arXiv subjects

Sung Ha Kang

Publications and source records attributed to Sung Ha Kang.

23 records · Page 2Linked to original sources

arXiv2020

Silhouette Vectorization by Affine Scale-space

Silhouettes or 2D planar shapes are extremely important in human communication, which involves many logos, graphics symbols and fonts in vector form. Many more shapes can be extracted from image by binarization or segmentation, thus in raster form that requires a vectorization. There is a need for disposing of a mathematically well defined and justified shape vectorization process, which in addition provides a minimal set of control points with geometric meaning. In this paper we propose a silhouette vectorization method which extracts the outline of a 2D shape from a raster binary image, and converts it to a combination of cubic Bézier polygons and perfect circles. Starting from the boundary curvature extrema computed at sub-pixel level, we identify a set of control points based on the affine scale-space induced by the outline. These control points capture similarity invariant geometric features of the given silhouette and give precise locations of the shape's corners.of the given silhouette. Then, piecewise Bézier cubics are computed by least-square fitting combined with an adaptive splitting to guarantee a predefined accuracy. When there are no curvature extrema identified, either the outline is recognized as a circle using the isoperimetric inequality, or a pair of the most distant outline points are chosen to initiate the fitting. Given their construction, most of our control points are geometrically stable under affine transformations. By comparing with other feature detectors, we show that our method can be used as a reliable feature point detector for silhouettes. Compared to state-of-the-art image vectorization software, our algorithm demonstrates superior reduction on the number of control points, while maintaining high accuracy.

cs.GR↗

arXiv2019

Fast Algorithms for Surface Reconstruction from Point Cloud

We consider constructing a surface from a given set of point cloud data. We explore two fast algorithms to minimize the weighted minimum surface energy in [Zhao, Osher, Merriman and Kang, Comp.Vision and Image Under., 80(3):295-319, 2000]. An approach using Semi-Implicit Method (SIM) improves the computational efficiency through relaxation on the time-step constraint. An approach based on Augmented Lagrangian Method (ALM) reduces the run-time via an Alternating Direction Method of Multipliers-type algorithm, where each sub-problem is solved efficiently. We analyze the effects of the parameters on the level-set evolution and explore the connection between these two approaches. We present numerical examples to validate our algorithms in terms of their accuracy and efficiency.

math.NA↗

arXiv2019

IDENT: Identifying Differential Equations with Numerical Time evolution

Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying coefficients add complexity to the problem. We assume that the governing partial differential equation (PDE) is a linear combination of a subset of a prescribed dictionary containing different differential terms, and the objective of this paper is to find the correct coefficients. We propose a new direction based on the fundamental idea of convergence analysis of numerical PDE schemes. We utilize Lasso for efficiency, and a performance guarantee is established based on an incoherence property. The main contribution is to validate and correct the results by Time Evolution Error (TEE). The new algorithm, called Identifying Differential Equations with Numerical Time evolution (IDENT), is explored for data with non-periodic boundary conditions, noisy data and PDEs with varying coefficients. From the recovery analysis of Lasso, we propose a new definition of Noise-to-Signal ratio, which better represents the level of noise in the case of PDE identification. We systematically analyze the effects of data generations and downsampling, and propose an order preserving denoising method called Least-Squares Moving Average (LSMA), to preprocess the given data. For the identification of PDEs with varying coefficients, we propose to add Base Element Expansion (BEE) to aide the computation. Various numerical experiments from basic tests to noisy data, downsampling effects and varying coefficients are presented.

math.NA↗

arXiv2018

Lattice Identification and Separation: Theory and Algorithm

Motivated by lattice mixture identification and grain boundary detection, we present a framework for lattice pattern representation and comparison, and propose an efficient algorithm for lattice separation. We define new scale and shape descriptors, which helps to considerably reduce the size of equivalence classes of lattice bases. These finitely many equivalence relations are fully characterized by modular group theory. We construct the lattice space $\mathscr{L}$ based on the equivalent descriptors and define a metric $d_{\mathscr{L}}$ to accurately quantify the visual similarities and differences between lattices. Furthermore, we introduce the Lattice Identification and Separation Algorithm (LISA), which identifies each lattice patterns from superposed lattices. LISA finds lattice candidates from the high responses in the image spectrum, then sequentially extracts different layers of lattice patterns one by one. Analyzing the frequency components, we reveal the intricate dependency of LISA's performances on particle radius, lattice density, and relative translations. Various numerical experiments are designed to show LISA's robustness against a large number of lattice layers, moiré patterns and missing particles.

eess.IV↗

arXiv2016

Optimal Sensor Positioning (OSP); A Probability Perspective Study

We propose a method to optimally position a sensor system, which consists of multiple sensors, each has limited range and viewing angle, and they may fail with a certain failure rate. The goal is to find the optimal locations as well as the viewing directions of all the sensors and achieve the maximal surveillance of the known environment. We setup the problem using the level set framework. Both the environment and the viewing range of the sensors are represented by level set functions. Then we solve a system of ordinary differential equations (ODEs) to find the optimal viewing directions and locations of all sensors together. Furthermore, we use the intermittent diffusion, which converts the ODEs into stochastic differential equations (SDEs), to find the global maximum of the total surveillance area. The numerical examples include various failure rates of sensors, different rate of importance of surveillance region, and 3-D setups. They show the effectiveness of the proposed method.

math.OC↗