Abstract
We present a novel adaptive sparse grid method for unsupervised image segmentation. The method is based on spectral clustering. The use of adaptive sparse grids achieves that the dimensions of the involved eigensystem do not depend on the number of pixels. In contrast to classical spectral clustering, our sparse-grid variant is therefore able to segment larger images. We evaluate the method on real-world images from the Berkeley Segmentation Dataset. The results indicate that images with 150,000 pixels can be segmented by solving an eigenvalue system of dimensions 500 × 500 instead of 150, 000 × 150, 000.
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References
Martin, D., Fowlkes, C., Tal, D., Malik, J.: A Database of Human Segmented Natural Images and its Application to Evaluating Segmentation Algorithms and Measuring Ecological Statistics. In: Proceedings of the 2001 IEEE International Conference on Computer Vision, vol. 2, pp. 416–423 (2001)
Peherstorfer, B., Pflüger, D., Bungartz, H.-J.: A Sparse-Grid-Based Out-of-Sample Extension for Dimensionality Reduction and Clustering with Laplacian Eigenmaps. In: Wang, D., Reynolds, M. (eds.) AI 2011. LNCS, vol. 7106, pp. 112–121. Springer, Heidelberg (2011)
von Luxburg, U.: A Tutorial on Spectral Clustering. Statistics and Computing 17(4), 395–416 (2007)
Fowlkes, C., Belongie, S., Chung, F., Malik, J.: Spectral Grouping Using the Nystrom Method. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(2), 214–225 (2004)
Alzate, C., Suykens, J.A.K.: Multiway Spectral Clustering with Out-of-Sample Extensions through Weighted Kernel PCA. IEEE Transactions on Pattern Analysis and Machine Intelligence 32(2), 335–347 (2010)
Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation 15(6), 1373–1396 (2003)
Bungartz, H.J., Griebel, M.: Sparse grids. Acta Numerica 13, 147–269 (2004)
Pflüger, D.: Spatially Adaptive Sparse Grids for High-Dimensional Problems. Verlag Dr. Hut, München (August 2010)
Bengio, Y., Paiement, J.F., Vincent, P.: Out-of-sample extensions for LLE, isomap, MDS, eigenmaps, and spectral clustering. In: Advances in Neural Information Processing Systems, pp. 177–184. MIT Press (2003)
Wu, X.: Efficient Statistical Computations for Optimal Color Quantization. In: Arvo, J. (ed.) Graphics Gems II, pp. 126–133. Academic Press (1991)
Adorf, J.: Nonlinear Clustering on Sparse Grids. Studienarbeit/SEP/IDP, Institut für Informatik, Technische Universität München (August 2012)
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Peherstorfer, B., Adorf, J., Pflüger, D., Bungartz, HJ. (2013). Image Segmentation with Adaptive Sparse Grids. In: Cranefield, S., Nayak, A. (eds) AI 2013: Advances in Artificial Intelligence. AI 2013. Lecture Notes in Computer Science(), vol 8272. Springer, Cham. https://doi.org/10.1007/978-3-319-03680-9_17
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DOI: https://doi.org/10.1007/978-3-319-03680-9_17
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03679-3
Online ISBN: 978-3-319-03680-9
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