Segmentation of ultrasound images of thyroid nodule for assisting fine needle aspiration cytology

The incidence of thyroid nodule is very high and generally increases with the age. Thyroid nodule may presage the emergence of thyroid cancer. The thyroid nodule can be completely cured if detected early. Fine needle aspiration cytology is a recognized early diagnosis method of thyroid nodule. There are still some limitations in the fine needle aspiration cytology, and the ultrasound diagnosis of thyroid nodule has become the first choice for auxiliary examination of thyroid nodular disease. If we could combine medical imaging technology and fine needle aspiration cytology, the diagnostic rate of thyroid nodule would be improved significantly. The properties of ultrasound will degrade the image quality, which makes it difficult to recognize the edges for physicians. Image segmentation technique based on graph theory has become a research hotspot at present. Normalized cut (Ncut) is a representative one, which is suitable for segmentation of feature parts of medical image. However, how to solve the normalized cut has become a problem, which needs large memory capacity and heavy calculation of weight matrix. It always generates over segmentation or less segmentation which leads to inaccurate in the segmentation. The speckle noise in B ultrasound image of thyroid tumor makes the quality of the image deteriorate. In the light of this characteristic, we combine the anisotropic diffusion model with the normalized cut in this paper. After the enhancement of anisotropic diffusion model, it removes the noise in the B ultrasound image while preserves the important edges and local details. This reduces the amount of computation in constructing the weight matrix of the improved normalized cut and improves the accuracy of the final segmentation results. The feasibility of the method is proved by the experimental results.Comment: 15pages,13figure

A class of second-order geometric quasilinear hyperbolic PDEs and their application in imaging science

In this paper, we study damped second-order dynamics, which are quasilinear hyperbolic partial differential equations (PDEs). This is inspired by the recent development of second-order damping systems for accelerating energy decay of gradient flows. We concentrate on two equations: one is a damped second-order total variation flow, which is primarily motivated by the application of image denoising; the other is a damped second-order mean curvature flow for level sets of scalar functions, which is related to a non-convex variational model capable of correcting displacement errors in image data (e.g. dejittering). For the former equation, we prove the existence and uniqueness of the solution. For the latter, we draw a connection between the equation and some second-order geometric PDEs evolving the hypersurfaces which are described by level sets of scalar functions, and show the existence and uniqueness of the solution for a regularized version of the equation. The latter is used in our algorithmic development. A general algorithm for numerical discretization of the two nonlinear PDEs is proposed and analyzed. Its efficiency is demonstrated by various numerical examples, where simulations on the behavior of solutions of the new equations and comparisons with first-order flows are also documented

A Second Order Non-Smooth Variational Model for Restoring Manifold-Valued Images

We introduce a new non-smooth variational model for the restoration of manifold-valued data which includes second order differences in the regularization term. While such models were successfully applied for real-valued images, we introduce the second order difference and the corresponding variational models for manifold data, which up to now only existed for cyclic data. The approach requires a combination of techniques from numerical analysis, convex optimization and differential geometry. First, we establish a suitable definition of absolute second order differences for signals and images with values in a manifold. Employing this definition, we introduce a variational denoising model based on first and second order differences in the manifold setup. In order to minimize the corresponding functional, we develop an algorithm using an inexact cyclic proximal point algorithm. We propose an efficient strategy for the computation of the corresponding proximal mappings in symmetric spaces utilizing the machinery of Jacobi fields. For the n-sphere and the manifold of symmetric positive definite matrices, we demonstrate the performance of our algorithm in practice. We prove the convergence of the proposed exact and inexact variant of the cyclic proximal point algorithm in Hadamard spaces. These results which are of interest on its own include, e.g., the manifold of symmetric positive definite matrices

Dictionary Learning-based Inpainting on Triangular Meshes

The problem of inpainting consists of filling missing or damaged regions in images and videos in such a way that the filling pattern does not produce artifacts that deviate from the original data. In addition to restoring the missing data, the inpainting technique can also be used to remove undesired objects. In this work, we address the problem of inpainting on surfaces through a new method based on dictionary learning and sparse coding. Our method learns the dictionary through the subdivision of the mesh into patches and rebuilds the mesh via a method of reconstruction inspired by the Non-local Means method on the computed sparse codes. One of the advantages of our method is that it is capable of filling the missing regions and simultaneously removes noise and enhances important features of the mesh. Moreover, the inpainting result is globally coherent as the representation based on the dictionaries captures all the geometric information in the transformed domain. We present two variations of the method: a direct one, in which the model is reconstructed and restored directly from the representation in the transformed domain and a second one, adaptive, in which the missing regions are recreated iteratively through the successive propagation of the sparse code computed in the hole boundaries, which guides the local reconstructions. The second method produces better results for large regions because the sparse codes of the patches are adapted according to the sparse codes of the boundary patches. Finally, we present and analyze experimental results that demonstrate the performance of our method compared to the literature

Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows

This paper concerns an extension of discrete gradient methods to finite-dimensional Riemannian manifolds termed discrete Riemannian gradients, and their application to dissipative ordinary differential equations. This includes Riemannian gradient flow systems which occur naturally in optimization problems. The Itoh--Abe discrete gradient is formulated and applied to gradient systems, yielding a derivative-free optimization algorithm. The algorithm is tested on two eigenvalue problems and two problems from manifold valued imaging: InSAR denoising and DTI denoising.Comment: Post-revision version. To appear in SIAM Journal on Scientific Computin

Discretization schemes and numerical approximations of PDE impainting models and a comparative evaluation on novel real world MRI reconstruction applications

While various PDE models are in discussion since the last ten years and are widely applied nowadays in image processing and computer vision tasks, including restoration, filtering, segmentation and object tracking, the perspective adopted in the majority of the relevant reports is the view of applied mathematician, attempting to prove the existence theorems and devise exact numerical methods for solving them. Unfortunately, such solutions are exact for the continuous PDEs but due to the discrete approximations involved in image processing, the results yielded might be quite unsatisfactory. The major contribution of This work is, therefore, to present, from an engineering perspective, the application of PDE models in image processing analysis, from the algorithmic point of view, the discretization and numerical approximation schemes used for solving them. It is of course impossible to tackle all PDE models applied in image processing in this report from the computational point of view. It is, therefore, focused on image impainting PDE models, that is on PDEs, including anisotropic diffusion PDEs, higher order non-linear PDEs, variational PDEs and other constrained/regularized and unconstrained models, applied to image interpolation/ reconstruction. Apart from this novel computational critical overview and presentation of the PDE image impainting models numerical analysis, the second major contribution of This work is to evaluate, especially the anisotropic diffusion PDEs, in novel real world image impainting applications related to MRI