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Combinatorial structure of rigid transformations in 2D digital images

Abstract : Rigid transformations are involved in a wide range of digital image processing applications. When applied on such discrete images, rigid transformations are however usually performed in their associated continuous space, then requiring a subsequent digitization of the result. In this article, we propose to study rigid transformations of digital images as a fully discrete process. In particular, we investigate a combinatorial structure modelling the whole space of digital rigid transformations on any subset of Z^2 of size N*N. We describe this combinatorial structure, which presents a space complexity O(N^9) and we propose an algorithm enabling to build it in linear time with respect to this space complexity. This algorithm, which handles real (i.e. non-rational) values related to the continuous transformations associated to the discrete ones, is however defined in a fully discrete form, leading to exact computation.
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https://hal.archives-ouvertes.fr/hal-00643734
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Submitted on : Monday, February 18, 2013 - 12:59:58 PM
Last modification on : Tuesday, June 23, 2020 - 10:12:47 PM
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Phuc Ngo, Yukiko Kenmochi, Nicolas Passat, Hugues Talbot. Combinatorial structure of rigid transformations in 2D digital images. Computer Vision and Image Understanding, Elsevier, 2013, 117 (4), pp.393-408. ⟨10.1016/j.cviu.2012.08.014⟩. ⟨hal-00643734v3⟩

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