Abstract
Shape analysis of landmarks is a fundamental problem in computer vision and multimedia. We propose a family of metrics called Fubini-Study distances defined in the complex projective space based on the seminal work of Kendall [11] for metric learning to measure the similarity between shape representations which are modeled directly by the equivalence classes of the 2D landmark configurations. Experiments conducted on the face landmarks for facial expression recognition demonstrate the competitiveness of the proposed method with respect to state-of-the-art approaches. A comparison with the metric defined in the Euclidean space has also been explored, proving that the Fubini-Study metric is more effective and discriminative than the Euclidean metric in identifying facial deformation.
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Acknowledgements
The proposed work was supported by the French State, managed by the National Agency for Research (ANR) under the Investments for the future program with reference ANR-16-IDEX-0004 ULNE. And we thank Prof. J-C. Alvarez Paiva from University of Lille for fruitful discussions on the formulation of the distance between shapes in complex projective spaces.
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Wu, Y., Daoudi, M. (2022). Metric Learning on Complex Projective Spaces. In: Berretti, S., Su, GM. (eds) Smart Multimedia. ICSM 2022. Lecture Notes in Computer Science, vol 13497. Springer, Cham. https://doi.org/10.1007/978-3-031-22061-6_9
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