3D steerable CNNs: Learning rotationally equivariant features in volumetric data

Maurice Weiler; Mario Geiger; Max Welling; Wouter Boomsma; Taco Cohen

3D steerable CNNs: Learning rotationally equivariant features in volumetric data

Maurice Weiler, Mario Geiger, Max Welling, Wouter Boomsma, Taco Cohen

Department of Computer Science

31 Citations (Scopus)

Abstract

We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations. These SE(3)-equivariant convolutions utilize kernels which are parameterized as a linear combination of a complete steerable kernel basis, which is derived analytically in this paper. We prove that equivariant convolutions are the most general equivariant linear maps between fields over R³. Our experimental results confirm the effectiveness of 3D Steerable CNNs for the problem of amino acid propensity prediction and protein structure classification, both of which have inherent SE(3) symmetry.

Original language	English
Publication date	2018
Number of pages	12
Publication status	Published - 2018
Event	32nd Annual Conference on Neural Information Processing Systems - Montreal, Montreal, Canada Duration: 2 Dec 2018 → 8 Dec 2018 Conference number: 32 https://nips.cc/Conferences/2018

Conference

Conference	32nd Annual Conference on Neural Information Processing Systems
Number	32
Location	Montreal
Country/Territory	Canada
City	Montreal
Period	02/12/2018 → 08/12/2018
Internet address	https://nips.cc/Conferences/2018

Cite this

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title = "3D steerable CNNs: Learning rotationally equivariant features in volumetric data",

abstract = "We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations. These SE(3)-equivariant convolutions utilize kernels which are parameterized as a linear combination of a complete steerable kernel basis, which is derived analytically in this paper. We prove that equivariant convolutions are the most general equivariant linear maps between fields over R3. Our experimental results confirm the effectiveness of 3D Steerable CNNs for the problem of amino acid propensity prediction and protein structure classification, both of which have inherent SE(3) symmetry.",

author = "Maurice Weiler and Mario Geiger and Max Welling and Wouter Boomsma and Taco Cohen",

year = "2018",

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note = "32nd Annual Conference on Neural Information Processing Systems, NeurIPS ; Conference date: 02-12-2018 Through 08-12-2018",

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T1 - 3D steerable CNNs: Learning rotationally equivariant features in volumetric data

AU - Weiler, Maurice

AU - Geiger, Mario

AU - Welling, Max

AU - Boomsma, Wouter

AU - Cohen, Taco

N1 - Conference code: 32

PY - 2018

Y1 - 2018

N2 - We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations. These SE(3)-equivariant convolutions utilize kernels which are parameterized as a linear combination of a complete steerable kernel basis, which is derived analytically in this paper. We prove that equivariant convolutions are the most general equivariant linear maps between fields over R3. Our experimental results confirm the effectiveness of 3D Steerable CNNs for the problem of amino acid propensity prediction and protein structure classification, both of which have inherent SE(3) symmetry.

AB - We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations. These SE(3)-equivariant convolutions utilize kernels which are parameterized as a linear combination of a complete steerable kernel basis, which is derived analytically in this paper. We prove that equivariant convolutions are the most general equivariant linear maps between fields over R3. Our experimental results confirm the effectiveness of 3D Steerable CNNs for the problem of amino acid propensity prediction and protein structure classification, both of which have inherent SE(3) symmetry.

UR - http://www.mendeley.com/research/3d-steerable-cnns-learning-rotationally-equivariant-features-volumetric-data

M3 - Paper

T2 - 32nd Annual Conference on Neural Information Processing Systems

Y2 - 2 December 2018 through 8 December 2018

ER -

3D steerable CNNs: Learning rotationally equivariant features in volumetric data

Abstract

Conference

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