Sungwoo Choi

The medial axis of a plane domain is defined to be the set of the centers of the maximal inscribed disks. It is essentially the cut loci of the inward unit normal bundle of the boundary. We prove that if a plane domain has finite number of boundary curves each of which consists of finite number of real analytic pieces, then the medial axis is a connected geometric graph in R 2 with finitely many vertices and edges. And each edge is a real analytic curve which can be extended in the C 1 manner at

In order to process video data efficiently, a video segmentation technique through scene change detection must be required. This is a fundamental operation used in many digital video applications such as digital libraries, video on demand (VOD), etc. Many of these advanced video applications require manipulations of compressed video signals. So, the scene change detection process is achieved by analyzing the video directly in the compressed domain, thereby avoiding the overhead of decompressing

The economic lot-scheduling problem (ELSP) is an important production scheduling problem that has been intensively studied over 40 years. Numerous heuristic algorithms have been developed since the problem is NP-hard. Dobson's heuristic has been regarded as the best in its performance. The present paper provides a hybrid genetic algorithm based on the time-varying lot sizes approach in the ELSP literature. Numerical experiments show that the hybrid genetic algorithm outperforms Dobson's heuristi

Despite its usefulness in many applications, the medial axis transform (MAT) is very sensitive to the change of the boundary in the sense that, even if a shape is perturbed only slightly, the Hausdorff distance between the MATs of the original shape and the perturbed one may be large. However, it is known that MATs of 2D domains are stable if we view this phenomenon with the one-sided Hausdorff distance. This result depends on the fact that MATs are stable if the differences between them are mea

Human dermal fibroblasts are known to express the alpha, delta, epsilon, and zeta isoforms of protein kinase C (PKC). We asked whether the growth of human dermal fibroblasts correlates with expression of a particular PKC isoform. Of total PKC activity measured in the presence of calcium, a condition permissive for activation of all PKC isoforms, 75%) was contributed by PKC-alpha, suggesting that PKC-alpha is the dominant isoform in human dermal fibroblasts. We then further studied PKC-alpha unde

We consider the static deflection of an infinite beam resting on a nonlinear and nonuniform elastic foundation. The governing equation is a fourth-order nonlinear ordinary differential equation. Using the Green's function for the well-analyzed linear version of the equation, we formulate a new integral equation which is equivalent to the original nonlinear equation. We find a function space on which the corresponding nonlinear integral operator is a contraction, and prove the existence and the u

Abstract For arbitrary two-point boundary condition, which makes the corresponding linear uniform problem well-posed, we obtain an existence and uniqueness result for the boundary value problem of finite beam deflection resting on arbitrary nonlinear non-uniform elastic foundation. The difference between the desired solution and the corresponding linear uniform one in $L^{\infty}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi><mml:mi>∞</mml:mi></mml:msup></

Although useful in many applications,\n the medial axis transform (MAT) has a few fit-falls,\n one of which is its extreme sensitivity to the boundary\n perturbation.\nIn this paper, we first summarizes the previous attempts to \n get around this by bounding the one-sided Hausdorff distance\n of the MAT with respect to the boundary perturbation.\nWe illustrate these results and their optimality with various examples.\nFinally, we suggest an application of them in pruning.\nIn particular, we disc

Medial axis transform (MAT) is a basic tool for shape analysis. However, in spite of its usefulness, it has some drawbacks, one of which is its instability under the boundary perturbation. We show that, although medial axis transform is unstable with respect to standard measures such as the Hausdorff distance, it is stable in a measure called relative Hausdorff distance for some "smoothed out" injective domains. In fact, we obtain an upper bound of the relative Hausdorff distance of the MAT of a

We analyze the eigenstructure of the integral operator $\mathcal{K}_{l, \alpha, k}$ which arise naturally from the beam deflection equation on linear elastic foundation with finite beam. We show that $\mathcal{K}_{l, \alpha, k}$ has countably infinite number of positive eigenvalues approaching 0 as the limit, and give explicit upper and lower bounds on each of them. Consequently, we obtain explicit upper and lower bounds on the $L^{2}$ -norm of the operator $\mathcal{K}_{l, \alpha, k}$ . We also