Structure Integral Transform Versus Radon Transform: A 2D Mathematical Tool for Invariant Shape Recognition
Abstract
Abstract:
In this paper, we present a novel mathematical tool, Structure Integral Transform (SIT), for invariant shape description and recognition. Different from the Radon Transform (RT), which integrates the shape image function over a 1D line in the image plane, the proposed SIT builds upon two orthogonal integrals over a 2D K-cross dissecting structure spanning across all rotation angles by which the shape regions are bisected in each integral. The proposed SIT brings the following advantages over the RT: 1) it has the extra function of describing the interior structural relationship within the shape which provides a ...
View more >Abstract: In this paper, we present a novel mathematical tool, Structure Integral Transform (SIT), for invariant shape description and recognition. Different from the Radon Transform (RT), which integrates the shape image function over a 1D line in the image plane, the proposed SIT builds upon two orthogonal integrals over a 2D K-cross dissecting structure spanning across all rotation angles by which the shape regions are bisected in each integral. The proposed SIT brings the following advantages over the RT: 1) it has the extra function of describing the interior structural relationship within the shape which provides a more powerful discriminative ability for shape recognition; 2) the shape regions are dissected by the K-cross in a coarse to fine hierarchical order that can characterize the shape in a better spatial organization scanning from the center to the periphery; and 3) it is easier to build a completely invariant shape descriptor. The experimental results of applying SIT to shape recognition demonstrate its superior performance over the well-known Radon transform, and the well-known shape contexts and the polar harmonic transforms.
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View more >Abstract: In this paper, we present a novel mathematical tool, Structure Integral Transform (SIT), for invariant shape description and recognition. Different from the Radon Transform (RT), which integrates the shape image function over a 1D line in the image plane, the proposed SIT builds upon two orthogonal integrals over a 2D K-cross dissecting structure spanning across all rotation angles by which the shape regions are bisected in each integral. The proposed SIT brings the following advantages over the RT: 1) it has the extra function of describing the interior structural relationship within the shape which provides a more powerful discriminative ability for shape recognition; 2) the shape regions are dissected by the K-cross in a coarse to fine hierarchical order that can characterize the shape in a better spatial organization scanning from the center to the periphery; and 3) it is easier to build a completely invariant shape descriptor. The experimental results of applying SIT to shape recognition demonstrate its superior performance over the well-known Radon transform, and the well-known shape contexts and the polar harmonic transforms.
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Journal Title
IEEE Transactions on Image Processing
Volume
25
Issue
12
Subject
Artificial Intelligence and Image Processing not elsewhere classified
Artificial Intelligence and Image Processing
Electrical and Electronic Engineering
Cognitive Sciences