Shape modeling is the study of the construction and analysis of digital representations of shape. A shape model is used as a surrogate for the actual object in areas such as biomedical modeling, robotics, computer animation, product design, and architecture. The shape model facilitates design, quantitative analysis, visualization, and planning. The underlying mathematical model of a surface in the shape model takes various forms: triangular mesh, B-spline surface, Bezier surface, subdivision surface, and others.
A present research focus of the Shape Lab is reconstruction and morphometry of the optic nerve head, in collaboration with the Department of Ophthalmology. Shape models of the optic nerve head allow the measurement of important structures, across various populations, deepening our understanding of optic neuropathies such as glaucoma. A classic problem in shape modeling research is the reconstruction of smooth curves and surfaces from point clouds; and point clouds of the optic nerve head, arising from OCT imaging or histology, pose an interesting challenge, as they are often noisy and sparse.
Along with reconstruction and morphometry, other research problems of interest in the Shape Lab are the extraction of point clouds and curves from images, the analysis of a curve or surface's tangent space, especially for the computation of bitangency, and the intersection and self-intersection of curves and surfaces.
Director of the Shape Lab: John K. Johnstone