Stable Computation of the CS Decomposition: Simultaneous Bidiagonalization

2012 ◽  
Vol 33 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Brian D. Sutton
Keyword(s):  
Cs Decomposition ◽  
Stable Computation

Stable Computation of Hahn Moments for Large Size 1D Signal Analysis

2020 ◽  
pp. 95-102
Author(s):  
Achraf Daoui ◽  
Omar El Ogri ◽  
Mohamed Yamni ◽  
Hicham Karmouni ◽  
Mhamed Sayyouri ◽  
...  
Keyword(s):  
Signal Analysis ◽  
Large Size ◽  
Stable Computation

Partial 3D Image Reconstruction by Cuboids Using Stable Computation of Hahn Polynomials

2021 ◽  
pp. 831-842
Author(s):  
Mohamed Amine Tahiri ◽  
Hicham Karmouni ◽  
Ahmed Tahiri ◽  
Mhamed Sayyouri ◽  
Hassan Qjidaa
Keyword(s):  
Image Reconstruction ◽  
3D Image ◽  
3D Image Reconstruction ◽  
Hahn Polynomials ◽  
Stable Computation

Computing the CS-Decomposition on Systolic Arrays

1986 ◽  
Vol 7 (4) ◽  
pp. 1121-1125 ◽  
Author(s):  
Franklin T. Luk ◽  
Sanzheng Qiao
Keyword(s):  
Systolic Arrays ◽  
Cs Decomposition

Stable Computation of the 2D Medial Axis Transform

1998 ◽  
Vol 08 (05n06) ◽  
pp. 577-598 ◽  
Author(s):  
Guy Evans ◽  
Alan Middleditch ◽  
Nick Miles
Keyword(s):  
Medial Axis ◽  
Medial Axis Transform ◽  
Element Mesh ◽  
Alternative Representation ◽  
Circular Arcs ◽  
Straight Line ◽  
Key Points ◽  
Stable Computation ◽  
Mathematical Definitions ◽  
Biological Shape

The medial axis transform of a 2D region was introduced by Blum in the 1960's as an aid to the description of biological shape. It is an alternative representation of a region which is often more amenable to analysis. This property has led to its use in diverse fields including pattern recognition and automatic finite element mesh generation. There are two widely agreed mathematical definitions for the medial axis transform which are closely related. It is shown that these definitions are not in general equivalent, despite being so far many types of region. In this paper, precise mathematical definitions of the medial axis transform and its key points (atoms) are given, and an O(n2) algorithm for its computation via those atoms presented. This algorithm is described in terms of simple polygons whose sole boundary consists of circular arcs and straight line segments, then extended to polygons with holes. It is shown how more complex edges could be accommodated. In comparison with existing algorithms it is simple to implement and stable in the presence of geometric degeneracy.

An efficient routine for computing symmetric real spherical harmonics for high orders of expansion

2005 ◽  
Vol 38 (3) ◽  
pp. 501-504 ◽  
Author(s):  
Andrzej Kudlicki ◽  
Małgorzata Rowicka ◽  
Mirosław Gilski ◽  
Zbyszek Otwinowski
Keyword(s):  
Electron Microscopy ◽  
Spherical Harmonics ◽  
Efficient Method ◽  
Protein Crystallography ◽  
High Order ◽  
Linear Combinations ◽  
Crystallographic Symmetry ◽  
Stable Computation ◽  
Very High

A numerically efficient method of constructing symmetric real spherical harmonics is presented. Symmetric spherical harmonics are real spherical harmonics with built-in invariance with respect to rotations or inversions. Such symmetry-invariant spherical harmonics are linear combinations of non-symmetric ones. They are obtained as eigenvectors of an appropriate operator, depending on symmetry. This approach allows for fast and stable computation up to very high order symmetric harmonic bases, which can be used in e.g. averaging of non-crystallographic symmetry in protein crystallography or refinement of large viruses in electron microscopy.

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