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Bayesian object recognition with baddeley's delta loss

Part of: Inference from stochastic processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Håvard Rue  and
Anne Randi Syversveen
Håvard Rue*
Affiliation:
Norwegian University of Science and Technology
Anne Randi Syversveen*
Affiliation:
Norwegian University of Science and Technology
*
∗ Postal address: Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7034 Trondheim, Norway.
∗ Postal address: Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7034 Trondheim, Norway.
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Abstract

A common problem in Bayesian object recognition using marked point process models is to produce a point estimate of the true underlying object configuration: the number of objects and the size, location and shape of each object. We use decision theory and the concept of loss functions to design a more reasonable estimator for this purpose, rather than using the common zero-one loss corresponding to the maximum a posteriori estimator. We propose to use the squared Δ-metric of Baddeley (1992) as our loss function and demonstrate that the corresponding optimal Bayesian estimator can be well approximated by combining Markov chain Monte Carlo methods with simulated annealing into a two-step algorithm. The proposed loss function is tested using a marked point process model developed for locating cells in confocal microscopy images.

Keywords

Bayesian inferenceunsymmetric loss functionsobject recognitiontemplate modelsMarkov chain Monte Carlo methodsmarked point processesdistance between imagesconfocal microscopy images

MSC classification

Primary: 62M30: Spatial processes
Secondary: 60G35: Signal detection and filtering
Type
Stochatic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 30 , Issue 1 , March 1998 , pp. 64 - 84
Copyright
Copyright © Applied Probability Trust 1998 

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References

Amit, Y., Grenander, U. and Piccioni, M. (1991). Structural image restoration through deformable templates. J. Amer. Statist. Assoc. 86, 376–387.Google Scholar
Baddeley, A. J. (1992). Errors in binary images and a Lp version of the Hausdorff metric. Nie. Arch. Wisk. 10, 157–183.Google Scholar
Baddeley, A. J. (1994). Contribution to the discussion of paper by Grenander and Miller (1994). J. R. Statist. Soc. B 56, 584–585.Google Scholar
Baddeley, A. J. and Möller, J. (1989). Nearest-neighbour Markov point processes and random sets. Int. Statist. Rev. 57, 89–121.Google Scholar
Baddeley, A. J. and Van Lieshout, M. N. M. (1991). Recognition of overlapping objects using Markov spatial processes. Research report BS-R9109. CWI, Amsterdam.Google Scholar
Baddeley, A. J. and Van Lieshout, M. N. M. (1993). Stochastic geometry models in high-level vision. In Statistics and Images. ed. Mardia, K. V. and Kanji, G. K., Vol. 20, Ch. 11. Carfax, Abingdon. pp. 235–256.Google Scholar
Besag, J., Green, P., Higdon, D. and Mengersen, K. (1995). Bayesian computation and stochastic systems (with discussion). Statist. Sci. 10, 3–66.Google Scholar
Borgefors, G. (1986). Distance transformations in digital images. Comp. Vis. Graph. Image Proc. 34, 344–371.CrossRefGoogle Scholar
Frigessi, A. and Rue, H. (1997). Bayesian image classification with Baddeley's delta loss. J. Comp. Graph. Statist. 6, 55–73.Google Scholar
Geman, S., Geman, D., Graffigne, C. and Dong, P. (1990). Boundary detection by constrained optimization. IEEE Trans. Pattern Anal. Machine Intell. 12, 609–628.Google Scholar
Geyer, C. (1996). Likelihood inference for spatial point processes. In Proc. Seminaire Européen de Statistique Tolouse 1996, Stochastic Geometry: Theory and Applications. ed. Kendall, W. S.. Springer, Berlin.Google Scholar
Geyer, C. J. and Möller, J. (1994). Simulation procedures and likelihood inference for spatial point processes. Scand. J. Statist. 21, 359–373.Google Scholar
Green, P. J. (1995). Reversible jump MCMC computation and Bayesian model determination. Biometrika 82, 711–732.Google Scholar
Grenander, U. (1993). General Pattern Theory. Oxford University Press, Oxford.Google Scholar
Grenander, U., Chow, Y. and Keenan, D. M. (1991). Hands: A Pattern Theoretic Study of Biological Shapes. Research Notes on Neural Computing. Springer, Berlin.Google Scholar
Grenander, U. and Manbeck, K. M. (1993). A stochastic model for defect detection in potatos. J. Comp. Graph. Statist. 2, 131–151.Google Scholar
Grenander, U. and Miller, M. I. (1994). Representations of knowledge in complex systems (with discussion). J. R. Statist. Soc. B 56, 549–603.Google Scholar
Hastings, W. K. (1970). Monte Carlo simulation methods using Markov chains and their applications. Biometrika 57, 97–109.Google Scholar
Phillips, D. B. and Smith, A. F. M. (1994). Bayesian faces via hierarchical template modeling. J. Amer. Statist. Assoc. 89, 1151–1163.CrossRefGoogle Scholar
Ripley, B. D. and Sutherland, A. I. (1990). Finding spiral structures in images of galaxies. Phil. Trans. R. Soc. A 332, 477–485.Google Scholar
Rue, H. (1995). New loss functions in Bayesian imaging. J. Amer. Statist. Assoc. 90, 900–908.CrossRefGoogle Scholar
Rue, H. (1997). A loss function model for the restoration of grey level images. Scand. J. Statist. 24, 103–114.Google Scholar
Serra, J. (1982). Image Analysis and Mathematical Morphology. Academic Press, New York.Google Scholar
Tierney, L. (1994). Markov chains for exploring posterior distributions (with discussion). Ann. Statist. 22, 1701–1762.Google Scholar
van Lieshout, M. N. M. (1994). Stochastic annealing for nearest-neighbour point processes with application to object recognition. Adv. Appl. Prob. 26, 281–300.Google Scholar
van Lieshout, M. N. M. (1995). Markov point processes and their applications in high-level imaging (with discussion). Bull. Int. Statist. Inst. LVI, 559–576.Google Scholar