequality constraint requires that the nonlinear least squares data term be bounded from above by a known tolerance factor. Finally, in order to accommodate the positive definite constraint on the diffusion tensor, it is expressed in terms of Cholesky factors and estimated. The constrained variational principle is solved using the augmented Lagrangian technique in conjunction with the limited memory quasi-Newton method. Experiments with complex-valued synthetic and real data are shown to depict the performance of our tensor field estimation and smoothing algorithm.

An Accelerated Linearized Alternating Direction Method of Multipliers

A novel model for boundary determination that incorporates prior shape information into geometric active contours is presented. The basic idea of this model is to minimize the energy functional depending on the information of the image gradient and the shape of interest, so that the boundary of the object can be captured either by higher magnitude of the image gradient or by the prior knowledge of its shape. The level set form of the proposed model is also provided. We present our experimental results on some synthetic images, functional MR brain images, and ultrasound images for which the existing active contour methods are not applicable. The existence of the solution to the proposed minimization problem is also discussed.

Image denoising and segmentation via nonlinear diffusion

To understand evolving pathology in the central nervous system (CNS) and develop effective treatments, it is essential to correlate the nerve fiber connectivity with the visualization of function. Diffusion tensor imaging (DTI) can provide the fundamental information required for viewing structural connectivity. We present a novel algorithm for automatic fiber tract mapping in the CNS specifically, the spinal cord. The automatic fiber tract mapping problem is solved in two phases, namely a data smoothing phase and a fiber tract mapping phase. In the former, smoothing is achieved via a new weighted total variation (TV)-norm minimization (for vector-valued data) which strives to smooth while retaining all relevant detail. For the fiber tract mapping, a smooth 3D vector field indicating the dominant anisotropic direction at each spatial location is computed from the smoothed data. Fiber tracts are then determined as the smooth integral curves of this vector field in a variational framework.

DT-MRI denoising and neuronal fiber tracking.

We present a novel framework, namely, accelerated alternating direction method of multipliers (AADMM), for acceleration of linearized ADMM. The basic idea of AADMM is to incorporate a multistep acceleration scheme into linearized ADMM. We demonstrate that for solving a class of convex composite optimization with linear constraints, the rate of convergence of AADMM is better than that of linearized ADMM, in terms of their dependence on the Lipschitz constant of the smooth component. Moreover, AADMM is capable of dealing with the situation when the feasible region is unbounded, as long as the corresponding saddle point problem has a solution. A backtracking algorithm is also proposed for practical performance.

Joint Image Registration and Segmentation

Abstract Image denoising and segmentation are fundamental problems in the field of image processing and computer vision with numerous applications. In this paper, we present a nonlinear PDE-based model for image denoising and segmentation which unifies the popular model of Alvarez, Lions and Morel (ALM) for image denoising and the Caselles, Kimmel and Sapiro model of geodesic “snakes”. Our model includes nonlinear diffusive as well as reactive terms and leads to quality denoising and segmentation results as depicted in the experiments presented here. We present a proof for the existence, uniqueness, and stability of the viscosity solution of this PDE-based model. The proof is in spirit similar to the proof of the ALM model; however, there are several differences which arise due to the presence of the reactive terms that require careful treatment/consideration. A fast implementation of our model is realized by embedding the model in a scale space and then achieving the solution via a dynamic system governed by a coupled system of first-order differential equations. The dynamic system finds the solution at a coarse scale and tracks it continuously to a desired fine scale. We demonstrate the smoothing and segmentation results on several real images.