Shape Analysis of Planar Multiply-Connected Objects Using Conformal Welding

Shape analysis is a central problem in the field of computer vision. In 2D shape analysis, classification and recognition of objects from their observed silhouettes are extremely crucial but difficult. It usually involves an efficient representation of 2D shape space with a metric, so that its mathe...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:IEEE transactions on pattern analysis and machine intelligence Ročník 36; číslo 7; s. 1384 - 1401
Hlavní autoři: Lui, Lok Ming, Zeng, Wei, Yau, Shing-Tung, Gu, Xianfeng
Médium: Journal Article
Jazyk:angličtina
Vydáno: Los Alamitos, CA IEEE 01.07.2014
IEEE Computer Society
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
and transforms
Applications
Applied sciences
Artificial intelligence
Computational models of vision
Computer science; control theory; systems
data structures
Educational institutions
Electronic mail
Equations
Exact sciences and technology
Image Processing and Computer Vision
Numerical algorithms
Pattern recognition. Digital image processing. Computational geometry
Reconstruction
Representations
Shape
Shape measurement
Signatures
Vision and Scene Understanding
Welding
Shape analysis
conformal modules
conformal welding
morphing
shape signature
multiply-connected shapes
Diffeomorphism
Variable geometry
Metric space
Shape measurement
Similarity
Welding
Image processing
Silhouette
Morphological analysis
Classification
Metamorphosis
Geometrical shape
Computer vision
Image morphing
Pattern recognition
Topology
Experimental study
Object recognition
Morphology
Metric
ISSN:0162-8828, 2160-9292, 1939-3539
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:Shape analysis is a central problem in the field of computer vision. In 2D shape analysis, classification and recognition of objects from their observed silhouettes are extremely crucial but difficult. It usually involves an efficient representation of 2D shape space with a metric, so that its mathematical structure can be used for further analysis. Although the study of 2D simply-connected shapes has been subject to a corpus of literatures, the analysis of multiply-connected shapes is comparatively less studied. In this work, we propose a representation for general 2D multiply-connected domains with arbitrary topologies using conformal welding. A metric can be defined on the proposed representation space, which gives a metric to measure dissimilarities between objects. The main idea is to map the exterior and interior of the domain conformally to unit disks and circle domains (unit disk with several inner disks removed), using holomorphic 1-forms. A set of diffeomorphisms of the unit circle S 1 can be obtained, which together with the conformal modules are used to define the shape signature. A shape distance between shape signatures can be defined to measure dissimilarities between shapes. We prove theoretically that the proposed shape signature uniquely determines the multiply-connected objects under suitable normalization. We also introduce a reconstruction algorithm to obtain shapes from their signatures. This completes our framework and allows us to move back and forth between shapes and signatures. With that, a morphing algorithm between shapes can be developed through the interpolation of the Beltrami coefficients associated with the signatures. Experiments have been carried out on shapes extracted from real images. Results demonstrate the efficacy of our proposed algorithm as a stable shape representation scheme.
Bibliografie:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-1
ObjectType-Feature-2
content type line 23
ISSN:0162-8828
2160-9292
1939-3539
DOI:10.1109/TPAMI.2013.215