Fast 3D Modeling with Approximated Convolutional Kernels

Vitor Guizilini, Fabio Ramos
Proceedings of The 2nd Conference on Robot Learning, PMLR 87:190-199, 2018.

Abstract

This paper introduces a novel regression methodology for 3D reconstruction, with applications in robotics tasks such as terrain modeling and implicit surface calculation. The proposed methodology is based on projections into a high-dimensional space, that is able to fit arbitrarily complex data as a continuous function using a series of kernel evaluations within a linear regression model. We avoid direct kernel calculation by employing a novel sparse random Fourier feature vector, that approximates any shift-invariant kernel as a series of dot products relative to a set of inducing points placed throughout the input space. The varying properties of these inducing points produce non-stationarity in the resulting model, and can be jointly learned alongside linear regression weights. Furthermore, we show how convolution with arbitrary kernels can be performed directly in this high-dimensional continuous space, by training a neural network to learn the Fourier transform of the convolutional output based on information from the input kernels. Experimental results in terrain modeling and implicit surface calculation show that the proposed framework is able to outperform similar techniques in terms of computational speed without sacrificing accuracy, while enabling efficient convolution with arbitrary kernels for tasks such as global localization and template matching within these applications.

Cite this Paper


BibTeX
@InProceedings{pmlr-v87-guizilini18a, title = {Fast 3D Modeling with Approximated Convolutional Kernels}, author = {Guizilini, Vitor and Ramos, Fabio}, booktitle = {Proceedings of The 2nd Conference on Robot Learning}, pages = {190--199}, year = {2018}, editor = {Billard, Aude and Dragan, Anca and Peters, Jan and Morimoto, Jun}, volume = {87}, series = {Proceedings of Machine Learning Research}, month = {29--31 Oct}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v87/guizilini18a/guizilini18a.pdf}, url = {https://proceedings.mlr.press/v87/guizilini18a.html}, abstract = {This paper introduces a novel regression methodology for 3D reconstruction, with applications in robotics tasks such as terrain modeling and implicit surface calculation. The proposed methodology is based on projections into a high-dimensional space, that is able to fit arbitrarily complex data as a continuous function using a series of kernel evaluations within a linear regression model. We avoid direct kernel calculation by employing a novel sparse random Fourier feature vector, that approximates any shift-invariant kernel as a series of dot products relative to a set of inducing points placed throughout the input space. The varying properties of these inducing points produce non-stationarity in the resulting model, and can be jointly learned alongside linear regression weights. Furthermore, we show how convolution with arbitrary kernels can be performed directly in this high-dimensional continuous space, by training a neural network to learn the Fourier transform of the convolutional output based on information from the input kernels. Experimental results in terrain modeling and implicit surface calculation show that the proposed framework is able to outperform similar techniques in terms of computational speed without sacrificing accuracy, while enabling efficient convolution with arbitrary kernels for tasks such as global localization and template matching within these applications. } }
Endnote
%0 Conference Paper %T Fast 3D Modeling with Approximated Convolutional Kernels %A Vitor Guizilini %A Fabio Ramos %B Proceedings of The 2nd Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2018 %E Aude Billard %E Anca Dragan %E Jan Peters %E Jun Morimoto %F pmlr-v87-guizilini18a %I PMLR %P 190--199 %U https://proceedings.mlr.press/v87/guizilini18a.html %V 87 %X This paper introduces a novel regression methodology for 3D reconstruction, with applications in robotics tasks such as terrain modeling and implicit surface calculation. The proposed methodology is based on projections into a high-dimensional space, that is able to fit arbitrarily complex data as a continuous function using a series of kernel evaluations within a linear regression model. We avoid direct kernel calculation by employing a novel sparse random Fourier feature vector, that approximates any shift-invariant kernel as a series of dot products relative to a set of inducing points placed throughout the input space. The varying properties of these inducing points produce non-stationarity in the resulting model, and can be jointly learned alongside linear regression weights. Furthermore, we show how convolution with arbitrary kernels can be performed directly in this high-dimensional continuous space, by training a neural network to learn the Fourier transform of the convolutional output based on information from the input kernels. Experimental results in terrain modeling and implicit surface calculation show that the proposed framework is able to outperform similar techniques in terms of computational speed without sacrificing accuracy, while enabling efficient convolution with arbitrary kernels for tasks such as global localization and template matching within these applications.
APA
Guizilini, V. & Ramos, F.. (2018). Fast 3D Modeling with Approximated Convolutional Kernels. Proceedings of The 2nd Conference on Robot Learning, in Proceedings of Machine Learning Research 87:190-199 Available from https://proceedings.mlr.press/v87/guizilini18a.html.

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