Abstract

In this paper, we propose a new PDE-based methodology for deformable surfaces that is capable of automatically evolving its shape to capture the geometric boundary of the data and simultaneously dis- cover its underlying topological structure. Our model can handle multiple types of data (such as volumetric data, 3D point clouds and 2D image data), using a common mathematical framework. The deformation be- havior of the model is governed by partial difierential equations (e.g. the weighted minimal surface flow). Unlike the level-set approach, our model always has an explicit representation of geometry and topology. The regularity of the model and the stability of the numerical integra- tion process are ensured by a powerful Laplacian tangential smoothing operator. By allowing local adaptive refinement of the mesh, the model can accurately represent sharp features. We have applied our model for shape reconstruction from volumetric data, unorganized 3D point clouds and multiple view images. The versatility and robustness of our model allow its application to the challenging problem of multiple view recon- struction. Our approach is unique in its combination of simultaneous use of a high number of arbitrary camera views with an explicit mesh that is intuitive and easy-to-interact-with. Our model-based approach auto- matically selects the best views for reconstruction, allows for visibility checking and progressive refinement of the model as more images become available. The results of our extensive experiments on synthetic and real data demonstrate robustness, high reconstruction accuracy and visual quality.