Methods using recurrence quantification analysis to analyze and generate images
View Patent ↗Methods for identifying and quantifying recurrent and deterministic patterns in digital images are provided. The methods, which are based on Recurrence Quantification Analysis (RQA), generate similarity or dissimilarity distance matrices for digital images that may be used to calculate a variety of quantitative characteristics for the images. Also provided are methods for identifying and imaging spatial distributions of time variable signals generated from dynamic systems. In these methods a time variable signal is recorded for a plurality of area or volume elements into which a dynamic system has been sectioned and RQA is used to calculate one or more RQA variables for each of the area or volume elements, which may then be used to generate a two or three dimensional image displaying the spatial distribution of the RQA variables across the system.
1. A method for quantifying recurrent patterns in digital images comprising a plurality of pixels, the method comprising:
(a) dividing a digital image into a plurality of overlapping value matrices;
(b) selecting a matrix from the plurality of overlapping value matrices;
(c) calculating a distance between the selected matrix and each of the remaining overlapping value matrices of the plurality of overlapping value matrices;
(d) arranging the calculated distance as a row or a column in a distance matrix; and
(e) repeating (b)-(d) for each value matrix of the plurality of overlapping value matrices selected as the matrix to provide a distance matrix;
(f) calculating a local recurrence value for each row or column in the provided distance matrix, wherein the local recurrence value is the fraction of value matrices in that row or column whose distance from the matrix selected for that row or column is less than a selected cut-off distance;
(g) calculating a value of a recurrence quantification analysis variable based on the calculated local recurrence values; and
(h) outputting the calculated value as an indication of a characteristic of the digital image.
2. The method of claim 1 , wherein dividing the digital image into the plurality of overlapping value matrices comprises:
(i) assigning pixels in the digital image values based on their color;
(j) defining a first value matrix by a window framing a plurality of pixels in the digital image;
(k) defining an additional value matrix by sliding the window over the image by a number of pixels; and
(l) repeating (k) until the digital image has been divided into a plurality of overlapping value matrices.
3. The method of claim 1 , further comprising, after (f), calculating a global recurrence value for the distance matrix based on the calculated local recurrence values.
4. The method of claim 3 , wherein calculating the recurrence quantification analysis variable is further based on the calculated global recurrence value.
5. The method of claim 3 , wherein the global recurrence value is the average of the calculated local recurrence values.
6. The method of claim 1 , wherein the calculated distance is a measure of dissimilarity between the selected matrix and each of the remaining overlapping value matrices of the plurality of overlapping value matrices.
7. The method of claim 1 , wherein the calculated distance is selected from the group consisting of a Euclidean distance, a squared Euclidean distance, a Manhattan distance, a Mahalanobis distance, a Minkowski distance, a cosine distance, a Jaccard distance, and a Chebychev distance.
8. The method of claim 1 , further comprising calculating the fraction of recurrences that lie below a selected topological cut-off distance.
9. The method of claim 1 , wherein outputting the calculated value comprises plotting the calculated local recurrence values as a function of their corresponding topological distance in the digital image.
10. The method of claim 9 , further comprising dividing the plot into equally-sized sections along a topological distance axis between an origin and a selected topological cut-off distance and calculating a short range determinism vector comprising an element for each section, wherein each element is the sum of the recurrences in its corresponding section.
11. The method of claim 9 , further comprising dividing the plot into equally-sized sections along the entire length of a topological distance axis and calculating a long range determinism vector comprising an element for each section, wherein each element is the sum of the recurrences in its corresponding section.
12. The method of claim 1 , wherein the digital image is a color image and the value for each pixel is the average of the red, green, and blue channels for that pixel.
13. The method of claim 1 , wherein the digital image is a digital photograph.
14. The method of claim 1 , wherein the digital image is generated from a microarray assay or an electrophoresis assay.
15. The method of claim 1 , wherein the digital image, is a magnetic resonance image, a radiograph image, an ultrasound image, or a cineangiography image.
16. The method of claim 1 wherein the recurrence quantification analysis variable is selected from the group consisting of a percent recurrence, a percent determinism, an entropy, a laminarity, a trapping time, a maximum length of vertical structures in a recurrence plot, a mean length of vertical structures in a recurrence plot, and a recurrence time.
17. A computer-readable medium including computer-readable instructions tangibly stored therein that, upon execution by a processor of an electronic device, cause the electronic device to:
(a) divide a digital image into a plurality of overlapping value matrices;
(b) select a matrix from the plurality of overlapping value matrices;
(c) calculate a distance between the selected matrix and each of the remaining overlapping value matrices of the plurality of overlapping value matrices;
(d) arrange the calculated distance as a row or a column in a distance matrix; and
(e) repeat (b)-(d) for each value matrix of the plurality of overlapping value matrices selected as the matrix to provide a distance matrix;
(f) calculate a local recurrence value for each row or column in the provided distance matrix, wherein the local recurrence value is the fraction of value matrices in that row or column whose distance from the matrix selected for that row or column is less than a selected cut-off distance;
(g) calculate a value of a recurrence quantification analysis variable based on the calculated local recurrence values; and
(h) output the calculated value as an indication of a characteristic of the digital image.
18. An electronic device comprising:
a processor; and
a computer-readable medium including computer-readable instructions stored therein that, upon execution by the processor, perform operations comprising
(a) dividing a digital image into a plurality of overlapping value matrices;
(b) selecting a matrix from the plurality of overlapping value matrices;
(c) calculating a distance between the selected matrix and each of the remaining overlapping value matrices of the plurality of overlapping value matrices;
(d) arranging the calculated distance as a row or a column in a distance matrix: and
(e) repeating (b)-(d) for each value matrix of the plurality of overlapping value matrices selected as the matrix to provide a distance matrix;
(f) calculating a local recurrence value for each row or colomn in the provided distance matrix, wherein the local recurrence value is the fraction of value matrices in that row or column whose distance from the matrix selected for that row or column is less than a selected cut-off distance;
(g) calculating a value of a recurrence quantification analysis variable based on the calculated local recurrence values; and
(h) outputting the calculated value as an indication of a characteristic of the digital image.