Abstract
Recent progress in per-pixel object class labeling of natural images can be attributed to the use of multiple types of image features and sound statistical learning approaches. Within the latter, Conditional Random Fields (CRF) are prominently used for their ability to represent interactions between random variables. Despite their popularity in computer vision, parameter learning for CRFs has remained difficult, popular approaches being cross-validation and piecewise training.
In this work, we propose a simple yet expressive tree-structured CRF based on a recent hierarchical image segmentation method. Our model combines and weights multiple image features within a hierarchical representation and allows simple and efficient globally-optimal learning of ≈ 105 parameters. The tractability of our model allows us to pose and answer some of the open questions regarding parameter learning applying to CRF-based approaches. The key findings for learning CRF models are, from the obvious to the surprising, i) multiple image features always help, ii) the limiting dimension with respect to current models is the amount of training data, iii) piecewise training is competitive, iv) current methods for max-margin training fail for models with many parameters.
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References
Lauritzen, S.L.: Graphical Models. Oxford University Press, Oxford (1996)
Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press, Cambridge (2009)
Lafferty, J., McCallum, A., Pereira, F.: Conditional random fields: Probabilistic models for segmenting and labeling sequence data. In: ICML (2001)
Sutton, C., McCallum, A.: An introduction to conditional random fields for relational learning. In: Introduction to Statistical Relational Learning. MIT Press, Cambridge (2007)
Kschischang, F.R., Frey, B.J., Loeliger, H.A.: Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory 47, 498–519 (2001)
Szummer, M., Kohli, P., Hoiem, D.: Learning CRFs using graph cuts. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part II. LNCS, vol. 5303, pp. 582–595. Springer, Heidelberg (2008)
Winn, J.M., Shotton, J.: The layout consistent random field for recognizing and segmenting partially occluded objects. In: CVPR (2006)
Shotton, J., Winn, J., Rother, C., Criminisi, A.: Textonboost for image understanding: Multi-class object recognition and segmentation by jointly modeling texture, layout, and context. IJCV 81 (2007)
Kumar, S., Hebert, M.: Discriminative random fields: A discriminative framework for contextual interaction in classification. In: ICCV (2003)
He, X., Zemel, R.S., Carreira-Perpiñán, M.Á.: Multiscale conditional random fields for image labeling. In: CVPR (2004)
Schnitzspan, P., Fritz, M., Schiele, B.: Hierarchical support vector random fields: Joint training to combine local and global features. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part II. LNCS, vol. 5303, pp. 527–540. Springer, Heidelberg (2008)
Nowozin, S., Lampert, C.H.: Global connectivity potentials for random field models. In: CVPR (2009)
Gould, S., Rodgers, J., Cohen, D., Elidan, G., Koller, D.: Multi-class segmentation with relative location prior. IJCV 80, 300–316 (2008)
Batra, D., Sukthankar, R., Chen, T.: Learning class-specific affinities for image labelling. In: CVPR (2008)
Reynolds, J., Murphy, K.: Figure-ground segmentation using a hierarchical conditional random field. In: CRV (2007)
Plath, N., Toussaint, M., Nakajima, S.: Multi-class image segmentation using conditional random fields and global classification. In: ICML (2009)
Kohli, P., Ladický, L., Torr, P.H.S.: Robust higher order potentials for enforcing label consistency. In: CVPR (2008)
Ladický, L., Russell, C., Kohli, P.: Associative hierarchical crfs for object class image segmentation. In: ICCV (2009)
Munoz, D., Bagnell, J.A., Vandapel, N., Hebert, M.: Contextual classification with functional max-margin markov networks. In: CVPR (2009)
Kumar, S., August, J., Hebert, M.: Exploiting inference for approximate parameter learning in discriminative fields: An empirical study. In: Rangarajan, A., Vemuri, B.C., Yuille, A.L. (eds.) EMMCVPR 2005. LNCS, vol. 3757, pp. 153–168. Springer, Heidelberg (2005)
Korc, F., Förstner, W.: Approximate parameter learning in conditional random fields: An empirical investigation. In: Rigoll, G. (ed.) DAGM 2008. LNCS, vol. 5096, pp. 11–20. Springer, Heidelberg (2008)
Parise, S., Welling, M.: Learning in Markov random fields: An empirical study. In: Joint Statistical Meeting, JSM 2005 (2005)
Finley, T., Joachims, T.: Training structural SVMs when exact inference is intractable. In: ICML (2008)
Willsky, A.S.: Multiresolution markov models for signal and image processing. Proceedings of the IEEE (2002)
Lim, J.J., Gu, C., Arbeláez, P., Malik, J.: Context by region ancestry. In: ICCV (2009)
Arbeláez, P.: Boundary extraction in natural images using ultrametric contour maps. In: Workshop on Perceptual Organization in Computer Vision (2006)
Everingham, M., Gool, L.V., Williams, C.K., Winn, J., Zisserman, A.: The PASCAL Visual Object Classes Challenge, VOC 2009 Results (2009), http://www.pascal-network.org/challenges/VOC/voc2009/workshop/
Shotton, J., Johnson, M., Cipolla, R.: Semantic texton forests for image categorization and segmentation. In: CVPR (2008)
Mooij, J.M.: libDAI: A free/open source C++ library for discrete approximate inference methods (2008), http://www.libdai.org/
Gehler, P., Nowozin, S.: On feature combination for multiclass object classification. In: ICCV (2009)
Bottou, L., Bousquet, O.: The tradeoffs of large scale learning. In: NIPS (2007)
Sutton, C.A., McCallum, A.: Piecewise training for undirected models. In: UAI (2005)
Tsochantaridis, I., Joachims, T., Hofmann, T., Altun, Y.: Large margin methods for structured and interdependent output variables. JMLR 6, 1453–1484 (2005)
Blaschko, M.B., Lampert, C.H.: Learning to localize objects with structured output regression. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part I. LNCS, vol. 5302, pp. 2–15. Springer, Heidelberg (2008)
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Nowozin, S., Gehler, P.V., Lampert, C.H. (2010). On Parameter Learning in CRF-Based Approaches to Object Class Image Segmentation. In: Daniilidis, K., Maragos, P., Paragios, N. (eds) Computer Vision – ECCV 2010. ECCV 2010. Lecture Notes in Computer Science, vol 6316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15567-3_8
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DOI: https://doi.org/10.1007/978-3-642-15567-3_8
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