Transporting Deformations of Face Emotions in the Shape Spaces: A Comparison of Different Approaches |
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Authors: | Piras Paolo Varano Valerio Louis Maxime Profico Antonio Durrleman Stanley Charlier Benjamin Milicchio Franco Teresi Luciano |
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Affiliation: | 1.Department of Cardiovascular, Respiratory, Nephrological and Geriatric Sciences, Sapienza University, Rome, Italy ;2.Department of Architecture, Roma Tre University, Rome, Italy ;3.Institut du Cerveau et de la Moelle (ICM), CNRS, Inserm, UPMC Université Paris 06, Sorbonne Université, Paris, France ;4.Inria Paris, Aramis Project-Team, Paris, 75013, France ;5.Dipartimento di Biologia Ambientale, Sapienza Università di Roma, Rome, Italy ;6.Institut Montpelliérain Alexander Grothendieck, CNRS, Université Montpellier, Montpellier, France ;7.Department of Engineering, Roma Tre University, Rome, Italy ;8.Department of Mathematics and Physics, Roma Tre University, Rome, Italy ; |
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Abstract: | Studying the changes of shape is a common concern in many scientific fields. We address here two problems: (1) quantifying the deformation between two given shapes and (2) transporting this deformation to morph a third shape. These operations can be done with or without point correspondence, depending on the availability of a surface matching algorithm, and on the type of mathematical procedure adopted. In computer vision, the re-targeting of emotions mapped on faces is a common application. We contrast here four different methods used for transporting the deformation toward a target once it was estimated upon the matching of two shapes. These methods come from very different fields such as computational anatomy, computer vision and biology. We used the large diffeomorphic deformation metric mapping and thin plate spline, in order to estimate deformations in a deformational trajectory of a human face experiencing different emotions. Then we use naive transport (NT), linear shift (LS), direct transport (DT) and fanning scheme (FS) to transport the estimated deformations toward four alien faces constituted by 240 homologous points and identifying a triangulation structure of 416 triangles. We used both local and global criteria for evaluating the performance of the 4 methods, e.g., the maintenance of the original deformation. We found DT, LS and FS very effective in recovering the original deformation while NT fails under several aspects in transporting the shape change. As the best method may differ depending on the application, we recommend carefully testing different methods in order to choose the best one for any specific application. |
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