Integral geometry

Integral geometry

Volterra-type integral geometry problems

Published in B Bertram, C Constanda, A Struthers, Integral methods in science and engineering, 2019

Problems of integral geometry arise in a natural way in the study of many mathematical models in domains having extensive applications, such as seismic prospecting, interpretation of the data of geophysical and aerospace observations, various processes described by kinetic equations, and so on [2]. The apparatus devised here is the mathematical basis of computerized tomography, a promising and intensively developed direction of modern science [3]. Wide classes of inverse problems for partial differential equations of various type reduce to the solution of problems of integral geometry (see [2] and the references given there).

Morphologic for knowledge dynamics: revision, fusion and abduction

View Article

Journal Information

Published in Journal of Applied Non-Classical Logics, 2023

Isabelle Bloch, Jérôme Lang, Ramón Pino Pérez, Carlos Uzcátegui

Mathematical morphology relies on concepts and tools from various branches of mathematics: algebra (lattice theory), topology, discrete geometry, integral geometry, geometrical probability, partial differential equations, etc. (Matheron, 1975; Serra, 1982); in fact any mathematical theory that deals with shapes, their combinations or their evolution, can be brought to contribute to morphological theory. When adopting a logics point of view, the algebraic framework is particularly relevant, and we will concentrate on it in the sequel.

Explore chapters and articles related to this topic

Volterra-type integral geometry problems

Morphologic for knowledge dynamics: revision, fusion and abduction