Belief Function Definition for Ensemble Methods - Application to Pedestrian Detection in Dense Crowds

Vandoni, Jennifer; Hegarar-Mascle, Sylvie Le; Aldea, Emanuel · 2018 · Crossref

DOI: 10.23919/icif.2018.8455313

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Summary

This paper addresses the challenge of pedestrian detection in high-density crowd scenes, where factors such as heavy occlusion, visual homogeneity, and small target sizes render standard detectors ineffective. The authors propose an ensemble method using the belief function framework to fuse outputs from multiple Support Vector Machine (SVM) detectors based on distinct visual descriptors, including Histogram of Oriented Gradients (HOG), Local Binary Patterns (LBP), and DAISY. The primary motivation is to handle two specific sources of imprecision: uncertainty in the calibration of SVM decision scores and spatial uncertainty arising from the proximity of pixels in crowded images. The methodology defines Basic Belief Assignments (BBAs) to model these imprecisions. First, the authors address calibration imprecision by deriving BBAs from SVM scores using a calibrated logistic sigmoid function. Instead of assigning a single probability, they apply mathematical morphology erosion and dilation in the score space to generate lower (Belief) and upper (Plausibility) bounds, effectively modeling the uncertainty of the calibration parameters. Second, they address spatial imprecision by applying morphological opening operations in the image domain to account for neighborhood consistency. The core contribution is a combined BBA allocation strategy that integrates both score-space and image-space imprecision into a single robust assignment, rather than treating them separately. These BBAs from multiple detectors are then combined using the conjunctive rule, and decisions are made via pignistic probability. Experiments were conducted on difficult high-density crowd images acquired during the Muslim pilgrimage in Makkah. The results demonstrate that the proposed combined fusion algorithm, which accounts for both calibration and spatial imprecision, outperforms approaches that consider only individual sources of imprecision. Specifically, the combined method yields better detection performance than strategies relying solely on score-space calibration or spatial neighborhood analysis. The study confirms that explicitly modeling the dual nature of imprecision in crowded scenes leads to more robust pedestrian detection compared to standard probabilistic fusion or simple concatenation of features. The significance of this work lies in its application of evidence theory to improve ensemble methods in challenging surveillance contexts. By providing a formal mechanism to handle both parametric uncertainty in classifier calibration and spatial ambiguity in dense crowds, the paper offers a more reliable framework for pedestrian detection than traditional methods. This approach is particularly relevant for safety-critical applications in large-scale social events where accurate detection is hindered by clutter and occlusion.

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• signal detection theory