Mutual symmetry detection
First Claim
1. A non-transitory computer-accessible memory medium that stores program instructions for detecting symmetries of configurations of discrete curves, wherein the program instructions are executable by a processor to perform:
- receiving configuration characterization information for a configuration of discrete curves, wherein the configuration comprises a plurality of discrete curves, and wherein the configuration characterization information comprises rotational symmetry groups for each of the plurality of discrete curves;
determining a greatest common divisor of the rotational symmetry groups of the discrete curves, wherein the greatest common divisor is a maximum possible object-based mutual rotational symmetry group for the configuration; and
storing the maximum possible object-based mutual rotational symmetry group, wherein the maximum possible object-based mutual rotational symmetry group is usable to perform pattern matching between configurations.
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Abstract
System and method for detecting symmetries of configurations of discrete curves. Configuration characterization information for a configuration of a plurality of discrete curves is received, where the configuration characterization information comprises rotational symmetry groups for each of the plurality of discrete curves. A greatest common divisor of the rotational symmetry groups of the discrete curves is determined, where the greatest common divisor is a maximum possible object-based mutual rotational symmetry group for the configuration. The determined value is stored, and is usable to perform pattern matching between configurations. This value may be compared to that of a target configuration to determine if the two configurations can match. Additional symmetry-based matching techniques are used to perform staged pattern matching between the two configurations, where the process may terminate as soon as one of the techniques determines that the configurations cannot match, or a matching algorithm determines that they match.
19 Citations
24 Claims
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1. A non-transitory computer-accessible memory medium that stores program instructions for detecting symmetries of configurations of discrete curves, wherein the program instructions are executable by a processor to perform:
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receiving configuration characterization information for a configuration of discrete curves, wherein the configuration comprises a plurality of discrete curves, and wherein the configuration characterization information comprises rotational symmetry groups for each of the plurality of discrete curves; determining a greatest common divisor of the rotational symmetry groups of the discrete curves, wherein the greatest common divisor is a maximum possible object-based mutual rotational symmetry group for the configuration; and storing the maximum possible object-based mutual rotational symmetry group, wherein the maximum possible object-based mutual rotational symmetry group is usable to perform pattern matching between configurations. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23)
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24. A computer-implemented method for detecting symmetries of configurations of discrete curves, comprising:
utilizing a computer to perform; receiving configuration characterization information for a configuration of discrete curves, wherein the configuration comprises a plurality of discrete curves, and wherein the configuration characterization information comprises rotational symmetry groups for each of the plurality of discrete curves; determining a greatest common divisor of the rotational symmetry groups of the discrete curves, wherein the greatest common divisor is a maximum possible object-based mutual rotational symmetry group for the configuration; and storing the maximum possible object-based mutual rotational symmetry group, wherein the maximum possible object-based mutual rotational symmetry group is usable to perform pattern matching between configurations.
Specification