Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cheeger, J.: A lower bound for the smallest eigenvalue of the laplacian. In: Problems in analysis, Princeton Univ. Press, Princeton (1970)
Liebowitz, D., Criminisi, A., Zisserman, A.: Creating architectural models from images. In: Proc. EuroGraphics, vol. 18, pp. 39–50 (1999)
Criminisi, A., Reid, I., Zisserman, A.: Single view metrology. Int. J. Comput. Vision 40, 123–148 (2000)
Horry, Y., Anjyo, K.I., Arai, K.: Tour into the picture: using a spidery mesh interface to make animation from a single image. In: SIGGRAPH 1997: Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, pp. 225–232. ACM Press/Addison-Wesley Publishing Co, New York, NY, USA (1997)
Hoiem, D., Efros, A.A., Hebert, M.: Automatic photo pop-up. ACM Trans. Graph. 24, 577–584 (2005)
Igarashi, T., Matsuoka, S., Tanaka, H.: Teddy: a sketching interface for 3d freeform design. In: SIGGRAPH 1999, pp. 409–416. ACM Press/Addison-Wesley Publishing Co., New York, NY, USA (1999)
Nealen, A., Igarashi, T., Sorkine, O., Alexa, M.: Fibermesh: designing freeform surfaces with 3d curves. ACM Trans. Graph. 26, 41 (2007)
Zhang, L., Dugas-Phocion, G., Samson, J.S., Seitz, S.M.: Single view modeling of free-form scenes. In: Proc. of CVPR, pp. 990–997 (2001)
Prasad, M., Zisserman, A., Fitzgibbon, A.W.: Single view reconstruction of curved surfaces. In: CVPR, pp. 1345–1354 (2006)
Oswald, M.R., Toeppe, E., Kolev, K., Cremers, D.: Non-parametric single view reconstruction of curved objects using convex optimization. In: Pattern Recognition (Proc. DAGM), Jena, Germany (2009)
Cohen, L.D., Cohen, I.: Finite-element methods for active contour models and balloons for 2-d and 3-d images. IEEE Trans. on Patt. Anal. and Mach. Intell. 15, 1131–1147 (1993)
Rother, C., Kolmogorov, V., Blake, A.: GrabCut: interactive foreground extraction using iterated graph cuts. ACM Trans. Graph. 23, 309–314 (2004)
Ambrosio, L., Fusco, N., Pallara, D.: Functions of bounded variation and free discontinuity problems. In: Oxford Mathematical Monographs, The Clarendon Press/Oxford University Press, New York (2000)
Chan, T., Esedoḡlu, S., Nikolova, M.: Algorithms for finding global minimizers of image segmentation and denoising models. SIAM Journal on Applied Mathematics 66, 1632–1648 (2006)
Pock, T., Cremers, D., Bischof, H., Chambolle, A.: An algorithm for minimizing the piecewise smooth mumford-shah functional. In: IEEE Int. Conf. on Computer Vision, Kyoto, Japan (2009)
Boyle, J.P., Dykstra, R.L.: An method for finding projections onto the intersection of convex sets in Hilbert spaces, vol. 37, pp. 28–47 (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Töppe, E., Oswald, M.R., Cremers, D., Rother, C. (2011). Image-Based 3D Modeling via Cheeger Sets. In: Kimmel, R., Klette, R., Sugimoto, A. (eds) Computer Vision – ACCV 2010. ACCV 2010. Lecture Notes in Computer Science, vol 6492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19315-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-19315-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19314-9
Online ISBN: 978-3-642-19315-6
eBook Packages: Computer ScienceComputer Science (R0)