Open AccessMatching of images based on their diffeomorphic mapping
Author(s) -
S. V. Lejhter,
С. Н. Чуканов
Publication year - 2018
Publication title -
kompʹûternaâ optika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 29
eISSN - 2412-6179
pISSN - 0134-2452
DOI - 10.18287/2412-6179-2018-42-1-96-104
Subject(s) - diffeomorphism , basis (linear algebra) , transformation (genetics) , artificial intelligence , image (mathematics) , mathematics , computer vision , gradient descent , computer science , algorithm , mathematical analysis , geometry , biochemistry , chemistry , artificial neural network , gene
We discuss a problem of comparison of two diffeomorphic images, namely, the source and target images of a diffeomorphism, which are given by two sets of points. The problem is solved on the basis of a method of constructing a minimized functional characterizing the evolution of the diffeomorphic source-to-target image transformation and a penalty for the image path deviation from the required trajectory. An algorithm for solving the diffeomorphic transformation equation is developed on the basis of the gradient descent method. The considered problem of comparison of two images can be used for constructing an optimal metamorphism of images, when there is no exact correspondence between the source and target images of the diffeomorphism.