Deep RBFNet: Point Cloud Feature Learning using Radial Basis Functions

Three-dimensional object recognition has recently achieved great progress thanks to the development of effective point cloud-based learning frameworks, such as PointNet and its extensions. However, existing methods rely heavily on fully connected layers, which introduce a significant amount of parameters, making the network harder to train and prone to overfitting problems. In this paper, we propose a simple yet effective framework for point set feature learning by leveraging a nonlinear activation layer encoded by Radial Basis Function (RBF) kernels. Unlike PointNet variants, that fail to recognize local point patterns, our approach explicitly models the spatial distribution of point clouds by aggregating features from sparsely distributed RBF kernels. A typical RBF kernel, e.g. Gaussian function, naturally penalizes long-distance response and is only activated by neighboring points. Such localized response generates highly discriminative features given different point distributions. In addition, our framework allows the joint optimization of kernel distribution and its receptive field, automatically evolving kernel configurations in an end-to-end manner. We demonstrate that the proposed network with a single RBF layer can outperform the state-of-the-art Pointnet++ in terms of classification accuracy for 3D object recognition tasks. Moreover, the introduction of nonlinear mappings significantly reduces the number of network parameters and computational cost, enabling significantly faster training and a deployable point cloud recognition solution on portable devices with limited resources.

[1]  Jianxiong Xiao,et al.  3D ShapeNets: A deep representation for volumetric shapes , 2014, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[2]  Martín Abadi,et al.  TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems , 2016, ArXiv.

[3]  Victor S. Lempitsky,et al.  Escape from Cells: Deep Kd-Networks for the Recognition of 3D Point Cloud Models , 2017, 2017 IEEE International Conference on Computer Vision (ICCV).

[4]  Hui Wang,et al.  Using Radial Basis Function Networks for Function Approximation and Classification , 2012 .

[5]  Li Yi,et al.  GeoNet: Deep Geodesic Networks for Point Cloud Analysis , 2019, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[6]  Nikos Komodakis,et al.  Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs , 2017, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[7]  Subhransu Maji,et al.  Multi-view Convolutional Neural Networks for 3D Shape Recognition , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[8]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[9]  A. Ben Hamza,et al.  Geodesic Object Representation and Recognition , 2003, DGCI.

[10]  D. Broomhead,et al.  Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

[11]  Leonidas J. Guibas,et al.  PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation , 2016, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[12]  Leonidas J. Guibas,et al.  PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space , 2017, NIPS.

[13]  Gernot Riegler,et al.  OctNet: Learning Deep 3D Representations at High Resolutions , 2016, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[14]  Gholam Ali Montazer,et al.  Radial Basis Function Neural Networks : A Review , 2018 .

[15]  Sebastian Scherer,et al.  VoxNet: A 3D Convolutional Neural Network for real-time object recognition , 2015, 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[16]  Meng Joo Er,et al.  Face recognition with radial basis function (RBF) neural networks , 2002, IEEE Trans. Neural Networks.

[17]  John Mark,et al.  Introduction to radial basis function networks , 1996 .

[18]  Leonidas J. Guibas,et al.  Volumetric and Multi-view CNNs for Object Classification on 3D Data , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[19]  Haibin Ling,et al.  Shape Classification Using the Inner-Distance , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  Richard K. Beatson,et al.  Reconstruction and representation of 3D objects with radial basis functions , 2001, SIGGRAPH.

[21]  Alexander J. Smola,et al.  Deep Sets , 2017, 1703.06114.

[22]  Yoshua Bengio,et al.  Gradient-based learning applied to document recognition , 1998, Proc. IEEE.

[23]  Yang Liu,et al.  O-CNN , 2017, ACM Trans. Graph..

[24]  P. S. Lewis,et al.  Function approximation and time series prediction with neural networks , 1990, 1990 IJCNN International Joint Conference on Neural Networks.

[25]  Leonidas J. Guibas,et al.  FPNN: Field Probing Neural Networks for 3D Data , 2016, NIPS.

[26]  Bernard Chazelle,et al.  Shape distributions , 2002, TOGS.