Differential Geometry in Computer Vision and Machine Learning

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About this Research Topic

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Background

Traditional machine learning, pattern recognition and data analysis methods often assume that input data can be represented well by elements of Euclidean space. While this assumption has worked well for many past applications, researchers have increasingly realized that most data in vision and pattern recognition is intrinsically non-Euclidean, i.e. standard Euclidean calculus does not apply. The exploitation of this geometrical information can lead to more accurate representation of the inherent structure of the data, better algorithms and better performance in practical applications. Riemannian geometric and topological computing are becoming increasingly popular in the computer vision and machine learning communities. Besides nice mathematical formulations, Riemannian computations based on the geometry of underlying manifolds are often faster and more stable than their classical, Euclidean counterparts. This Research Topic focuses on both advances in geometric methods and its diverse applications of broad interest.

The goal of this Research Topic is to invite papers that advance both methodological approaches rooted in geometry, as well as application papers that throw light on the utility of these methods for applications of interest in computer vision, robotics, health analytics, and scientific applications. We encourage both theory papers as well as applied papers, and particularly encourage interdisciplinary and collaborative work across disciplines.

Topics of interest include, but are not limited to:
• Deep learning and geometry
• Riemannian methods in computer vision
• Statistical shape analysis: detection, estimation, and inference
• Statistical analysis on manifolds
• Manifold-valued features and learning
• Machine learning on nonlinear manifolds
• Shape detection, tracking, and retrieval
• Topological methods in structure analysis
• Functional Data Analysis: Hilbert manifolds, Visualization
• Applications: medical imaging and analysis, graphics, biometrics, activity recognition, bioinformatics, etc.

Keywords: Differential geometry, topological data analysis, deep learning, time-series modeling

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