Figure 1

Principle of the solenoidal coordinate method. Upper panel: The construction of the P-periodic solenoids is based on three steps: i) the signal support is divided into segments of length P, ii) the segments are converted into circles, iii) the circles are aligned with respect to the locking up points. Lower panel: A set of sites (in red, upper left corner) come from a pattern that periodically repeats at some period P (blurred red points). Some of the initial periodic sites are missing (false negative, missing data) or have different positions (noise), and random sites have been added (false positive, contaminated data). The position of the sites in a solenoidal coordinate of period P (lower left panel) reveals some alignment properties along the solenoid axis. A projection upon the face view of the solenoid converts the alignments into clustered points (rightmost panel). The SCM scoring function aims at rewarding both dense regions (indicated in blue) and poor regions (indicated in yellow).