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Wald's Sequential Analysis for Time-constrained Vision Problems

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Unifying Perspectives in Computational and Robot Vision

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 8))

In many decision problems in computer vision, both classification errors and time to decision characterise the quality of an algorithmic solution. This is especially true for applications of vision to robotics where real-time response is typically required.

Time-constrained classification, detection and matching problems can be often formalised in the framework of sequential decision-making. We show how to derive quasi-optimal time-constrained solutions for three different vision problems by applying Wald’s sequential analysis. In particular, we adapt and generalise Wald’s sequential probability ratio test (SPRT) and apply it to the three vision problems: (i) face detection, (ii) real-time detection of distinguished regions (interest points) and (iii) establishing correspondences by the RANSAC algorithm with application e.g. in SLAM, 3D reconstruction and object recognition.

In the face detection problem, we are interested in learning the fastest detector satisfying constraints on false positive and false negative rates.We solve the problem by WaldBoost [15], a combination of Wald’s sequential probability ratio test and AdaBoost learning [2]. The solution can be viewed as a principled way to build a close-to-optimal “cascade of classifiers” [22]. Naturally, the approach is applicable to other classes of objects.

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Authors and Affiliations

  1. Department of Cybernetics, Czech Technical University in Prague, 121 35, Prague, Czech Republic

    Jiří Matas & Jan Šochman

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  1. Jiří Matas
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  2. Jan Šochman
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Editors and Affiliations

  1. CSC – CAS/ CVAP, Royal Institute of Technology, 10044, Stockholm, Sweden

    Danica Kragic

  2. Department of Information Technology, Lappeenranta University of Technology, 20, 53851, Lappeenranta, Finland

    Ville Kyrki

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Matas, J., Šochman, J. (2008). Wald's Sequential Analysis for Time-constrained Vision Problems. In: Kragic, D., Kyrki, V. (eds) Unifying Perspectives in Computational and Robot Vision. Lecture Notes in Electrical Engineering, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-75523-6_5

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  • DOI: https://doi.org/10.1007/978-0-387-75523-6_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-75521-2

  • Online ISBN: 978-0-387-75523-6

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