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Efficient detection of second-degree variations in 2D and 3D images
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
2001 (English)In: Journal of Visual Communication and Image Representation, ISSN 1047-3203, E-ISSN 1095-9076, Vol. 12, no 3, 255-305 p.Article in journal (Refereed) Published
Abstract [en]

Estimation of local second-degree variation should be a natural first step in computerized image analysis, just as it seems to be in human vision. A prevailing obstacle is that the second derivatives entangle the three features signal strength (i.e. magnitude or energy), orientation and shape. To disentangle these features we propose a technique where the orientation of an arbitrary pattern f is identified with the rotation required to align the pattern with its prototype p. This is more strictly formulated as solving the derotating equation. The set of all possible prototypes spans the shape-space of second degree variation. This space is one-dimensional for 2Dimages, two-dimensional for 3D-images. The derotation decreases the original dimensionality of the response vector from three to two in the 2D-case and from six to three in the 3D-case, in both cases leaving room only for magnitude and shape in the prototype. The solution to the derotation and a full understanding of the result requires i) mapping the derivatives of the pattern f onto the orthonormal basis of spherical harmonics, and ii) identifying the eigenvalues of the Hessian with the derivatives of the prototype p. But once the shape-space is established the possibilities to put together independent discriminators for magnitude, orientation, and shape are easy and almost limitless.

Place, publisher, year, edition, pages
2001. Vol. 12, no 3, 255-305 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-21576DOI: 10.1006/jvci.2000.0472OAI: oai:DiVA.org:liu-21576DiVA: diva2:241538
Note
Original Publication: Per-Erik Danielsson, Qingfen Lin and Qin-Zhong Ye, Efficient detection of second-degree variations in 2D and 3D images, 2001, Journal of Visual Communication and Image Representation, (12), 3, 255-305. http://dx.doi.org/10.1006/jvci.2000.0472 Copyright: Elsevier Science B.V., Amsterdam http://www.elsevier.com/ Available from: 2009-10-04 Created: 2009-10-04 Last updated: 2017-12-13

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Danielsson, Per-ErikLin, QingfenYe, Qin-Zhong

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