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Definition and Estimation of Dimension in Facial Expression Space

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Human-Computer Interaction. Theory, Methods and Tools (HCII 2021)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12762))

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Abstract

It has recently been shown that the facial expression space as a psychophysical image space is a Riemann space where the metric tensor is defined by the JND (Just-Noticeable-Difference) discrimination thresholds at every point in the space. The major obstacle to understand this space is how to estimate the metric tensor in high dimensions which requires an inaccessible number of psychophysical experiments. In this paper we address two fundamental issues: methods to estimate the Riemann metric tensor in a high dimensional space and how to define and to determine the effective dimensions of Riemann spaces and psychophysical spaces. We introduce new definitions for these dimensions and novel algorithms for estimating the high dimensional Riemann metric tensor and for dimension reduction to low dimensional subspaces. We then apply these algorithms to the facial expressions space. The Riemann metric tensor of the high dimensional facial expression space is estimated from psychophysical measurements of JND data. We apply these methods to investigate the facial expression space. We describe our experiments to estimate the effective dimension (together with upper and lower bounds) of Riemann manifolds and psychophysical spaces.

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Acknowledgment

This research is supported by the MIC/SCOPE #181603006.

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Authors and Affiliations

  1. Department of Information and System Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo, Tokyo, Japan

    Masashi Shinto & Jinhui Chao

  2. The Institute of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo, Tokyo, Japan

    Reiner Lenz

Authors
  1. Masashi Shinto
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  2. Reiner Lenz
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  3. Jinhui Chao
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Corresponding author

Correspondence to Jinhui Chao .

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Editors and Affiliations

  1. The Open University of Japan, Chiba, Japan

    Masaaki Kurosu

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Shinto, M., Lenz, R., Chao, J. (2021). Definition and Estimation of Dimension in Facial Expression Space. In: Kurosu, M. (eds) Human-Computer Interaction. Theory, Methods and Tools. HCII 2021. Lecture Notes in Computer Science(), vol 12762. Springer, Cham. https://doi.org/10.1007/978-3-030-78462-1_47

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  • DOI: https://doi.org/10.1007/978-3-030-78462-1_47

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-78461-4

  • Online ISBN: 978-3-030-78462-1

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