# zbMATH — the first resource for mathematics

Multiview depth parameterisation with second order regularisation. (English) Zbl 1444.68263
Aujol, Jean-François (ed.) et al., Scale space and variational methods in computer vision. 5th international conference, SSVM 2015, Lège-Cap Ferret, France, May 31 – June 4, 2015. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9087, 551-562 (2015).
Summary: In this paper we consider the problem of estimating depth maps from multiple views within a variational framework. Previous work has demonstrated that multiple views improve the depth reconstruction, and that higher order regularisers model a good prior for typical real-world 3D scenes. We build on these findings and stress an important aspect that has not been considered in variational multiview depth estimation so far: We investigate several parameterisations of the unknown depth. This allows us to show, both analytically and experimentally, that directly working with depth values introduces an undesirable bias. As a remedy, we reveal that an inverse depth parameterisation is generally preferable. Our analysis clearly points out its benefits w.r.t. the data and the smoothness term. We verify these theoretical findings by means of experiments.
For the entire collection see [Zbl 1362.68008].
##### MSC:
 68T45 Machine vision and scene understanding 49N90 Applications of optimal control and differential games
LSD-SLAM; DTAM
Full Text:
##### References:
 [1] Curless, B., Levoy, M.: A volumetric method for building complex models from range images. In: Proc. SIGGRAPH 1996, vol. 3, New Orleans, LA, pp. 303-312, August 1996 [2] Zach, C., Pock, T., Bischof, H.: A globally optimal algorithm for robust TV-$$L^1$$ range image integration. In: Proc. Ninth International Conference on Computer Vision, Rio de Janeiro, Brazil, pp. 1-8, October 2007 [3] Zach, C.: Fast and high quality fusion of depth maps. In: Proc. Fourth International Symposium on 3D Data Processing, Visualization and Transmission, Atlanta, GA, pp. 1-8, June 2008 [4] March, R.: Computation of stereo disparity using regularization. Pattern Recognition Letters 8(3), 181-187 (1988) [5] Mansouri, A.R., Mitiche, A., Konrad, J.: Selective image diffusion: Application to disparity estimation. In: Proc. IEEE International Conference on Image Processing, Chicago, IL, pp. 284-288, October 1998 [6] Scharstein, D., Szeliski, R.: Stereo matching with non-linear diffusion. International Journal of Computer Vision 28, 155-174 (1998) [7] Slesareva, N., Bruhn, A., Weickert, J.: Optic Flow Goes Stereo: A Variational Method for Estimating Discontinuity-Preserving Dense Disparity Maps. In: Kropatsch, W.G., Sablatnig, R., Hanbury, A. (eds.) DAGM 2005. LNCS, vol. 3663, pp. 33-40. Springer, Heidelberg (2005) [8] Zimmer, H., Bruhn, A., Valgaerts, L., Breuß, M., Weickert, J., Rosenhahn, B., Seidel, H.P.: PDE-based anisotropic disparity-driven stereo vision. In: Proc. Vision, Modeling, and Visualization, Konstanz, Germany, Akademische Verlagsgesellschaft Aka, pp. 263-272, October 2008 [9] Valgaerts, L., Bruhn, A., Weickert, J.: A Variational Model for the Joint Recovery of the Fundamental Matrix and the Optical Flow. In: Rigoll, G. (ed.) DAGM 2008. LNCS, vol. 5096, pp. 314-324. Springer, Heidelberg (2008) [10] Ranftl, R., Gehrig, S., Pock, T., Bischof, H.: Pushing the limits of stereo using variational stereo estimation. In: Proc. IEEE Intelligent Vehicles Symposium, Alcala de Henares, Spain, pp. 401-407 (2012) [11] Hewer, A., Weickert, J., Seibert, H., Scheffer, T., Diebels, S.: Lagrangian strain tensor computation with higher order variational models. In: Proc. British Machine Vision Conference. BMVA Press, Bristol (September 2013) [12] Ranftl, R., Bredies, K., Pock, T.: Non-local Total Generalized Variation for Optical Flow Estimation. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds.) ECCV 2014, Part I. LNCS, vol. 8689, pp. 439-454. Springer, Heidelberg (2014) [13] Bredies, K., Kunisch, K., Pock, T.: Total generalized variation. SIAM Journal on Imaging Sciences 3(3), 492-526 (2010) · Zbl 1195.49025 [14] Chambolle, A., Lions, P.L.: Image recovery via total variation minimization and related problems. Numerische Mathematik 76(2), 167-188 (1997) · Zbl 0874.68299 [15] Robert, L., Deriche, R.: Dense depth map reconstruction: A minimization and regularization approach which preserves discontinuities. In: Buxton, B., Cipolla, R. (eds.) ECCV 1996. Lecture Notes in Computer Science, vol. 1064, pp. 439-451. Springer, Berlin (1996) [16] Stühmer, J., Gumhold, S., Cremers, D.: Real-Time Dense Geometry from a Handheld Camera. In: Goesele, M., Roth, S., Kuijper, A., Schiele, B., Schindler, K. (eds.) Pattern Recognition. LNCS, vol. 6376, pp. 11-20. Springer, Heidelberg (2010) [17] Semerjian, B.: A New Variational Framework for Multiview Surface Reconstruction. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds.) ECCV 2014, Part VI. LNCS, vol. 8694, pp. 719-734. Springer, Heidelberg (2014) [18] Civera, J., Davison, A.J., Montiel, J.: Inverse depth parametrization for monocular SLAM. IEEE Transactions on Robotics 24(5), 932-945 (2008) [19] Newcombe, R.A., Lovegrove, S.J., Davison, A.J.: DTAM: Dense tracking and mapping in real-time. In: Proc. IEEE International Conference on Computer Vision, Barcelona, Spain, pp. 2320-2327, November 2011 [20] Engel, J., Schöps, T., Cremers, D.: LSD-SLAM: Large-Scale Direct Monocular SLAM. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds.) ECCV 2014, Part II. LNCS, vol. 8690, pp. 834-849. Springer, Heidelberg (2014) [21] Grewenig, S., Weickert, J., Schroers, C., Bruhn, A.: Cyclic schemes for PDE-based image analysis. Technical Report 327, Saarland University, Saarbrücken, Germany (March 2013) · Zbl 1398.68600 [22] Scharstein, D. · Zbl 1012.68731
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.