# MKConv: Multidimensional Feature Representation for Point Cloud Analysis

arXiv: https://arxiv.org/abs/2107.12655 · HTML: https://mlsanity.com/paper/2107.12655/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 42 references that are in the map.
- First posted on arXiv 27 Jul 2021.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [3D Semantic Segmentation with Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1711.10275/) (2017)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Relation-Shape Convolutional Neural Network for Point Cloud Analysis](https://mlsanity.com/paper/1904.07601/) (2019)
- [SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filters](https://mlsanity.com/paper/1803.11527/) (2018)
- [PointASNL: Robust Point Clouds Processing using Nonlocal Neural Networks with Adaptive Sampling](https://mlsanity.com/paper/2003.00492/) (2020)
- [SqueezeSegV2: Improved Model Structure and Unsupervised Domain Adaptation for Road-Object Segmentation from a LiDAR Point Cloud](https://mlsanity.com/paper/1809.08495/) (2018)
- [PAConv: Position Adaptive Convolution with Dynamic Kernel Assembling on Point Clouds](https://mlsanity.com/paper/2103.14635/) (2021)
- [SO-Net: Self-Organizing Network for Point Cloud Analysis](https://mlsanity.com/paper/1803.04249/) (2018)
- [SEGCloud: Semantic Segmentation of 3D Point Clouds](https://mlsanity.com/paper/1710.07563/) (2017)
- [SPLATNet: Sparse Lattice Networks for Point Cloud Processing](https://mlsanity.com/paper/1802.08275/) (2018)
- [Escape from Cells: Deep Kd-Networks for the Recognition of 3D Point Cloud Models](https://mlsanity.com/paper/1704.01222/) (2017)
- [ShellNet: Efficient Point Cloud Convolutional Neural Networks using Concentric Shells Statistics](https://mlsanity.com/paper/1908.06295/) (2019)
- [DensePoint: Learning Densely Contextual Representation for Efficient Point Cloud Processing](https://mlsanity.com/paper/1909.03669/) (2019)
- [Interpolated Convolutional Networks for 3D Point Cloud Understanding](https://mlsanity.com/paper/1908.04512/) (2019)
- [Monte Carlo Convolution for Learning on Non-Uniformly Sampled Point Clouds](https://mlsanity.com/paper/1806.01759/) (2018)
- [ConvPoint: Continuous Convolutions for Point Cloud Processing](https://mlsanity.com/paper/1904.02375/) (2019)
- [PointSIFT: A SIFT-like Network Module for 3D Point Cloud Semantic Segmentation](https://mlsanity.com/paper/1807.00652/) (2018)
- [FPConv: Learning Local Flattening for Point Convolution](https://mlsanity.com/paper/2002.10701/) (2020)

## Built on by (most cited first, 6 of 6)

- [Point Cloud Pre-training with Diffusion Models](https://mlsanity.com/paper/2311.14960/) (2023)
- [Advancements in Point Cloud Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2308.12113/) (2023)
- [Joint Representation Learning for Text and 3D Point Cloud](https://mlsanity.com/paper/2301.07584/) (2023)
- [LATFormer: Locality-Aware Point-View Fusion Transformer for 3D Shape Recognition](https://mlsanity.com/paper/2109.01291/) (2021)
- [Composite Convolution: a Flexible Operator for Deep Learning on 3D Point Clouds](https://mlsanity.com/paper/2209.11796/) (2022)
- [Small but Mighty: Enhancing 3D Point Clouds Semantic Segmentation with U-Next Framework](https://mlsanity.com/paper/2304.00749/) (2023)

## Abstract (arXiv)

Despite the remarkable success of deep learning, an optimal convolution operation on point clouds remains elusive owing to their irregular data structure. Existing methods mainly focus on designing an effective continuous kernel function that can handle an arbitrary point in continuous space. Various approaches exhibiting high performance have been proposed, but we observe that the standard pointwise feature is represented by 1D channels and can become more informative when its representation involves additional spatial feature dimensions. In this paper, we present Multidimensional Kernel Convolution (MKConv), a novel convolution operator that learns to transform the point feature representation from a vector to a multidimensional matrix. Unlike standard point convolution, MKConv proceeds via two steps. (i) It first activates the spatial dimensions of local feature representation by exploiting multidimensional kernel weights. These spatially expanded features can represent their embedded information through spatial correlation as well as channel correlation in feature space, carrying more detailed local structure information. (ii) Then, discrete convolutions are applied to the multidimensional features which can be regarded as a grid-structured matrix. In this way, we can utilize the discrete convolutions for point cloud data without voxelization that suffers from information loss. Furthermore, we propose a spatial attention module, Multidimensional Local Attention (MLA), to provide comprehensive structure awareness within the local point set by reweighting the spatial feature dimensions. We demonstrate that MKConv has excellent applicability to point cloud processing tasks including object classification, object part segmentation, and scene semantic segmentation with superior results.