3-D Symmetry Detection and Analysis Using the Pseudo-polar Fourier Transform

Symmetry detection and analysis in 3 D images is a fundamental task in a gamut of scientific fields such as computer vision, medical imaging and pattern recognition to name a few. In this work, we present a computational approach to 3 D symmetry detection and analysis. Our analysis is conducted in t...

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Vydané v:International journal of computer vision Ročník 90; číslo 2; s. 166 - 182
Hlavní autori: Bermanis, Amit, Averbuch, Amir, Keller, Yosi
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Boston Springer US 01.11.2010
Springer
Springer Nature B.V
Predmet:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Artificial Intelligence
Biological and medical sciences
Computer Imaging
Computer Science
Computer science; control theory; systems
Computer vision
Exact sciences and technology
Fourier transforms
Image Processing and Computer Vision
Investigative techniques, diagnostic techniques (general aspects)
Machine vision
Medical imaging equipment
Medical sciences
Pattern Recognition
Pattern Recognition and Graphics
Pattern recognition. Digital image processing. Computational geometry
Representations
Rotational
Studies
Symmetry
Symmetry detection
Theoretical computing
Three dimensional
Vision
Pseudo-polar
3D symmetry
Symmetry groups
Computer vision
Fourier transformation
Image processing
Polar coordinate
Group theory
Inversion
Pattern recognition
Image analysis
Symmetry group
Algorithm complexity
Medical imagery
Tridimensional image
Symmetry
ISSN:0920-5691, 1573-1405
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Popis
Shrnutí:Symmetry detection and analysis in 3 D images is a fundamental task in a gamut of scientific fields such as computer vision, medical imaging and pattern recognition to name a few. In this work, we present a computational approach to 3 D symmetry detection and analysis. Our analysis is conducted in the Fourier domain using the pseudo-polar Fourier transform. The pseudo-polar representation enables to efficiently and accurately analyze angular volumetric properties such as rotational symmetries. Our algorithm is based on the analysis of the angular correspondence rate of the given volume and its rotated and rotated-inverted replicas in their pseudo-polar representations. We also derive a novel rigorous analysis of the inherent constraints of 3 D symmetries via groups-theory based analysis. Thus, our algorithm starts by detecting the rotational symmetry group of a given volume, and the rigorous analysis results pave the way to detect the rest of the symmetries. The complexity of the algorithm is O ( N 3 log ( N )), where N × N × N is the volumetric size in each direction. This complexity is independent of the number of the detected symmetries. We experimentally verified our approach by applying it to synthetic as well as real 3 D objects.
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ISSN:0920-5691
1573-1405
DOI:10.1007/s11263-010-0356-4