Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Two-dimensional pattern matching with rotations
Theoretical Computer Science
Configurations induced by discrete rotations: periodicity and quasi-periodicity properties
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Characterization of bijective discretized rotations
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
New Complexity Bounds for Image Matching under Rotation and Scaling
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Computing admissible rotation angles from rotated digital images
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Exact, scaled image rotations in finite Radon transform space
Pattern Recognition Letters
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A discrete rotation algorithm can be apprehended as a parametric map fα from $\mathbb Z[i]$ to $\mathbb Z[i]$, whose resulting permutation “looks like” the map induced by an Euclidean rotation. For this kind of algorithm, to be incremental means to compute successively all the intermediate rotated copies of an image for angles in-between 0 and a destination angle. The discretized rotation consists in the composition of an Euclidean rotation with a discretization; the aim of this article is to describe an algorithm which computes incrementally a discretized rotation. The suggested method uses only integer arithmetic and does not compute any sine nor any cosine. More precisely, its design relies on the analysis of the discretized rotation as a step function: the precise description of the discontinuities turns to be the key ingredient that makes the resulting procedure optimally fast and exact. A complete description of the incremental rotation process is provided, also this result may be useful in the specification of a consistent set of definitions for discrete geometry.