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Bi-capacity Choquet Integral for Sensor Fusion with Label Uncertainty

Hersh Vakharia, Xiaoxiao Du

TL;DR

A novel Choquet integral-based fusion framework, named Bi-MIChI (pronounced “bi-mi-kee”), which uses bi-capacities to represent the interactions between pairs of subsets of the input sensor sources on a bi-polar scale, which allows for extended non-linear interactions between the sensor sources and can lead to interesting fusion results.

Abstract

Sensor fusion combines data from multiple sensor sources to improve reliability, robustness, and accuracy of data interpretation. The Fuzzy Integral (FI), in particular, the Choquet integral (ChI), is often used as a powerful nonlinear aggregator for fusion across multiple sensors. However, existing supervised ChI learning algorithms typically require precise training labels for each input data point, which can be difficult or impossible to obtain. Additionally, prior work on ChI fusion is often based only on the normalized fuzzy measures, which bounds the fuzzy measure values between [0, 1]. This can be limiting in cases where the underlying scales of input data sources are bipolar (i.e., between [-1, 1]). To address these challenges, this paper proposes a novel Choquet integral-based fusion framework, named Bi-MIChI (pronounced "bi-mi-kee"), which uses bi-capacities to represent the interactions between pairs of subsets of the input sensor sources on a bi-polar scale. This allows for extended non-linear interactions between the sensor sources and can lead to interesting fusion results. Bi-MIChI also addresses label uncertainty through Multiple Instance Learning, where training labels are applied to "bags" (sets) of data instead of per-instance. Our proposed Bi-MIChI framework shows effective classification and detection performance on both synthetic and real-world experiments for sensor fusion with label uncertainty. We also provide detailed analyses on the behavior of the fuzzy measures to demonstrate our fusion process.

Bi-capacity Choquet Integral for Sensor Fusion with Label Uncertainty

TL;DR

A novel Choquet integral-based fusion framework, named Bi-MIChI (pronounced “bi-mi-kee”), which uses bi-capacities to represent the interactions between pairs of subsets of the input sensor sources on a bi-polar scale, which allows for extended non-linear interactions between the sensor sources and can lead to interesting fusion results.

Abstract

Sensor fusion combines data from multiple sensor sources to improve reliability, robustness, and accuracy of data interpretation. The Fuzzy Integral (FI), in particular, the Choquet integral (ChI), is often used as a powerful nonlinear aggregator for fusion across multiple sensors. However, existing supervised ChI learning algorithms typically require precise training labels for each input data point, which can be difficult or impossible to obtain. Additionally, prior work on ChI fusion is often based only on the normalized fuzzy measures, which bounds the fuzzy measure values between [0, 1]. This can be limiting in cases where the underlying scales of input data sources are bipolar (i.e., between [-1, 1]). To address these challenges, this paper proposes a novel Choquet integral-based fusion framework, named Bi-MIChI (pronounced "bi-mi-kee"), which uses bi-capacities to represent the interactions between pairs of subsets of the input sensor sources on a bi-polar scale. This allows for extended non-linear interactions between the sensor sources and can lead to interesting fusion results. Bi-MIChI also addresses label uncertainty through Multiple Instance Learning, where training labels are applied to "bags" (sets) of data instead of per-instance. Our proposed Bi-MIChI framework shows effective classification and detection performance on both synthetic and real-world experiments for sensor fusion with label uncertainty. We also provide detailed analyses on the behavior of the fuzzy measures to demonstrate our fusion process.
Paper Structure (17 sections, 7 equations, 7 figures, 7 tables, 1 algorithm)

This paper contains 17 sections, 7 equations, 7 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Bi-capacity & Choquet Integral Applications
  4. Multiple Instance Learning
  5. Multiple Instance Choquet Integral
  6. Bi-capacity ChI Definitions
  7. The Proposed Bi-MIChI
  8. Objective Function 1: without $\mathbf{g}_{\emptyset, \emptyset}=0$
  9. Objective Function 2: with $\mathbf{g}_{\emptyset, \emptyset}=0$
  10. Optimization Algorithm
  11. Experiments
  12. Synthetic Dataset
  13. Simulated Experiment 1 with Bipolar Labels
  14. Simulated Experiment 2 with $[0,1]$ Labels
  15. Low-Light Pedestrian Detection
  16. ...and 2 more sections

Figures (7)

  • Figure 1: Illustration of bi-capacity element relationships given three sources. Red shows an example path of monotonicity.
  • Figure 2: Flowchart for the Bi-MIChI algorithm.
  • Figure 3: Colorbar for experimental results.
  • Figure 4: The Synthetic Experiment results. (a)-(c) are the sources for fusion, (d) shows positive bags in green and negative bags in red, (e) shows the ground truth on the bipolar scale, and (e) shows the fusion result of our Bi-MIChI using objective function 1. (g) shows the ground truth where the non-negative is neutral (label 0). (h) shows the fusion results of our Bi-MIChI using objective function 2, but without the absolute value on the Bi-capacity Choquet term in Eq. \ref{['eq:j_plus_new']}. (i) shows the fusion results of our Bi-MIChI using the complete objective function 2. All images follow the colorbar in Fig. \ref{['fig:colorbar']}.
  • Figure 5: KAIST Pedestrian RGB and thermal image pair with ground truth bounding boxes. The images containing the green boxes are over exposed for easier viewing.
  • ...and 2 more figures