A novel mathematical framework for topological triangle characterization in 2D meshes is the basis of a system for object detection from images. The system relies on a set of topological operators and their supporting topological data structure to guarantee a precise control of topological changes introduced as a result of inserting and removing triangles from mesh models. The approach enables object models to be created directly from the images without a previous segmentation step. Automatic approaches for modeling objects from images are scarce partly because the process of creating the models typically involves a costly (and generally user-driven) segmentation step to obtain the necessary geometrical information. This issue is critical, for example, in procedures such as surgical planning and physiological studies, or in the simulation of elastic deformation and fluid flow. Our approach is a first step towards automatic mesh generation from images, which may represent a significant progress to a range of applications that handle geometric models. The approach is used to extract robust models from medical images, in order to illustrate how the aggregation of topological information can empower a simple thresholding technique for object detection, making up for the lack of geometrical information in the images.
Zhang, F., Heiney, P. A., Srinivasan, A., Naciri, J., & Ratna, B. (2006). Structure of nematic liquid crystalline elastomers under uniaxial deformation. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 73(2). https://doi.org/10.1103/PhysRevE.73.021701