Abstract
We explore the 3D reconstruction of objects from a single view within an interactive framework by using silhouette information. In order to deal with the highly ill-posed nature of the problem we propose two different reconstruction priors: a shape and a volume prior and cast them into a variational problem formulation. For both priors we show that the corresponding relaxed optimization problem is convex. This leads to unique solutions which are independent of initialization and which are either globally optimal (shape prior) or can be shown to lie within bounds from the optimal solution (volume prior). We analyze properties of the proposed priors with regard to the reconstruction results as well as their impact on the minimization problem. By employing an implicit volumetric representation our reconstructions enjoy complete topological freedom. Being parameter-based, our interactive reconstruction tool allows for intuitive and easy to use modeling of the reconstruction result.
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.
Similar content being viewed by others
References
Oswald, M.R., Töppe, E., Kolev, K., Cremers, D.: Non-parametric single view reconstruction of curved objects using convex optimization. In: Denzler, J., Notni, G., Süße, H. (eds.) Pattern Recognition. LNCS, vol. 5748, pp. 171–180. Springer, Heidelberg (2009)
Toeppe, E., Oswald, M.R., Cremers, D., Rother, C.: Image-based 3D modeling via cheeger sets. In: Kimmel, R., Klette, R., Sugimoto, A. (eds.) ACCV 2010, Part I. LNCS, vol. 6492, pp. 53–64. Springer, Heidelberg (2011)
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, USA (1997)
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)
Hoiem, D., Efros, A.A., Hebert, M.: Automatic photo pop-up. ACM Trans. Graph 24, 577–584 (2005)
Sturm, P.F., Maybank, S.J.: A method for interactive 3d reconstruction of piecewise planar objects from single images. In: Proc. BMVC, pp. 265–274 (1999)
Terzopoulos, D., Witkin, A., Kass, M.: Symmetry-seeking models and 3d object reconstruction. IJCV 1, 211–221 (1987)
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)
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, USA (1999)
Nealen, A., Igarashi, T., Sorkine, O., Alexa, M.: Fibermesh: designing freeform surfaces with 3d curves. ACM Trans. Graph. 26, 41 (2007)
Prasad, M., Zisserman, A., Fitzgibbon, A.W.: Single view reconstruction of curved surfaces. In: CVPR, pp. 1345–1354 (2006)
Joshi, P., Carr, N.: Repoussé: Automatic inflation of 2d art. In: Eurographics Workshop on Sketch-Based Modeling (2008)
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)
Boykov, Y.Y., Jolly, M.P.: Interactive graph cuts for optimal boundary region segmentation of objects in n-d images. In: ICCV, vol. 1, pp. 105–112 (2001)
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. The Clarendon Press Oxford University Press, New York (2000)
Kolev, K., Klodt, M., Brox, T., Cremers, D.: Continuous global optimization in multview 3d reconstruction. International Journal of Computer Vision (2009)
Klodt, M., Schoenemann, T., Kolev, K., Schikora, M., Cremers, D.: An experimental comparison of discrete and continuous shape optimization methods. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part I. LNCS, vol. 5302, pp. 332–345. Springer, Heidelberg (2008)
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)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Töppe, E., Oswald, M.R., Cremers, D., Rother, C. (2011). Silhouette-Based Variational Methods for Single View Reconstruction. In: Cremers, D., Magnor, M., Oswald, M.R., Zelnik-Manor, L. (eds) Video Processing and Computational Video. Lecture Notes in Computer Science, vol 7082. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24870-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-24870-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24869-6
Online ISBN: 978-3-642-24870-2
eBook Packages: Computer ScienceComputer Science (R0)