# Medial Spectral Coordinates for 3D Shape Analysis

arXiv: https://arxiv.org/abs/2111.13295 · HTML: https://mlsanity.com/paper/2111.13295/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 61 references that are in the map.
- First posted on arXiv 26 Nov 2021.

## Builds on (most cited first, 19 of 19)

- [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)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020)
- [Local Spectral Graph Convolution for Point Set Feature Learning](https://mlsanity.com/paper/1803.05827/) (2018)
- [Dynamic GCN: Context-enriched Topology Learning for Skeleton-based Action Recognition](https://mlsanity.com/paper/2007.14690/) (2020)
- [SampleNet: Differentiable Point Cloud Sampling](https://mlsanity.com/paper/1912.03663/) (2019)
- [Learning Geometry-Disentangled Representation for Complementary Understanding of 3D Object Point Cloud](https://mlsanity.com/paper/2012.10921/) (2020)
- [SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation](https://mlsanity.com/paper/1612.00606/) (2016)
- [3D Shape Segmentation with Projective Convolutional Networks](https://mlsanity.com/paper/1612.02808/) (2016)
- [Geometry Sharing Network for 3D Point Cloud Classification and Segmentation](https://mlsanity.com/paper/1912.10644/) (2019)
- [Efficient Deformable Shape Correspondence via Kernel Matching](https://mlsanity.com/paper/1707.08991/) (2017)
- [Learning to Segment 3D Point Clouds in 2D Image Space](https://mlsanity.com/paper/2003.05593/) (2020)
- [Spectral Generalized Multi-Dimensional Scaling](https://mlsanity.com/paper/1311.2187/) (2013)
- [SEG-MAT: 3D Shape Segmentation Using Medial Axis Transform](https://mlsanity.com/paper/2010.11488/) (2020)
- [Appearance Shock Grammar for Fast Medial Axis Extraction from Real Images](https://mlsanity.com/paper/2004.02677/) (2020)
- [AMAT: Medial Axis Transform for Natural Images](https://mlsanity.com/paper/1703.08628/) (2017)
- [PIG-Net: Inception based Deep Learning Architecture for 3D Point Cloud Segmentation](https://mlsanity.com/paper/2101.11987/) (2021)

## Built on by (most cited first, 3 of 3)

- [MedShapeNet -- A Large-Scale Dataset of 3D Medical Shapes for Computer Vision](https://mlsanity.com/paper/2308.16139/) (2023)
- [Multiple Sclerosis Lesions Segmentation using Attention-Based CNNs in FLAIR Images](https://mlsanity.com/paper/2201.01832/) (2022)
- [MLGCN: An Ultra Efficient Graph Convolution Neural Model For 3D Point Cloud Analysis](https://mlsanity.com/paper/2303.17748/) (2023)

## Abstract (arXiv)

In recent years there has been a resurgence of interest in our community in the shape analysis of 3D objects represented by surface meshes, their voxelized interiors, or surface point clouds. In part, this interest has been stimulated by the increased availability of RGBD cameras, and by applications of computer vision to autonomous driving, medical imaging, and robotics. In these settings, spectral coordinates have shown promise for shape representation due to their ability to incorporate both local and global shape properties in a manner that is qualitatively invariant to isometric transformations. Yet, surprisingly, such coordinates have thus far typically considered only local surface positional or derivative information. In the present article, we propose to equip spectral coordinates with medial (object width) information, so as to enrich them. The key idea is to couple surface points that share a medial ball, via the weights of the adjacency matrix. We develop a spectral feature using this idea, and the algorithms to compute it. The incorporation of object width and medial coupling has direct benefits, as illustrated by our experiments on object classification, object part segmentation, and surface point correspondence.