Minimum Sobolev Norm Schemes and Applications in Image Processing
نویسندگان
چکیده
This paper describes an extension of the Minimum Sobolev Norm interpolation scheme to an approximation scheme. A fast implementation of the MSN interpolation method using the methods for Hierarchical Semiseparable (HSS) matrices is described and experimental results are provided. The approximation scheme is introduced along with a numerically stable solver. Several numerical results are provided comparing the interpolation scheme, the approximation scheme and Thin Plate Splines. A method to decompose images into smooth and rough components is presented. A metric that could be used to distinguish edges and textures in the rough component is also introduced. Suitable examples are provided for both the above.
منابع مشابه
A New Iterative Algorithm for Multivalued Nonexpansive Mappping and Equlibruim Problems with Applications
In this paper, we introduce two iterative schemes by a modified Krasnoselskii-Mann algorithm for finding a common element of the set of solutions of equilibrium problems and the set of fixed points of multivalued nonexpansive mappings in Hilbert space. We prove that the sequence generated by the proposed method converges strongly to a common element of the set of solutions of equilibruim proble...
متن کاملOn the Pixel Expansion of Hypergraph Access Structures in Visual Cryptography Schemes
In a visual cryptography scheme, a secret image is encoded into n shares, in the form of transparencies. The shares are then distributed to n participants. Qualified subsets of participants can recover the secret image by superimposing their transparencies, but non-qualified subsets of participants have no information about the secret image. Pixel expansion, which represents the number of subpi...
متن کاملA survey on digital data hiding schemes: principals, algorithms, and applications
This paper investigates digital data hiding schemes. The concept of information hiding will be explained at first, and its traits, requirements, and applications will be described subsequently. In order to design a digital data hiding system, one should first become familiar with the concepts and criteria of information hiding. Having knowledge about the host signal, which may be audio, image, ...
متن کاملSome new characterizations of Sobolev spaces
Abstract: This talk is on some new characterizations of Sobolev spaces which are based on non-local functionals whose roots are from definition of the fractional Sobolev spaces. New types of the Poincare inequality, the Sobolev inequality, and the Reillich Kondrachov compactness theorem will also be discussed. Possible applications for image processing will be mentioned. This is partially joint...
متن کاملDFG–Schwerpunktprogramm 1114 Mathematical methods for time series analysis and digital image processing Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings III: Frames
We study the optimal approximation of the solution of an operator equation A(u) = f by certain n-term approximations with respect to specific classes of frames. We consider worst case errors, where f is an element of the unit ball of a Sobolev or Besov space Bt q(Lp(Ω)) and Ω ⊂ Rd is a bounded Lipschitz domain; the error is always measured in the Hs-norm. We study the order of convergence of th...
متن کامل