IMAGE PROCESSING METHOD BASED ON THE FINITE ELEMENT METHOD FOR DIRECTLY SOLVING INVERSE PROBLEMS IN STRUCTURAL MECHANICS

摘要

The present disclosure relates to an image processing method including the following steps: receiving a deformation or displacement image; defining a meshing of the deformation image; assigning a respective pair of unknown variables to each node of the meshing; detecting one (or more) node(s) located at the boundary between two different materials of the body studied; enriching the node(s) detected; calculating a basic matrix for each basic cell of the meshing; assembling the basic matrixes in order to obtain an overall structural matrix; calculating a resilience image of the body based on the overall structural matrix.

主权项

1. A method for image processing allowing the formation of an elasticity image of a body according to the material(s) making up the body, the method comprising the steps of:
receiving a deformation image illustrating a displacement or deformation field of the points of the body as a function of a pressure difference in the body; defining a meshing of the deformation image, the meshing step applying a finite element method, the meshing including a plurality of elementary cells each delimiting a same material and each including at least three nodes, each node belonging to one or several adjacent cells to the meshing; assigning to each node i of the meshing a pair of unknown nodal variables, each pair being representative of elastic properties to be determined; detecting at least one node common to at least two adjacent elementary cells delimiting different materials; enriching the at least one detected common node, the enrichment step including replacing the pair of unknown variables assigned to the detected common node with at least two pairs of enrichment unknown variables, each pair of enrichment unknown variables of the detected common node being assigned to a respective elementary cell from among the at least two adjacent elementary cells delimiting different materials; calculating an elementary matrix for each elementary cell of the meshing so as to obtain a plurality of elementary matrices, the elementary matrices being calculated by taking into account pairs of unknown variables assigned to the elementary cells, and pairs of unknown variables assigned to the elementary cells; assembling the elementary matrices of the plurality of elementary matrices in order to obtain a structure matrix; and calculating an elasticity image of the body from the deformation image and from the structure matrix.