New Methods of Three-Dimensional Images Recognition Based on Stochastic Geometry and Functional Analysis

A new approach to 3D objects recognition based on modern methods of stochastic geometry and functional analysis is proposed in the paper. A detailed mathematical description of the method developed on the approach is also presented. The 3D trace transform allows creating an invariant description of spatial objects, which better resist distortion and coordinate noise than the one, obtained as a result of the object normalization procedure, does. The ability to control properties of developed features increases intellectual capacities of the 3D trace transform significantly, which can be mentioned as its undeniable advantage. The justification of the proposed theory and mathematical model is a variety of worked out theoretical examples of hypertriplet features that have particular described properties. The paper considers in detail scan techniques of the hypertrace transform and its mathematical model as well as approaches to developing and distinguishing informative features.