Abstract
This paper explores the application of semi-qualitative probabilistic networks (SQPNs) that combine numeric and qualitative information to computer vision problems. Our version of SQPN allows qualitative influences and imprecise probability measures using intervals. We describe an Imprecise Dirichlet model for parameter learning and an iterative algorithm for evaluating posterior probabilities, maximum a posteriori and most probable explanations. Experiments on facial expression recognition and image segmentation problems are performed using real data.
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Bartlett, M.S., Littlewort, G.C., Frank, M.G., Lainscsek, C., Fasel, I.R., Movellan, J.R., 2006. Automatic recognition of facial actions in spontaneous expressions. Journal of Multimedia, 1(6), 22–35.
Bernard, J.M., 2005. An introduction to the imprecise dirichlet model for multinomial data. International Journal of Approximate Reasoning, 39(2–3), 123–150.
Cano, A., Gómez, M., Moral, S., 2007. Credal nets with probabilities estimated with an extreme imprecise dirichlet model. In International Symposium on Imprecise Probabilities: Theory and Applications, 57–66.
Caselles, V., Kimmel, R., Sapiro G., 1997. Geodesic active contours. International Journal of Computer Vision, 22(1), 61–79.
Couso, I., Moral, S., Walley, P., 1999. Examples of independence for imprecise probabilities. In International Symposium on Imprecise Probabilities and Their Applications, 121–130, Ghent, Belgium.
Cozman, F.G., 2000. Credal networks. Artificial Intelligence, 120, 199–233.
da Rocha, J.C.F., Cozman, F.G., 2002. Inference with separately specified sets of probabilities in credal networks. In Conference on Uncertainty in Artificial Intelligence, 430–437, Morgan Kaufmann, San Francisco.
da Rocha, J.C.F., Cozman, F.G., de Campos, C.P., 2003. Inference in polytrees with sets of probabilities. In Conference on Uncertainty in Artificial Intelligence, 217–224, Morgan Kaufmann, New York.
de Campos, C.P., Cozman, F.G., 2004. Inference in credal networks using multilinear programming. In Second Starting AI Researcher Symposium, 50–61, IOS Press, Valencia.
de Campos, C.P., Cozman, F.G., 2005a. Belief updating and learning in semi-qualitative probabilistic networks. In Conference on Uncertainty in Artificial Intelligence, 153–160.
de Campos, C.P., Cozman, F.G., 2005b. The inferential complexity of Bayesian and credal networks. In International Joint Conference on Artificial Intelligence, 1313–1318.
Druzdzel, M.J., Henrion, M., 1993. Efficient reasoning in qualitative probabilistic networks. In AAAI Conference on Artificial Intelligence, 548–553.
Ekman, P., Friesen, W.V., 1978. Facial action coding system: A technique for the measurement of facial movement. Consulting Psychologists Press, Palo Alto, CA.
Fasel, B., Luettin, J., 2003. Automatic facial expression analysis: A survey. Pattern Recognition, 36, 259–275.
Gonzalez, R.C., Woods, R.E., 2002. Digital Image Processing, 2nd edition. Addison-Wesley.
Harris, C., Stephens, M.J., 1988. A combined corner and edge detector. In Alvey Vision Conference, 147–151. Manchester.
Kanade, T., Cohn, J.F., Tian, Y., 2000. Comprehensive database for facial expression analysis. In IEEE International Conference on Automatic Face and Gesture Recognition, 46–53.
Kass, M., Witkin, A., Terzopoulos, D., 1988. Snakes: Active contour models. International Journal of Computer Vision, 1, 321–331.
Lukatskii, A.M., Shapot, D.V., 2001. Problems in multilinear programming. Computational Mathematics and Mathematical Physics, 41(5), 638–648.
Pantic, M., Rothkrantz, L.J.M., 2000. Automatic analysis of facial expressions: The state of the art. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(12), 1424–1445.
Parsons, S., Dohnal, M., 1993. A semiqualitative approach to reasoning in probabilistic networks. Applied Artificial Intelligence, 7, 223–235.
Renooij, S., van der Gaag, L.C., 1999. Enhancing QPNs for trade-off resolution. In Conference on Uncertainty in Artificial Intelligence, 559–566.
Renooij, S., van der Gaag, L.C., 2000. Exploiting non-monotonic influences in qualitative belief networks. In International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems, 1285–1290, Madrid.
Renooij, S., van der Gaag, L.C., 2002. From qualitative to quantitative probabilistic networks. In Conference on Uncertainty in Artificial Intelligence, 422–429, Morgan Kaufmann Publishers, San Francisco.
Tong, Y., Liao, W., Ji, Q., 2007. Facial action unit recognition by exploiting their dynamic and semantic relationships. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1683–1699.
Walley, P., 1991. Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London.
Walley, P., 1996. Inferences from multinomial data: Learning about a bag of marbles. Journal of the Royal Statistical Society B, 58(1), 3–57.
Wellman, M.P., 1990. Fundamental concepts of qualitative probabilistic networks. Artificial Intelligence, 44(3), 257–303.
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de Campos, C.P., Zhang, L., Tong, Y. et al. Semi-Qualitative Probabilistic Networks in Computer Vision Problems. J Stat Theory Pract 3, 197–210 (2009). https://doi.org/10.1080/15598608.2009.10411920
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DOI: https://doi.org/10.1080/15598608.2009.10411920