Generic Phase Curl Localisation for an Individual Identification of Turing-patterned Animals

A variety of animal species carry permanent markings on their coats, be that for the purpose of survival-boosting camouflage [4, 14] or signalling [5, 8]. In many cases, these prominently visible surface patterns are composed of spots and stripes, which are suspected to originate from reactiondiffusion (RD) systems first described by Turing [15]. As a consequence of this deterministic, yet chaotic formation process, resulting markings often differ significantly from individual to individual while following a wider theme typical for a species [11]. Figure 1 illustrates the extent of observable coat variations in two sample species: African penguins and plains zebras. In this paper we describe minutiae detection in Turing patterns based on the detection of phase curls. The technique compactly captures individuality of RD patterns by robustly localising and typing sparse phase singularities. The foundations of the approach are discussed in detail and we give theoretical and experimental evidence for a generic applicability as a tool for individual animal identification. Finally, we briefly discuss real-world applications that have utilised the technique and can provide extended evaluations.