Journal for Geometry and Graphics 16 (2012), No. 1, 081--095
Copyright Heldermann Verlag 2012
Shape and Image Interrogation with Curvature Extremalities
Shin Yoshizawa
Bio-Research Infrastructure Construction Team, RIKEN, 2-1 Hirosawa Wako, Saitama 351-0198, Japan
shin@riken.jp
Alexander Belyaev
Vision, Image & Signal Processing, ERPem, Heriot-Watt-University, Edinburgh, EH14 4AS, England
a.belyaev@hw.ac.uk
Hideo Yokota
Bio-Research Infrastructure Construction Team, RIKEN, 2-1 Hirosawa Wako, Saitama 351-0198, Japan
hyokota@riken.jp
Reliable detection of surface creases defined via loci of the principal curvatures along their corresponding curvature lines is important for many geometrical and graphical applications. Multivariate analogues of such creases have received a considerable attention in recent studies on multidimensional image visualization and analysis.
In this paper, we propose a numerically efficient and reliable approach for estimating multidimensional curvature extremalities and detecting ridge-like structures in multidimensional images. The approach is based on local fitting of hypercubic polynomials and calculating their extremalities by using newly derived formulas. We also propose a new thresholding scheme for removing spurious and unessential extremalities. We test our approach by detecting crease structures on 2D and 3D real-world images and demonstrating their ability to capture salient geometric image features.
Keywords: Curvature extremalities, multidimensional ridges and creases, multivariate image analysis.
MSC: 68U05; 53A30
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