Signature verification based on topological stochastic models
The systems and methods relate to electronic signature verification based on topological stochastic models (TSM). The TSM may be trained on samples of known authentic signatures of a signee. Training the TSM may include TSM features extraction on the training samples to extract feature vectors, TSM features aggregation to aggregate the feature vectors, and optimal threshold estimation to determine an optimal threshold value. The optimal threshold value and overall aggregate of feature vectors may be used to evaluate feature vectors extracted from a signature to be verified. For example, a distance between the resulting feature vector extracted from the input sequence and the aggregated feature vector is determined. The distance is compared to the optimal threshold value to determine whether the signature in the input image is verified. The signature in the input image is verified if the distance is less than or equal to the optimal threshold value.
1 . A system of authenticating a signature, comprising:
a memory configured to store a topological stochastic model (TSM) trained to authenticate signatures, the TSM comprising an aggregate vector of eigenvalues that is aggregated from vectors of eigenvalues corresponding to respective authentic signatures of a signee;
a processor programmed to:
access an input image of a signee to be authenticated;
identify the TSM trained to authenticate signatures from the signee;
obtain a binary image of the input image;
split the binary image into a plurality of partitions;
assign a symbol to each partition of the plurality of partitions;
identify pixel coordinates in the binary image that include at least a portion of the input image;
determine a sequence of symbols representing a topological traversal path of the signature based on the identified pixel coordinates in the binary image, the sequence of symbols corresponding to the partitions that correspond to the identified pixel coordinates;
determine an input stochastic transition matrix based on the sequence;
generate an input vector of eigenvalues based on the input stochastic transition matrix;
determine a distance between the input vector of eigenvalues and the aggregate vector of eigenvalues of the TSM; and
determine whether the input image is authentic based on the distance.
2 . The system of claim 1 , wherein the plurality of partitions are each shaped as a rectangle.
3 . The system of claim 1 , wherein to determine whether the input image is authentic, the processor is further programmed to: compare the distance to an optimal threshold value; and determine that the input image is authentic when the distance is greater than the optimal threshold value.
4 . The system of claim 1 , wherein to obtain the binary image, the processor is programmed to: convert a red-green-blue (RGB) image of the input image to a grayscale image; and convert the grayscale image to the binary image.
5 . A non-transitory computer-readable medium storing instructions that, when executed by a processor, programs the processor to:
access an input image of a signee to be authenticated; identify a topological stochastic model (TSM) trained to authenticate signatures from the signee, the TSM comprising an aggregate vector of eigenvalues that is aggregated from vectors of eigenvalues corresponding to respective authentic signatures of a signee;
obtain a binary image of the input image;
split the binary image into a plurality of partitions;
assign a symbol to each partition of the plurality of partitions;
identify pixel coordinates in the binary image that include at least a portion of the input image;
determine a sequence of symbols representing a topological traversal path of the signature based on the identified pixel coordinates in the binary image, the sequence of symbols corresponding to the partitions that correspond to the identified pixel coordinates;
determine an input stochastic transition matrix based on the sequence;
generate an input vector of eigenvalues based on the input stochastic transition matrix;
determine a distance between the input vector of eigenvalues and the aggregate vector of eigenvalues of the TSM; and
determine whether the input image is authentic based on the distance.
6 . The non-transitory computer-readable medium of claim 5 , wherein the plurality of partitions are each shaped as a rectangle.
7 . The non-transitory computer-readable medium of claim 5 , wherein to determine whether the input image is authentic, the instructions when executed by the processor, further program the processor to:
compare the distance to an optimal threshold value; and determine that the input image is authentic when the distance is greater than the optimal threshold value.
8 . The non-transitory computer-readable medium of claim 5 , wherein to obtain the binary image, the instructions when executed by the processor, further program the processor to:
convert a red-green-blue (RGB) image of the input image to a grayscale image; and
convert the grayscale image to the binary image.
9 . A method of training a topological stochastic model (TSM) for signature verification, comprising:
accessing, by a computing device, a first sample of an authentic signature of a person and a second sample of the authentic signature of the person;
generating, by the computing device, a first vector of eigenvalues for the first authentic signature based on TSM feature extraction on the first authentic signature;
generating, by the computing device, a second vector of eigenvalues for the second authentic signature based on TSM feature extraction on the second authentic signature;
aggregating, by the computing device, the first vector of eigenvalues and the second vector of eigenvalues; and
generating, by the computing device, an aggregate vector of eigenvalues based on the aggregating, wherein the aggregate vector of eigenvalues is used as an authentication model against which an input image is authenticated.
10 . The method of claim 9 , wherein aggregating the first vector of eigenvalues and the second vector of eigenvalues comprises determining a mean of the first vector of eigenvalues and the second vector of eigenvalues.
11 . The method of claim 9 , the method further comprising:
performing an optimal threshold estimation to determine a threshold value based on the aggregate vector of eigenvalues, the first vector of eigenvalues and the second vector of eigenvalues.
12 . The method of claim 11 , the method further comprising:
determining an optimal threshold value against which a distance between the aggregate vector of eigenvalues and an input vector of eigenvalues for the input image is evaluated to determine whether the input image is authentic.
13 . The method of claim 12 , wherein determining the optimal threshold value comprises:
determining a maximum value from among: a first distance between the aggregate vector of eigenvalues and the first vector of eigenvalues and a second distance between the aggregate vector of eigenvalues and the second vector of eigenvalues.
14 . The method of claim 9 , wherein generating the first vector of eigenvalues for the first authentic signature based on TSM feature extraction on the first authentic signature comprises:
obtaining a binary image of the first authentic signature for processing.
15 . The method of claim 14 , wherein an image of the first authentic signature comprises a red-green-blue (RGB) image, and wherein obtaining the binary image comprises: converting the RGB image to a grayscale image; and converting the grayscale image to the binary image.
16 . The method of claim 14 , wherein an image of the first authentic signature comprises a grayscale image, and wherein obtaining the binary image comprises: converting the grayscale image to the binary image.
17 . The method of claim 14 , wherein the TSM feature extraction further comprises: converting xy coordinates of the binary image to a plurality of symbols that each represent a portion of the first authentic signature.
18 . The method of claim 17 , wherein a number of the plurality of symbols that is generated is defined by an integer K to generate K equal rectangles based on the xy coordinates of the binary image.
19 . The method of claim 17 , wherein the TSM feature extraction further comprises: generating a stochastic transition matrix based on the plurality of symbols, wherein the first vector of eigenvalues is generated based on the stochastic transition matrix.
20 . The method of claim 19 , wherein generating the stochastic transition matrix comprises:
determining a sequence of the plurality of symbols with respect to the xy coordinates; and
determining a number of transitions from one symbol to another symbol based on the sequence.