Increasing accuracy of discrete curve transform estimates for curve matching in four or more dimensions
First Claim
1. A computer-accessible memory medium that stores program instructions for estimating a rotational shift between a first discrete curve and a second discrete curve, wherein the program instructions are executable to perform:
- receiving a first discrete curve and a second discrete curve, wherein the second discrete curve is a rotationally shifted version of the first discrete curve, wherein the first discrete curve and the second discrete curve each comprises a respective curve in at least four dimensions;
estimating a rotational shift between the first discrete curve and the second discrete curve based on the first discrete curve and the second discrete curve, wherein said estimating the rotational shift between the first discrete curve and the second discrete curve based on the first discrete curve and the second discrete curve comprises calculating;
wherein y and z refer respectively to points in the first discrete curve and the second discrete curve, indexed by n and d, wherein n denotes a particular point of N points, and d denotes dimension up to a maximum of D;
updating a cumulative rotational shift based on the estimated rotational shift;
generating a rotationally shifted version of the second discrete curve based on the cumulative rotational shift;
performing said estimating, said updating, and said generating in an iterative manner using the respective rotationally shifted discrete curve for each iteration until a stopping condition occurs, thereby determining a final estimate of the rotational shift between the first discrete curve and the second discrete curve; and
storing the final estimate of the rotational shift, wherein the final estimate of the rotational shift is useable to perform discrete curve matching.
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Abstract
System and method for estimating a rotational shift between a first discrete curve and a second discrete curve, where the second discrete curve is a rotationally shifted version of the first discrete curve. First and second discrete curves are received. A rotational shift between the first discrete curve and the second discrete curve is estimated based on the first discrete curve and the second discrete curve. A cumulative rotational shift is updated based on the estimated rotational shift. A rotationally shifted version of the second discrete curve is generated based on the cumulative rotational shift. The estimating, updating, and generating are performed in an iterative manner using the respective rotationally shifted discrete curve for each iteration until a stopping condition occurs, thereby determining a final estimate of the rotational shift between the first discrete curve and the second discrete curve. The final estimate may be used to perform curve matching.
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Citations
23 Claims
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1. A computer-accessible memory medium that stores program instructions for estimating a rotational shift between a first discrete curve and a second discrete curve, wherein the program instructions are executable to perform:
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receiving a first discrete curve and a second discrete curve, wherein the second discrete curve is a rotationally shifted version of the first discrete curve, wherein the first discrete curve and the second discrete curve each comprises a respective curve in at least four dimensions; estimating a rotational shift between the first discrete curve and the second discrete curve based on the first discrete curve and the second discrete curve, wherein said estimating the rotational shift between the first discrete curve and the second discrete curve based on the first discrete curve and the second discrete curve comprises calculating; wherein y and z refer respectively to points in the first discrete curve and the second discrete curve, indexed by n and d, wherein n denotes a particular point of N points, and d denotes dimension up to a maximum of D; updating a cumulative rotational shift based on the estimated rotational shift; generating a rotationally shifted version of the second discrete curve based on the cumulative rotational shift; performing said estimating, said updating, and said generating in an iterative manner using the respective rotationally shifted discrete curve for each iteration until a stopping condition occurs, thereby determining a final estimate of the rotational shift between the first discrete curve and the second discrete curve; and storing the final estimate of the rotational shift, wherein the final estimate of the rotational shift is useable to perform discrete curve matching. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19)
wherein the value of the estimated rotational shift is normalized with respect to the index.
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13. The memory medium of claim 12,
wherein an estimated a rotational shift value of 1 corresponds to a cyclic shift of one point in the second discrete curve. -
14. The memory medium of claim 1, wherein the second discrete curve is rotationally shifted from the first discrete curve by less than a rotational distance between successive points in the second discrete curve.
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15. The memory medium of claim 1, wherein the second discrete curve is rotationally shifted from the first discrete curve by less than or equal to 5 degrees.
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16. The memory medium of claim 1, wherein the second discrete curve is rotationally shifted from the first discrete curve by less than or equal to 1 degree.
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17. The memory medium of claim 1, wherein said rotational shifting the second discrete curve based on the estimated rotational shift to generate a respective rotationally shifted discrete curve further comprises:
interpolating the second discrete curve.
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18. The memory medium of claim 1, wherein the program instructions are further executable to perform:
outputting the final estimate of the rotational shift between the first discrete curve and the second discrete curve.
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19. The memory medium of claim 1, wherein the program instructions are further executable to perform:
performing curve matching on the first discrete curve and the second discrete curve using the final estimate of the rotational shift, thereby generating results indicating a degree of match between the first discrete curve and the second discrete curve.
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20. A method for estimating a rotational shift between a first discrete curve and a second discrete curve, the method comprising:
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receiving a first discrete curve and a second discrete curve, wherein the second discrete curve is a rotationally shifted version of the first discrete curve; estimating a rotational shift between the first discrete curve and the second discrete curve based on the first discrete curve and the second discrete curve, wherein said estimating the rotational shift between the first discrete curve and the second discrete curve based on the first discrete curve and the second discrete curve comprises calculating; wherein y and z refer respectively to points in the first discrete curve and the second discrete curve, indexed by n and d, wherein n denotes a particular point of N points, and d denotes dimension up to a maximum of D; updating a cumulative rotational shift based on the estimated rotational shift; generating a rotationally shifted version of the second discrete curve based on the cumulative rotational shift; and performing said estimating, said updating, and said generating in an iterative manner using the respective rotationally shifted discrete curve for each iteration until a stopping condition occurs, thereby determining a final estimate of the rotational shift between the first discrete curve and the second discrete curve; and storing the final estimate of the rotational shift, wherein the final estimate of the rotational shift is useable to perform discrete curve matching.
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21. A system for estimating a rotational shift between a first discrete curve and a second discrete curve, the system comprising:
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a processor; a memory medium coupled to the processor; an input coupled to the processor and the memory medium; and an output coupled to the processor and the memory medium; wherein the input is operable to receive a first discrete curve and a second discrete curve, wherein the second discrete curve is a rotationally shifted version of the first discrete curve, and wherein the first discrete curve and the second discrete curve each comprises a respective sequence of points in at least three dimensions; wherein the memory medium stores program instructions which are executable by the processor to; estimate a rotational shift between the first discrete curve and the second discrete curve based on the first discrete curve and the second discrete curve, wherein said estimating the rotational shift between the first discrete curve and the second discrete curve based on the first discrete curve and the second discrete curve comprises calculating; wherein y and z refer respectively to points in the first discrete curve and the second discrete curve, indexed by n and d, wherein n denotes a particular point of N points, and d denotes dimension up to a maximum of D; update a cumulative rotational shift based on the estimated rotational shift; generate a rotationally shifted version of the second discrete curve based on the cumulative rotational shift; and perform said estimating, said updating, and said generating in an iterative manner using the respective rotationally shifted discrete curve for each iteration until a stopping condition occurs, thereby determining a final estimate of the rotational shift between the first discrete curve and the second discrete curve; wherein the output is operable to output the final estimate of the rotational shift between the first discrete curve and the second discrete curve, and wherein the final estimate of the rotational shift is useable to perform discrete curve matching.
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22. A system for estimating a rotational shift between a first discrete curve and a second discrete curve, the system comprising:
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means for receiving a first discrete curve and a second discrete curve, wherein the second discrete curve is a rotationally shifted version of the first discrete curve, wherein the first discrete curve and the second discrete curve each comprises a respective curve in at least three dimensions; means for estimating a rotational shift between the first discrete curve and the second discrete curve based on the first discrete curve and the second discrete curve, wherein said estimating the rotational shift between the first discrete curve and the second discrete curve based on the first discrete curve and the second discrete curve comprises calculating; wherein y and z refer respectively to points in the first discrete curve and the second discrete curve, indexed by n and d, wherein n denotes a particular point of N points, and d denotes dimension up to a maximum of D; means for updating a cumulative rotational shift based on the estimated rotational shift; means for generating a rotationally shifted version of the second discrete curve based on the cumulative rotational shift; means for performing said estimating, said updating, and said generating in an iterative manner using the respective rotationally shifted discrete curve for each iteration until a stopping condition occurs, thereby determining a final estimate of the rotational shift between the first discrete curve and the second discrete curve; and means for storing the final estimate of the rotational shift, wherein the final estimate of the rotational shift is useable to perform discrete curve matching.
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23. A programmable hardware element configured for estimating a rotational shift between a first discrete curve and a second discrete curve, wherein the programmable hardware element is configured to perform:
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receiving a first discrete curve and a second discrete curve, wherein the second discrete curve is a rotationally shifted version of the first discrete curve, wherein the first discrete curve and the second discrete curve each comprises a respective curve in at least three dimensions; estimating a rotational shift between the first discrete curve and the second discrete curve based on the first discrete curve and the second discrete curve, wherein said estimating the rotational shift between the first discrete curve and the second discrete curve based on the first discrete curve and the second discrete curve comprises calculating; wherein y and z refer respectively to points in the first discrete curve and the second discrete curve, indexed by n and d, wherein n denotes a particular point of N points, and d denotes dimension up to a maximum of D; updating a cumulative rotational shift based on the estimated rotational shift; generating a rotationally shifted version of the second discrete curve based on the cumulative rotational shift; performing said estimating, said updating, and said generating in an iterative manner using the respective rotationally shifted discrete curve for each iteration until a stopping condition occurs, thereby determining a final estimate of the rotational shift between the first discrete curve and the second discrete curve; and storing the final estimate of the rotational shift, wherein the final estimate of the rotational shift is useable to perform discrete curve matching.
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Specification