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Welcome to Riemannian Computing in Computer Vision

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Riemannian Computing in Computer Vision

Abstract

The computer vision community has registered a strong progress over the last few years due to: (1) improved sensor technology, (2) increased computation power, and (3) sophisticated statistical tools. Another important innovation, albeit relatively less visible, has been the involvement of differential geometry in developing vision frameworks. Its importance stems from the fact that despite large sizes of vision data (images and videos), the actual interpretable variability lies on much lower-dimensional manifolds of observation spaces. Additionally, natural constraints in mathematical representations of variables and desired invariances in vision-related problems also lead to inferences on relevant nonlinear manifolds. Riemannian computing in computer vision (RCCV) is the scientific area that integrates tools from Riemannian geometry and statistics to develop theoretical and computational solutions in computer vision. Tools from RCCV has led to important developments in low-level feature extraction, mid-level object characterization, and high-level semantic interpretation of data. In this chapter we provide background material from differential geometry, examples of manifolds commonly encountered in vision applications, and a short summary of past and recent developments in RCCV. We also summarize and categorize contributions of the remaining chapters in this volume.

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Acknowledgements

The authors would like to acknowledge the support received from National Science Foundation grants #1320267 and #1319658 during the preparation of this edited volume.

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Authors and Affiliations

  1. Department of Statistics, Florida State University, Tallahassee, FL, USA

    Anuj Srivastava

  2. School of Arts, Media, Engineering & Electrical Engineering, Arizona State University, Tempe, AZ, USA

    Pavan K. Turaga

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  1. Anuj Srivastava
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  2. Pavan K. Turaga
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Correspondence to Anuj Srivastava .

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Editors and Affiliations

  1. Arizona State University, Tempe, Arizona, USA

    Pavan K. Turaga

  2. Florida State University, Tallahassee, Florida, USA

    Anuj Srivastava

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Srivastava, A., Turaga, P.K. (2016). Welcome to Riemannian Computing in Computer Vision. In: Turaga, P., Srivastava, A. (eds) Riemannian Computing in Computer Vision. Springer, Cham. https://doi.org/10.1007/978-3-319-22957-7_1

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  • DOI: https://doi.org/10.1007/978-3-319-22957-7_1

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