Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Sweeping arrangements of curves
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Efficient pattern matching with scaling
Journal of Algorithms
Landmark-based registration using features identified through differential geometry
Handbook of medical imaging
Recent Developments in the Theory of Arrangements of Surfaces
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Combinatorial Methods for Approximate Pattern Matching under Rotations and Translations in 3D arrays
SPIRE '00 Proceedings of the Seventh International Symposium on String Processing Information Retrieval (SPIRE'00)
ACM Computing Surveys (CSUR)
Combinatorial Bounds and Algorithmic Aspects of Image Matching under Projective Transformations
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Real Two Dimensional Scaled Matching
Algorithmica
Theoretical Computer Science
Quasi-Affine Transformation in 3-D: Theory and Algorithms
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
On the complexity of affine image matching
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Affine image matching is uniform TC0-complete
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Sufficient conditions for topological invariance of 2d images under rigid transformations
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
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Rigid transformations are involved in a wide range of digital image processing applications. When applied on discrete images, rigid transformations are usually performed in their associated continuous space, requiring a subsequent digitization of the result. In this article, we propose to study rigid transformations of digital images as fully discrete processes. In particular, we investigate a combinatorial structure modelling the whole space of digital rigid transformations on arbitrary subset of Z^2 of size NxN. We describe this combinatorial structure, which presents a space complexity O(N^9) and we propose an algorithm enabling to construct it in linear time with respect to its 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.