# A Survey on Non-rigid 3D Shape Analysis

arXiv: https://arxiv.org/abs/1812.10111 · HTML: https://mlsanity.com/paper/1812.10111/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Dec 2018.

## Built on by (most cited first, 10 of 10)

- [GLASS: Geometric Latent Augmentation for Shape Spaces](https://mlsanity.com/paper/2108.03225/) (2021)
- [4D Atlas: Statistical Analysis of the Spatiotemporal Variability in Longitudinal 3D Shape Data](https://mlsanity.com/paper/2101.09403/) (2021)
- [Dynamic Neural Surfaces for Elastic 4D Shape Representation and Analysis](https://mlsanity.com/paper/2503.03132/) (2025)
- [A Riemannian Approach for Spatiotemporal Analysis and Generation of 4D Tree-shaped Structures](https://mlsanity.com/paper/2408.12443/) (2024)
- [Advances and Trends in the 3D Reconstruction of the Shape and Motion of Animals](https://mlsanity.com/paper/2508.16062/) (2025)
- [Procrustes Analysis with Deformations: A Closed-Form Solution by Eigenvalue Decomposition](https://mlsanity.com/paper/2206.14528/) (2022)
- [ARC-Flow : Articulated, Resolution-Agnostic, Correspondence-Free Matching and Interpolation of 3D Shapes Under Flow Fields](https://mlsanity.com/paper/2503.02606/) (2025)
- [TreeSRNF: Square-Root Normal Fields for Generative Modelling of the Geometric and Structural Variability in Tree-like 3D Objects](https://mlsanity.com/paper/2607.13456/) (2026)
- [Probabilistic Registration for Gaussian Process 3D shape modelling in the presence of extensive missing data](https://mlsanity.com/paper/2203.14113/) (2022)
- [NeuralSRNF: Neural Square Root Normal Fields for the Statistical Shape Analysis and Generation of Nonrigid 3D and 4D Objects](https://mlsanity.com/paper/2609.27728/) (2026)

## Abstract (arXiv)

Shape is an important physical property of natural and manmade 3D objects that characterizes their external appearances. Understanding differences between shapes and modeling the variability within and across shape classes, hereinafter referred to as shape analysis, are fundamental problems to many applications, ranging from computer vision and computer graphics to biology and medicine. This chapter provides an overview of some of the recent techniques that studied the shape of 3D objects that undergo non-rigid deformations including bending and stretching. Recent surveys that covered some aspects such classification, retrieval, recognition, and rigid or nonrigid registration, focused on methods that use shape descriptors. Descriptors, however, provide abstract representations that do not enable the exploration of shape variability. In this chapter, we focus on recent techniques that treated the shape of 3D objects as points in some high dimensional space where paths describe deformations. Equipping the space with a suitable metric enables the quantification of the range of deformations of a given shape, which in turn enables (1) comparing and classifying 3D objects based on their shape, (2) computing smooth deformations, i.e. geodesics, between pairs of objects, and (3) modeling and exploring continuous shape variability in a collection of 3D models. This article surveys and classifies recent developments in this field, outlines fundamental issues, discusses their potential applications in computer vision and graphics, and highlights opportunities for future research. Our primary goal is to bridge the gap between various techniques that have been often independently proposed by different communities including mathematics and statistics, computer vision and graphics, and medical image analysis.