Yoon Mo Jung

MULTIPHASE IMAGE SEGMENTATION VIA MODICA-MORTOLA PHASE TRANSITION ∗

We propose a novel multiphase segmentation model built upon the celebrated phase transition model of Modica and Mortola in material sciences and a properly synchronized fitting term that complements it. The proposed sine-sinc model outputs a single multiphase distribution from which each individual segment or phase can be easily extracted. Theoretical analysis is developed for the

Environmentally Robust Motion Detection for Video Surveillance

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Fast segmentation of ultrasound images using robust Rayleigh distribution decomposition

-convergence behavior of the proposed model and the existence of its minimizers. Since the model is not quadratic nor convex, for computation we adopted the convex-concave procedure (CCCP) that has been developed in the literatures of both computational nonlinear PDEs and neural computation. Numerical details and experiments on both synthetic and natural images are presented.

First-order modeling and stability analysis of illusory contours

Most video surveillance systems require to manually set a motion detection sensitivity level to generate motion alarms. The performance of motion detection algorithms, embedded in closed circuit television (CCTV) camera and digital video recorder (DVR), usually depends upon the preselected motion sensitivity level, which is expected to work in all environmental conditions. Due to the preselected sensitivity level, false alarms and detection failures usually exist in video surveillance systems. The proposed motion detection model based upon variational energy provides a robust detection method at various illumination changes and noise levels of image sequences without tuning any parameter manually. We analyze the structure mathematically and demonstrate the effectiveness of the proposed model with numerous experiments in various environmental conditions. Due to the compact structure and efficiency of the proposed model, it could be implemented in a small embedded system.

Impedance Imaging With First-Order TV Regularization

The segmentation of left ventricle in ultrasound imaging of human heart would provide an important clinical parameter for the evaluation of cardiac functions including volume stroke or ejection fraction and wall motion tracking. We propose a fast segmentation method to reduce laborious manual efforts and conveniently provide robust and stable cardiac quantification to users. The proposed method provides a very simple energy functional form using a predetermined Rayleigh distribution parameter so that the corresponding steepest descent approach with some shape constraints on contour is still capable of fast segmentation. We present several experimental results on two-dimensional echocardiography data for the performance of the proposed model. The experiments show that the proposed model is especially useful when a part of target boundary is seriously corrupted.

Analysis and Blocking of Error Propagation by Region-Dependent Noisy Data in MREIT

In visual cognition, illusions help elucidate certain intriguing latent perceptual functions of the human vision system, and their proper mathematical modeling and computational simulation are therefore deeply beneficial to both biological and computer vision. Inspired by existent prior works, the current paper proposes a first-order energy-based model for analyzing and simulating illusory contours. The lower complexity of the proposed model facilitates rigorous mathematical analysis on the detailed geometric structures of illusory contours. After being asymptotically approximated by classical active contours, the proposed model is then robustly computed using the celebrated level-set method of Osher and Sethian [S. Osher, J.A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (12) (1988) 12-49] with a natural supervising scheme. Potential cognitive implications of the mathematical results are addressed, and generic computational examples are demonstrated and discussed.

A regularization technique for closed contour segmentation in ultrasound images

EIT problem is a typical inverse problem with serious ill-posedness. In general, regularization techniques are necessary for such ill-posed inverse problems. To overcome ill-posedness, the total variation (TV) regularization is widely used and it is also successfully applied to EIT. For realtime monitoring, a fast and robust image reconstruction algorithm is required. By exploiting recent advances in optimization, we propose a first-order TV algorithm for EIT, which simply consists of matrix-vector multiplications and in which the sparse structure of the system can be easily exploited. Furthermore, a typical smoothing parameter to overcome nondifferentibility of the TV term is not needed and a closed form solution can be applied in part using soft thresholding. It shows a fast reconstruction in the beginning. Numerical experiments using simulated data and real experimental data support our claim.

A coordinate descent homotopy method for linearly constrained nonsmooth convex minimization

Magnetic resonance electrical impedance tomography (MREIT) aims to visualize a conductivity distribution inside the human body. In MREIT, we inject current to produce a current density

Illusory Shapes via First-Order Phase Transition and Approximation

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Inpainting based metal reduction in dental X-ray computed tomography

and magnetic flux density