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Minimal Free Space Constraints for Implicit Distance Bounds

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Advances in Visual Computing (ISVC 2020)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12510))

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Abstract

A general approach for fitting implicit models to sensor data is to optimize an objective function measuring the quality of the fit. The objective function often involves evaluating the model’s implicit function at several points in space. When the model is expensive to evaluate, the number of points can become a bottleneck, making the use of volumetric information, such as free space constraints, challenging. When the model is the Euclidean distance function to its surface, previous work has been able to integrate free space constraints in the optimization problem, such that the number of distance computations is linear in the scene’s surface area. Here, we extend this work to only require the model’s implicit function to be a bound of the Euclidean distance. We derive necessary and sufficient conditions for the model to be consistent with free space. We validate the correctness of the derived constraints on implicit model fitting problems that benefit from the use of free space constraints.

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Acknowledgments

This work is partly supported by the Research Council of Norway through the Centre of Excellence funding scheme, project number 223254, NTNU AMOS.

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Authors and Affiliations

  1. Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway

    Simen Haugo & Annette Stahl

Authors
  1. Simen Haugo
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  2. Annette Stahl
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Corresponding author

Correspondence to Simen Haugo .

Editor information

Editors and Affiliations

  1. University of Nevada Reno, Reno, NV, USA

    George Bebis

  2. Stony Brook University, Stony Brook, NY, USA

    Zhaozheng Yin

  3. Drexel University, Philadelphia, PA, USA

    Edward Kim

  4. RWTH Aachen University, Aachen, Germany

    Jan Bender

  5. University of Edinburgh, Edinburgh, UK

    Kartic Subr

  6. IBM Research – Cambridge, Cambridge, MA, USA

    Bum Chul Kwon

  7. University of Waterloo, Waterloo, ON, Canada

    Jian Zhao

  8. Graz University of Technology, Graz, Austria

    Denis Kalkofen

  9. The Hong Kong Polytechnic University, Hong Kong, Hong Kong

    George Baciu

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Haugo, S., Stahl, A. (2020). Minimal Free Space Constraints for Implicit Distance Bounds. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2020. Lecture Notes in Computer Science(), vol 12510. Springer, Cham. https://doi.org/10.1007/978-3-030-64559-5_8

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  • DOI: https://doi.org/10.1007/978-3-030-64559-5_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-64558-8

  • Online ISBN: 978-3-030-64559-5

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