Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Efficient pattern matching with scaling
Journal of Algorithms
A survey of image registration techniques
ACM Computing Surveys (CSUR)
Geometric matching under noise: combinatorial bounds and algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Information Processing Letters
Digital image analysis: selected techniques and applications
Digital image analysis: selected techniques and applications
Image and Video Compression for Multimedia Engineering
Image and Video Compression for Multimedia Engineering
Optimal Exact and Fast Approximate Two Dimensional Pattern Matching Allowing Rotations
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
Alphabet Independent and Dictionary Scaled Matching
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
A Rotation Invariant Filter for Two-Dimensional String Matching
CPM '98 Proceedings of the 9th Annual Symposium on Combinatorial Pattern Matching
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Two-dimensional pattern matching with rotations
Theoretical Computer Science
Low distortion maps between point sets
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The complexity of low-distortion embeddings between point sets
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Handbook of Image and Video Processing (Communications, Networking and Multimedia)
Handbook of Image and Video Processing (Communications, Networking and Multimedia)
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
On the complexity of affine image matching
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Faster two dimensional scaled matching
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
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
New Complexity Bounds for Image Matching under Rotation and Scaling
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
New complexity bounds for image matching under rotation and scaling
Journal of Discrete Algorithms
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The problem of two-dimensional pattern matching invariant under a given class of admissible transformations $\mathcal{F}$ is to find in text Tmatches of transformed versions f(P) of the pattern P, for all fin $\mathcal{F}$. In this paper, pattern matching invariant under compositions of real scaling and rotation are investigated. We give a new discretization technique for this class of transformations and prove sharp lower and upper bounds on the number of different possibilities to transform a pattern in this way. Subsequently, we present the first efficient pattern matching algorithm invariant under compositions of scaling and rotation. The algorithm works in time O(m2n6) for patterns of size m2and texts of size n2. Our method can also be applied to the image matching problem, the well known issue in the image processing research.