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Fig. 1 | Journal of the European Optical Society-Rapid Publications

Fig. 1

From: Deriving image features for autonomous classification from time-series recurrence plots

Fig. 1

Schematic workflow. a) Extraction of the outer contour line of the object (red line). The cyan dot indicates the mass centroid. b) For each point of the red contour line the distance to the centroid is measured according to a predefined norm and normalised. The greatest distance is stored as first element in a list u (1). All other distances u (i) are enumerated clockwise from this starting point (blue line). The red line is the distance list augmented by (m-1)*t elements, recycling the beginning of u. Parameters m and t are given by the subsequent embedding. c) From list u (i) a set of m dimensional vectors is derived, each having m elements of u with an equidistant spacing of t. The chronology of u (i) is embedded in v (i). d). A phase space trajectory in m dimensional space can be constructed from v (here shown for an example with m = 3). Numbers attached to some points of the phase space trajectory refer to index i of the original contour line. e) For each point i of the phase space trajectory the distance to any other point j is measured and tabulated. This can be plotted as a colour heat map. f) In a later step it is checked, whether the respective distance is greater than a given threshold ε (Heaviside operator). The result is tabulated as a square, symmetric and binary matrix, the recurrence plot (RP). White dots indicate that the distance between v (i) and v (j) is greater than ε. On the main diagonal points are compared against themselves. Thus, the distance is always zero. From the RP a number of numerical features are derived in the subsequent recurrence quantification analysis (RQA, refer to the text). g) The enclosed white coherent areas within a RP have been termed “eyes”. Due to the circular data structure and above mentioned augmentation the truncated eyes along the borders need to be interpreted as connected structures on the opposite sides of the plot. This is displayed by matching colours of associated eyes. This plot serves as a basis for the eye structure quantification (ESQ, see text)

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