Last updated October 11, 2007

Sung Ha Kang

Assistant Professor
Department of Mathematics
University of Kentucky

Mailing Address :
715 Patterson Office Tower
University of Kentucky
Lexington, KY 40506-0027

Main Math office : 859)257-3336
Fax : 859)257-4078

Office: POT 837 (Patterson Office Tower)
Phone: 859) 257 - 6815
Mail : skang@ms.uky.edu


Research Interest
My research area is in this general area of mathematical image processing via PDE/variational functional based approaches. In particular, I have been investigating various problem arising from 1) image reconstructions such as image denoising, image deblurring, image inpainting and image dejittering, 2) color image analysis including denoising, decomposition, and colorization, and 3) multiphase image segmentation and image quantization.

Mathematical image processing: Past and current research

1) Image Reconstruction: inpainting, dejittering and deblurring

(a) Image Inpainting refers to a specific image restoration task, where missing or damaged portions of an image are reconstructed. Digital image inpainting became very popular thanks to the work by Bertalmio, Sapiro, Caselles, and Ballester [ Proc. Siggraph 2000] where the authors use third order partial differential equations (PDE) to diffuse the known image information into the missing regions along the level lines. Masnou and Morel [Proc. IEEE Int'l Conf on Image Proces. 1998] drew our attention to variational models.

(b) Image and Video Dejittering occurs when the horizontal lines of video image frames are randomly displaced due to the corruption of synchronization signals or electromagnetic interference during video transmission.


(c) Image and deblurring is one of the classic image restoration problems and the difficulties lie on the ill-poseness of this problem. For example, typically only a blurry out of focus image, such as in Figure 3(a), is given to be deblurred to a clear and focused image.
With my Ph. D student, I proposed a blind deconvolution method, Total variation blind deconvolution using shock filters, which dramatically improves the result of blind-deconvolution.


2) Color Image analysis: denoising, decomposition and colorization

(a) Color Spaces and denoising: Chan, Kang and Shen, we explored various color spaces for the best color image denoising. We studied the Chromaticity-Brightness (CB) model and Hue-Saturation-Value (HSV) model, and found out it is best to treat color as one component, but independently to the brightness.

(b) Color image decomposition: With Aujol, I have consider color image decomposition in Color Image Decomposition and Restoration. This is one of the first work on color texture analysis.

(c) Colorization refers to an image processing task which recovers color of gray scale images when only small regions with color are given. In Variational Models for Image Colorization via Chromaticity and Brightness Decomposition, we proposed and analyzed couple of variational models for colorization. Figure 4. shows an example of texture colorization using image decomposition techniques.


3) Image segmentation and Quantization
Image Segmentation is a classical problem in image processing. From Geman and Geman's mixture random-field models [IEEE PAMI 1984] to Mumford and Shah's piecewise smooth variational image models [Comm. Pure Appl. Math. 1989], segmentation has been extensively studied by various researchers. One of the most influential methods is the level-set approach by Chan and Vese [IEEE Trans. Image Proc. 2001].



Refereed Publications

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