# A Kendall Shape Space Approach to 3D Shape Estimation from 2D Landmarks

arXiv: https://arxiv.org/abs/2207.12687 · HTML: https://mlsanity.com/paper/2207.12687/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 26 Jul 2022.

## Builds on (most cited first, 9 of 9)

- [VNect: Real-time 3D Human Pose Estimation with a Single RGB Camera](https://mlsanity.com/paper/1705.01583/) (2017)
- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [Robust Estimation of 3D Human Poses from a Single Image](https://mlsanity.com/paper/1406.2282/) (2014)
- [General Dynamic Scene Reconstruction from Multiple View Video](https://mlsanity.com/paper/1509.09294/) (2015)
- [Procrustean Regression Networks: Learning 3D Structure of Non-Rigid Objects from 2D Annotations](https://mlsanity.com/paper/2007.10961/) (2020)
- [3D Shape Estimation from 2D Landmarks: A Convex Relaxation Approach](https://mlsanity.com/paper/1411.2942/) (2014)
- [Few-Shot Single-View 3-D Object Reconstruction with Compositional Priors](https://mlsanity.com/paper/2004.06302/) (2020)
- [Geodesic analysis in Kendall's shape space with epidemiological applications](https://mlsanity.com/paper/1906.11950/) (2019)
- [KShapeNet: Riemannian network on Kendall shape space for Skeleton based Action Recognition](https://mlsanity.com/paper/2011.12004/) (2020)

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

- [Few-shot Image Generation via Information Transfer from the Built Geodesic Surface](https://mlsanity.com/paper/2401.01749/) (2024)
- [FAGStyle: Feature Augmentation on Geodesic Surface for Zero-shot Text-guided Diffusion Image Style Transfer](https://mlsanity.com/paper/2408.10533/) (2024)
- [FRPSS: Feature Rearrangement in Pre-Shape Space for Single-Image Generation](https://mlsanity.com/paper/2609.16594/) (2026)

## Abstract (arXiv)

3D shapes provide substantially more information than 2D images. However, the acquisition of 3D shapes is sometimes very difficult or even impossible in comparison with acquiring 2D images, making it necessary to derive the 3D shape from 2D images. Although this is, in general, a mathematically ill-posed problem, it might be solved by constraining the problem formulation using prior information. Here, we present a new approach based on Kendall's shape space to reconstruct 3D shapes from single monocular 2D images. The work is motivated by an application to study the feeding behavior of the basking shark, an endangered species whose massive size and mobility render 3D shape data nearly impossible to obtain, hampering understanding of their feeding behaviors and ecology. 2D images of these animals in feeding position, however, are readily available. We compare our approach with state-of-the-art shape-based approaches, both on human stick models and on shark head skeletons. Using a small set of training shapes, we show that the Kendall shape space approach is substantially more robust than previous methods and results in plausible shapes. This is essential for the motivating application in which specimens are rare and therefore only few training shapes are available.