Abstract
Interpolation methods that rely on partial differential equations can reconstruct images with high quality from a few prescribed pixels. A whole class of compression codecs exploits this concept to store images in terms of a sparse grey value representation. Recently, Brinkmann et al. (2015) have suggested an alternative approach: They propose to store gradient data instead of grey values. However, this idea has not been evaluated and its potential remains unknown. In our paper, we compare gradient and grey value data for homogeneous diffusion inpainting w.r.t. two different aspects: First, we evaluate the reconstruction quality, given a comparable amount of data of both kinds. Second, we assess how well these sparse representations can be stored in compression applications. To this end, we establish a framework for optimising and encoding the known data. It allows a fair comparison of both the grey value and the gradient approach. Our evaluation shows that gradient-based reconstructions avoid visually distracting singularities involved in the reconstructions from grey values, thus improving the visual fidelity. Surprisingly, this advantage does not carry over to compression due to the high sensitivity to quantisation.
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References
Belhachmi, Z., Bucur, D., Burgeth, B., Weickert, J.: How to choose interpolation data in images. SIAM J. Appl. Math. 70(1), 333–352 (2009)
Bertalmío, M., Sapiro, G., Caselles, V., Ballester, C.: Image inpainting. In: Proceedings of the SIGGRAPH 2000, New Orleans, LI, pp. 417–424, July 2000
Brinkmann, E.-M., Burger, M., Grah, J.: Regularization with sparse vector fields: from image compression to TV-type reconstruction. In: Aujol, J.-F., Nikolova, M., Papadakis, N. (eds.) SSVM 2015. LNCS, vol. 9087, pp. 191–202. Springer, Heidelberg (2015). doi:10.1007/978-3-319-18461-6_16
Carlsson, S.: Sketch based coding of grey level images. Sig. Process. 15(1), 57–83 (1988)
Chen, Y., Ranftl, R., Pock, T.: A bi-level view of inpainting-based imagecompression. In: Proceedings of the 19th Computer Vision Winter Workshop, Křtiny, Czech Republic, pp. 19–26, Feb 2014
Frankot, R.T., Chellappa, R.: A method for enforcing integrability in shapefrom shading algorithms. IEEE Trans. Pattern Anal. Mach. Intell. 10(4), 439–451 (1988)
Galić, I., Weickert, J., Welk, M., Bruhn, A., Belyaev, A., Seidel, H.P.: Image compression with anisotropic diffusion. J. Math. Imaging Vis. 31(2–3), 255–269 (2008)
Hoeltgen, L., Setzer, S., Weickert, J.: An optimal control approach to find sparse data for laplace interpolation. In: Heyden, A., Kahl, F., Olsson, C., Oskarsson, M., Tai, X.-C. (eds.) EMMCVPR 2013. LNCS, vol. 8081, pp. 151–164. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40395-8_12
Mahoney, M.: Adaptive weighing of context models for lossless data compression. Technical report, CS-2005-16, Florida Institute of Technology, Melbourne, FL, December 2005
Mainberger, M., Bruhn, A., Weickert, J., Forchhammer, S.: Edge-basedcompression of cartoon-like images with homogeneous diffusion. Pattern Recogn. 44(9), 1859–1873 (2011)
Mainberger, M., Hoffmann, S., Weickert, J., Tang, C.H., Johannsen, D., Neumann, F., Doerr, B.: Optimising spatial and tonal data for homogeneous diffusion inpainting. In: Bruckstein, A.M., Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds.) SSVM 2011. LNCS, vol. 6667, pp. 26–37. Springer, Heidelberg (2012). doi:10.1007/978-3-642-24785-9_3
Masnou, S., Morel, J.M.: Level lines based disocclusion. In: Proceedings of the 1998 IEEE International Conference on Image Processing, Chicago, IL, vol. 3, pp. 259–263, October 1998
Melnikov, Y.A., Melnikov, M.Y.: Green’s Functions: Construction and Applications. De Gruyter, Berlin (2012)
Ochs, P., Chen, Y., Brox, T., Pock, T.: iPiano: inertial proximal algorithm for nonconvex optimization. SIAM J. Appl. Math. 7(2), 1388–1419 (2014)
Pennebaker, W.B., Mitchell, J.L.: JPEG: Still Image Data Compression Standard. Springer, New York (1992)
Peter, P., Hoffmann, S., Nedwed, F., Hoeltgen, L., Weickert, J.: Evaluating the true potential of diffusion-based inpainting in a compression context. Sig. Process. Image Commun. 46, 40–53 (2016)
Schmaltz, C., Peter, P., Mainberger, M., Ebel, F., Weickert, J., Bruhn, A.: Understanding, optimising, and extending data compression with anisotropic diffusion. Int. J. Comput. Vis. 108(3), 222–240 (2014)
Taubman, D.S., Marcellin, M.W. (eds.): JPEG 2000: Image Compression Fundamentals, Standards and Practice. Kluwer, Boston (2002)
Zeng, G., Ahmed, N.: A block coding technique for encoding sparse binary patterns. IEEE Trans. Acoust. Speech Sig. Process. 37(5), 778–780 (1989)
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Schneider, M., Peter, P., Hoffmann, S., Weickert, J., Meinhardt-Llopis, E. (2016). Gradients versus Grey Values for Sparse Image Reconstruction and Inpainting-Based Compression. In: Blanc-Talon, J., Distante, C., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2016. Lecture Notes in Computer Science(), vol 10016. Springer, Cham. https://doi.org/10.1007/978-3-319-48680-2_1
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DOI: https://doi.org/10.1007/978-3-319-48680-2_1
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