Graph Recognition by Forming Wave Kernel Invariants

Currently, much attention is paid to spectral methods of pattern recognition. Methods of heat and wave kernel signatures have an advantage in terms of the level of descriptor information content and, as a consequence, in terms of discriminant level. The paper considers a method for constructing a shape descriptor function - a wave kernel, which has a high level of discriminant in relation to other spectral recognition methods. Existing descriptors can be divided into two classes depending on the invariance of the parameters. Classical approaches are invariant with respect to rigid motion. The paper presents approximations of wave kernel signatures by functions of the energy logarithm. Based on the approximation of signatures, isometric invariants of graphs representing object shapes are determined. The normalized distance between wave kernel signatures is determined. The novelty of the work lies in the development of approximating functions of wave kernel signatures and coefficients of these functions - invariants of graphs representing the shapes of objects. The significance (practical and scientific) of constructing approximating functions of signatures and coefficients of these functions lies in the possibility of increasing the level of discriminancy in relation to other spectral recognition methods.