Youngjoon Cha

The Error-Amended Sharp Edge (EASE) Scheme for Image Zooming

This paper proposes a new interpolation method, called the error-amended sharp edge (EASE) scheme, which is a modified bilinear method. In order to remove/reduce interpolation artifacts such as image blur and the checkerboard effect (ringing), EASE tries to amend the interpolation error by employing the classical interpolation error theorem in an edge-adaptive fashion. EASE is applied for image zooming by both integer and noninteger magnification factors. The new interpolation scheme has proved to result in high-resolution images having clearer and sharper edges than linear interpolation methods, for all synthetic and natural images we have tested. EASE can be implemented with ease; it turns out to be similarly efficient as cubic interpolation schemes

Edge-forming methods for color image zooming

This paper introduces edge-forming schemes for image zooming of color images by general magnification factors. In order to remove/reduce artifacts arising in image interpolation, such as image blur and the checkerboard effect, an edge-forming method is suggested to be applied as a postprocess of standard interpolation methods. The method is based on nonconvex nonlinear partial differential equations. The equations are carefully discretized, incorporating numerical schemes of anisotropic diffusion, to be able to form reliable edges satisfactorily. The alternating direction implicit (ADI) method is employed for an efficient simulation of the model. It has been numerically verified that the resulting algorithm can form clear edges in 2 to 3 ADI iterations. Various results are given to show th effectiveness and reliability of the algorithm.

Curvature Interpolation Method for Image Zooming

We introduce a novel image zooming algorithm, called the curvature interpolation method (CIM), which is partial-differential-equation (PDE)-based and easy to implement. In order to minimize artifacts arising in image interpolation such as image blur and the checkerboard effect, the CIM first evaluates the curvature of the low-resolution image. After interpolating the curvature to the high-resolution image domain, the CIM constructs the high-resolution image by solving a linearized curvature equation, incorporating the interpolated curvature as an explicit driving force. It has been numerically verified that the new zooming method can produce clear images of sharp edges which are already denoised and superior to those obtained from linear methods and PDE-based methods of no curvature information. Various results are given to prove effectiveness and reliability of the new method.

Edge-Forming Methods for Image Zooming

The article is concerned with edge-forming methods to be applied as a post-process for image zooming. Image zooming via standard interpolation methods often produces the so-called checkerboard effect, in particular, when the magnification factor is large. In order to remove the artifact and to form reliable edges, a nonlinear semi-discrete model and its numerical algorithm are suggested along with anisotropic edge-forming numerical schemes. The algorithm is analyzed for stability and choices of parameters. For image zooming by integer factors, a few iterations of the algorithm can form clear and sharp edges for gray-scale images. Various examples are presented to show effectiveness and efficiency of the newly-suggested edge-forming strategy.

Existence and uniqueness of endemic states for the age-structured S–I–R epidemic model

The existence and uniqueness of positive steady states for the age structured S-I-R epidemic model with intercohort transmission is considered. Threshold results for the existence of endemic states are established for most cases. Uniqueness is shown in each case. Threshold used are explicitly computable in terms of demographic and epidemiological parameters of the model.

Image Zooming by Curvature Interpolation and Iterative Refinement

This article is concerned with an effective PDE-based image zooming method which is an improvement of the so-called curvature interpolation method (CIM) previously developed in [H. Kim, Y. Cha, and S. Kim, IEEE Trans. Image Process., 20 (2011), pp. 1895--1903]. The new algorithm incorporates an iterative application of the CIM in order to be an interpolator and to construct a reliable image surface utilizing a generalized curvature source term estimated from the low resolution image. It also employs an effective 9-point scheme for the curvature evaluation which in turn makes the constructed image surface involve no observable ringing artifacts. It has been experimentally verified that the new method results in a high resolution image of clear and sharp edges and cloudless textures, showing qualities of superresolution. Its convergence is analyzed; various results are given to show effectiveness and reliability of the new method. The proposed method has proved not only superior to state-of-the-art methods ...

PDE-Based Interpolation Methods for Image Super Resolution

This article presents an efficient PDE-based interpolation algorithm for image super resolution (SR). Conventional PDE-based interpolation methods can produce sharp edges; however, they are approximators and tend to weaken fine structures. In order to overcome the drawback, a texture enhancement method is incorporated as a post-process of PDE-based interpolation methods. The post-process turns out to make the resulting algorithm an interpolator. It has been numerically verified that the resulting algorithm restores sharp edges and enhances fine structures satisfactorily, outperforming traditional methods. The suggested algorithm has also proved efficient enough to be applicable for real-time processing for resolution enhancement of images and video clips that are downloaded through internet connections or wireless communications. Numerical examples are shown to verify the claim.

Error-Amended Sharp Edge (EASE) Schemes for Image Interpolation

This article proposes a new interpolation method, called the error-amended sharp edge (EASE) scheme. EASE is a modified bilinear method which tries to amend the interpolation error in an edge-adaptive way by employing the interpolation error theorem. The resulting scheme has proved to result in zoomed images having sharper edges than bilinear, C1-bicubic, and C2-bicubic interpolation methods. EASE is similarly efficient as cubic interpolation methods and can be implemented with ease.

Parallel domain decomposition methods for high-order finite element solutions of the helmholtz problem

The article is concerned with a parallel iterative domain decomposition algorithm for high-order finite element solutions of the Helmholtz wave equation. The iteration is performed in a block-Jacobi manner. For the interface operator, a Robin interface boundary condition is employed in a modified form which allows possible discontinuities of the discrete normal flux on the subdomain interfaces. The convergence of the algorithm is analyzed using energy estimates. Numerical results are given to show the effectiveness and parallel efficiency of the algorithm for the simulation of high-frequency waves in heterogeneous media in the two-dimensional space. The algorithm is carried out on a 16-node Linux cluster; it has been observed more than 97% parallel efficiency for all tested problems.