An exmaple from Silhouette Vectorization: from pixelized image (a), vectorization gives scalable SVG image in (h), which can represent any resolution.

Curvature based variational models **************************************************

Curvature is one of the fundamental properties in understanding curves and level lines. Using curvature, there are many interesting application one can explore, such as inpainting, illusory contours, following human vision perception. However, computation and analysis remain to be challenging. In the following, application to point cloud reconstruction, survey of variational models with curvature terms, fast algorithms, illusory countor and inpainting application are presented.

An exmaple of using curvature regularized surface reconstruction from point cloud.
(a) without curvature constraint and (c) with curvature constraint.

An exmaple from illusory shapes. From given image (a), illusory object is recovered in (b) and occluded objects in (c).

Image and Signal Decomposition **************************************************

The given signal in left (blue) is decomposed to piecewise constant, shades and noise.

The given signal in left (blue) is decomposed to Jump, Oscillation and Trend: using non-convex term for piecewise constant component, harmonic norm for smooth component, and G-norm for noise component.

Lattice identification **************************************************

Motivated by the problems of lattice mixture identification and grain irregularity detection in material science research, we developed a framework for lattice pattern representation and comparison and propose an efficient algorithm for lattice separation. We define new scale and shape descriptors, which considerably reduce the size of equivalence classes of lattice bases.

Lattice is characterized in this paper and Lattice comparison measure is introduced. This allows to distinguish lattics mixture. The given lattice mixture can be separated to three separate lattics patterns.

Grain regions can be Lattice is characterized in this paper and Lattice comparison measure is introduced. This allows to distinguish lattics mixture. The given lattice mixture can be separated to three separate lattics patterns.

Marco Barchiesi, Sung Ha Kang, Triet Le, Massimiliano Morini, Marcello Ponsiglione, ``A variational model for infinite perimeter segmentations based on Lipschitz level set functions: denoising while keeping finely oscillatory boundaries", Accepted SIAM Multiscale Modeling and Simulation 2010.

We proposed a new model of image segmentation which captures the oscillatory boundary while denoising the image. A typical segmentation model uses the total length penalization regularization, and this term is replaced by the area of the boundary neighborhood in the new model. The objective is to keep fine details and irregularities of the boundaries while denoising additive Gaussian noise. This is an initiating work on capturing the fine details of the boundary in image segmentation problem.
(a) Given noisy image. (b) and (c) are segmentation results this model, where Minkowski content is used in place of the typical total length term. With a different choice of parameters, one can segment the image similar to that of piecewise constant Mumford-Shah model (b) or capture more details of the boundary as in (c).This model allows the boundary with infinite perimeter, as long as it can be included in the epsilon bound.



Image Segmentation and Phase Transistion **************************************************

Using a well-potential is frequently studied in material science problems of phase transition, which has recently been introduced to imaging applications. These connections between phase transition model and image segmentation are quite natural: the phases in material sciences are characterized by densities and tensions, while in imaging object segments are characterized by some key visual features such as intensities and orientations.

Image Inpainting **************************************************

Tony F. Chan and Sung Ha Kang, `` Error Analysis for Image Inpainting'', Journal of Mathematical Imaging and Vision, Volume 26, pages 85-103, 2006. (full color images available at: UCLA CAM 04-72).
This is the first work on error analysis for image inpainting. For general inpainting experiments, local inpainting methods work well for narrow inpainting domains, and the error bounds give analysis on this phenomenon.

Color analysis and Colorization**************************************************

Sung Ha Kang and Jianhong Shen, ``Video dejittering by Bake and Shake", Image and Vision Computing, Volume 24, Issue 2, Pages 143-152, 2006. Full color images available at UCLA CAM 04-60.
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. This method gives very robust numerical results.

James H. Money and Sung Ha Kang, ``Total variation semi-blind deconvolution using shock filters", Image and vision computing, Volume 26, Issue 2, Pages 302-314, 2008. Preprint IMA preprint 2106, March 2006.

Image deblurring is one of the classical but difficult problems due to its ill-posedness. The objective is to recover out-of-focus images. A blurry image is typically assumed to be generated via Gaussian kernel convoluted with the original image. We propose a method which is free from assumptions on the type of a blur kernel. This methos can also capture a motion blur.

(a) One frame from the original. (e) The temporal mean of the deblured frames showing straight lines. (f) Using the proposed model with image fusion showing more clear details.

The flow chart of the proposed stemP algorithm.


Example of RNA prediciton using the proposed StemP algorithm shown in (c).

Path planning   Top

The POLSA example: (a) Initial path. (b) The resulting optimal path (also disentangled). The length reduced from 10.587 to 5.322, and the number of connecting points is reduced to 13.