Image-Based 3D Modeling via Cheeger Sets

We propose a novel variational formulation for generating 3D models of objects from a single view. Based on a few user scribbles in an image, the algorithm automatically extracts the object silhouette and subsequently determines a 3D volume by minimizing the weighted surface area for a fixed user-specified volume. The respective energy can be efficiently minimized by means of convex relaxation techniques, leading to visually pleasing smooth surfaces within a matter of seconds. In contrast to existing techniques for single-view reconstruction, the proposed method is based on an implicit surface representation and a transparent optimality criterion, assuring high-quality 3D models of arbitrary topology with a minimum of user input.

[1]  Daniel Cremers,et al.  Non-parametric Single View Reconstruction of Curved Objects Using Convex Optimization , 2009, DAGM-Symposium.

[2]  Ken-ichi Anjyo,et al.  Tour into the picture: using a spidery mesh interface to make animation from a single image , 1997, SIGGRAPH.

[3]  Satoshi Matsuoka,et al.  Teddy: A Sketching Interface for 3D Freeform Design , 1999, SIGGRAPH Courses.

[4]  Mila Nikolova,et al.  Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models , 2006, SIAM J. Appl. Math..

[5]  Ronald F. Gariepy.  FUNCTIONS OF BOUNDED VARIATION AND FREE DISCONTINUITY PROBLEMS (Oxford Mathematical Monographs) , 2001 .

[6]  J. Cheeger.  A lower bound for the smallest eigenvalue of the Laplacian , 1969 .

[7]  Alexei A. Efros,et al.  Automatic photo pop-up , 2005, SIGGRAPH 2005.

[8]  R. Dykstra,et al.  A Method for Finding Projections onto the Intersection of Convex Sets in Hilbert Spaces , 1986 .

[9]  L. Ambrosio,et al.  Functions of Bounded Variation and Free Discontinuity Problems , 2000 .

[10]  Marc Alexa,et al.  FiberMesh: designing freeform surfaces with 3D curves , 2007, SIGGRAPH 2007.

[11]  Antonio Criminisi,et al.  Creating Architectural Models from Images , 1999, Comput. Graph. Forum.

[12]  Laurent D. Cohen,et al.  Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Images , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Daniel Cremers,et al.  An algorithm for minimizing the Mumford-Shah functional , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[14]  B. Gelbaum,et al.  Problems in analysis , 1964 .

[15]  Li Zhang,et al.  Single view modeling of free-form scenes , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[16]  Ian D. Reid,et al.  Single View Metrology , 2000, International Journal of Computer Vision.

[17]  Andrew Blake,et al.  "GrabCut" , 2004, ACM Trans. Graph..

[18]  Andrew W. Fitzgibbon,et al.  Single View Reconstruction of Curved Surfaces , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).