A Color Elastica Model for Vector-Valued Image Regularization

Dear All,

You are cordially invited to an online academic seminar to be delivered by Prof. Xue-Cheng TAI (Hong Kong Baptist University) on June 7 (Tuesday). This seminar will discuss "A Color Elastica Model for Vector-Valued Image Regularization".

Seminar Introduction

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Time & Date: 10:00 - 11:00 am, June 7 (Tuesday)

Venue: Zoom Online Meeting

Zoom meeting ID: 930 0631 2878

Passcode: 20220607

Host: Prof. Xiaoping WANG

Speaker: Prof. Xue-Cheng TAI

Abstract:

Models related to the Euler’s elastica energy have proven to be useful for many applications including image processing. Extending elastica models to color images and multichannel data is a challenging task, as stable and consistent numerical solvers for these geometric models often involve high order derivatives. Like the single channel Euler’s elastica model and the total variation (TV) models, geometric measures that involve high order derivatives could help when considering image formation models that minimize elastic properties. In the past, the Polyakov action from high energy physics has been successfully applied to color image processing. Here, we introduce an addition to the Polyakov action for color images that minimizes the color manifold curvature. The color image curvature is computed by applying of the Laplace–Beltrami operator to the color image channels. When reduced to gray-scale images, while selecting appropriate scaling between space and color, the proposed model minimizes the Euler’s elastica operating on the image level sets. Finding a minimizer for the proposed nonlinear geometric model is a challenge we address in this paper. Specifically, we present an operator-splitting method to minimize the proposed functional. The non-linearity is decoupled by introducing three vector-valued and matrix-valued variables. The problem is then converted into solving for the steady state of an associated initial-value problem. The initial-value problem is time-split into three fractional steps, such that each sub-problem has a closed form solution, or can be solved by fast algorithms. The efficiency and robustness of the proposed method are demonstrated by systematic numerical experiments.

This talk is based on joint work with: Hao Liu, Ron Kimmel and Roland Glowinski.

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Biography

Prof. Xue-Cheng TAI

Prof Xue-Cheng TAI is currently at the Department of Mathematics, Hong Kong Baptist University. He received his Ph.D. degree from the University of Jyvaskyla, Finland. His research interests include Numerical methods for partial differential equations, optimization techniques, inverse problems, and image processing. He has done significant research work in his research areas and published many research works in top quality international conference and journals. He served as organizing and program committee members for a number of international conferences and has been often invited for international conferences. He has served as referees and reviewers for many premier conferences and journals.

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