- Autor (es):
- Ernesto Bribiesca

- Tipo:
- Journal Article

An easy measure of tortuosity for enclosing surfaces of 3D objects composed of face-connect voxels is presented. We consider that any 3D object composed of face-connected voxels has three implicit surface areas: the enclosing surface area, that corresponds to the sum of the areas of the external plane faces of the voxels which form the visible faces of the solid; the contact surface area that corresponds to the sum of the areas of the contact surfaces which are common to two voxels; and total surface area that corresponds to the sum of all the surface areas of the faces of the all voxels of the solid. The relation among these different surface areas allowed us to define the proposed measure of tortuosity for enclosing surfaces of voxel-based objects. The measure proposed here of tortuosity is invariant under translation, rotation, scaling, and mirror and rotational symmetries. This measure of tortuosity is preserved at different resolutions and is valid for objects holding holes and tunnels. Also, the proposed measure of tortuosity is normalized into a continuous range from 0 to 1 which allows us to improve the object classification. Thus, the minimum and maximum values of tortuosity for enclosing surfaces of voxel-based objects are described. Different families of particular objects are generated based on the above-mentioned concepts. Finally, we present the computation of tortuosity of different kind of voxel-based objects from the real world including examples of brain structures

Bribiesca, E. (2021). A measure of tortuosity for enclosing surfaces of voxel-based objects. *SN Computer Science,* *2*(3) doi:10.1007/s42979-021-00565-0