scholarly journals Stochastic Approximation for Optimization in Shape Spaces

2021 ◽  
Vol 31 (1) ◽  
pp. 348-376
Author(s):  
Caroline Geiersbach ◽  
Estefania Loayza-Romero ◽  
Kathrin Welker
Keyword(s):  
Stochastic Approximation ◽  
Shape Spaces

scholarly journals Transporting Deformations of Face Emotions in the Shape Spaces: A Comparison of Different Approaches

2021 ◽  
Author(s):  
Paolo Piras ◽  
Valerio Varano ◽  
Maxime Louis ◽  
Antonio Profico ◽  
Stanley Durrleman ◽  
...  
Keyword(s):  
Computer Vision ◽  
Shape Change ◽  
Surface Matching ◽  
Human Face ◽  
Matching Algorithm ◽  
Mathematical Procedure ◽  
Shape Spaces ◽  
Diffeomorphic Deformation ◽  
Common Application ◽  
Scientific Fields

AbstractStudying 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.

scholarly journals An Introduction to Development of Centralized and Distributed Stochastic Approximation Algorithm with Expanding Truncations

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 174
Author(s):  
Wenxiao Zhao
Keyword(s):  
Approximation Algorithm ◽  
Stochastic Approximation ◽  
Probabilistic Method ◽  
Principal Component ◽  
Stochastic Approximation Algorithm ◽  
The Past ◽  
Systems And Control ◽  
Ode Method ◽  
Centralized Algorithm ◽  
And Control

The stochastic approximation algorithm (SAA), starting from the pioneer work by Robbins and Monro in 1950s, has been successfully applied in systems and control, statistics, machine learning, and so forth. In this paper, we will review the development of SAA in China, to be specific, the stochastic approximation algorithm with expanding truncations (SAAWET) developed by Han-Fu Chen and his colleagues during the past 35 years. We first review the historical development for the centralized algorithm including the probabilistic method (PM) and the ordinary differential equation (ODE) method for SAA and the trajectory-subsequence method for SAAWET. Then, we will give an application example of SAAWET to the recursive principal component analysis. We will also introduce the recent progress on SAAWET in a networked and distributed setting, named the distributed SAAWET (DSAAWET).

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