Journal article
ZerNet: Convolutional Neural Networks on Arbitrary Surfaces Via Zernike Local Tangent Space Estimation
Computer graphics forum, Vol.39(6), pp.204-216
09/2020
DOI: 10.1111/cgf.14012
Abstract
In this paper, we propose a novel formulation extending convolutional neural networks (CNN) to arbitrary two‐dimensional manifolds using orthogonal basis functions called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific trends and phenomena, where accurate numerical quantification of geometric features is critical. Recently, CNNs have demonstrated a substantial improvement in extracting and codifying geometric features. However, the progress is mostly centred around computer vision and its applications where an inherent grid‐like data representation is naturally present. In contrast, many geometry processing problems deal with curved surfaces and the application of CNNs is not trivial due to the lack of canonical grid‐like representation, the absence of globally consistent orientation and the incompatible local discretizations. In this paper, we show that the Zernike polynomials allow rigourous yet practical mathematical generalization of CNNs to arbitrary surfaces. We prove that the convolution of two functions can be represented as a simple dot product between Zernike coefficients and the rotation of a convolution kernel is essentially a set of 2 × 2 rotation matrices applied to the coefficients. The key contribution of this work is in such a computationally efficient but rigorous generalization of the major CNN building blocks.
In this paper, we propose a novel formulation extending convolutional neural networks (CNN) to arbitrary two‐dimensional manifolds using orthogonal basis functions called Zernike polynomials.
Details
- Title: Subtitle
- ZerNet: Convolutional Neural Networks on Arbitrary Surfaces Via Zernike Local Tangent Space Estimation
- Creators
- Zhiyu Sun - University of IowaEthan Rooke - University of IowaJerome Charton - University of IowaYusen He - University of IowaJia Lu - University of IowaStephen Baek - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Computer graphics forum, Vol.39(6), pp.204-216
- DOI
- 10.1111/cgf.14012
- ISSN
- 0167-7055
- eISSN
- 1467-8659
- Number of pages
- 13
- Language
- English
- Date published
- 09/2020
- Academic Unit
- Iowa Technology Institute; Industrial and Systems Engineering; Mechanical Engineering; Radiation Oncology
- Record Identifier
- 9984196631602771
Metrics
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