Surface reconstruction using deformable models with interior and boundary constraints

A technique is introduced for 3-D surface reconstruction and graphic animation using elastic, deformable models. The basic structure used is an imaginary elastic grid, which is made of membranous, thin-plate type material. This elastic grid is bent, twisted, compressed, and stretched into any desirable 3-D shape, or from one flexible state to another. The desired shape can be specified by the shape constraints derived automatically from images of a real 3-D object, or by an analytic surface function. Shape reconstruction is guided by a set of imaginary springs that enforce the consistency in the position, orientation, and/or curvature measurements of the elastic grid and the desired shape. The dynamics of a reconstruction process is regulated by the Hamilton principle or the principle of the least action. Implementation results using simple analytic shapes and images of real free-form objects are presented. The authors believe that their model is widely applicable in many surface reconstruction and graphic animation processes