Training Bayesian networks for image segmentation

Xiaojuan Feng, Christopher K. I. Williams

    Research output: Unpublished contribution to conferenceUnpublished Conference Paperpeer-review


    We are concerned with the problem of image segmentation in which each pixel is assigned to one of a predefined finite number of classes. In Bayesian image analysis, this requires fusing together local predictions for the class labels with a prior model of segmentations. Markov Random Fields (MRFs) have been used to incorporate some of this prior knowledge, but this not entirely satisfactory as inference in MRFs is NP-hard. The multiscale quadtree model of Bouman and Shapiro (1994) is an attractive alternative, as this is a tree-structured belief network in which inference can be carried out in linear time (Pearl 1988). It is an hierarchical model where the bottom-level nodes are pixels, and higher levels correspond to downsampled versions of the image. The conditional-probability tables (CPTs) in the belief network encode the knowledge of how the levels interact. In this paper we discuss two methods of learning the CPTs given training data, using (a) maximum likelihood and the EM algorithm and (b) emphconditional maximum likelihood (CML). Segmentations obtained using networks trained by CML show a statistically-significant improvement in performance on synthetic images. We also demonstrate the methods on a real-world outdoor-scene segmentation task.
    Original languageEnglish
    Number of pages11
    Publication statusPublished - 24 Sept 1998
    EventProceedings of SPIE vol 3457 -
    Duration: 24 Sept 199824 Sept 1998


    OtherProceedings of SPIE vol 3457

    Bibliographical note

    Vol. 3457 DOI 10.1117/12.323459 Copyright Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic electronic or print reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.


    • Bayesian image analysis
    • image segmentation
    • Random Fields
    • quadtree model
    • Bouman and Shapiro
    • hierarchical model
    • conditional-probability tables
    • synthetic images
    • real-world
    • outdoor-scene
    • segmentation task


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