Surface reconstruction using deformable models with interior and boundary constraints

The authors introduce a technique for 3D surface reconstruction using elastic deformable-models. The model used is an imaginary elastic grid, which is made of membranous, thin-plate-type material. The elastic grid can bent, twisted, compressed, and stretched into any desired 3D shape, which is specified by the shape constraints derived automatically from images of a real 3D object. 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 surface reconstruction process is regulated by Hamilton´s principle or the principle of the least action. Furthermore, a 1D deformable template that borders the elastic grid may be used. This companion boundary template is attracted/repelled by image forces to conform with the silhouette of the imaged object. Implementation results using simple analytic shapes and images of real objects are presented