ZerNet: Convolutional Neural Networks on Arbitrary Surfaces Via Zernike Local Tangent Space Estimation

dc.contributor.authorSun, Zhiyuen_US
dc.contributor.authorRooke, Ethanen_US
dc.contributor.authorCharton, Jeromeen_US
dc.contributor.authorHe, Yusenen_US
dc.contributor.authorLu, Jiaen_US
dc.contributor.authorBaek, Stephenen_US
dc.contributor.editorBenes, Bedrich and Hauser, Helwigen_US
dc.description.abstractIn 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.en_US
dc.description.seriesinformationComputer Graphics Forum
dc.publisher© 2020 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltden_US
dc.subject3D shape matching
dc.subjectdatabases of geometric models/shape retrieval
dc.subjectcomputer vision ‐ shape recognition
dc.subjectmethods and applications
dc.titleZerNet: Convolutional Neural Networks on Arbitrary Surfaces Via Zernike Local Tangent Space Estimationen_US