# 3D Shape Estimation from 2D Landmarks: A Convex Relaxation Approach

arXiv: https://arxiv.org/abs/1411.2942 · HTML: https://mlsanity.com/paper/1411.2942/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2014.

## Built on by (most cited first, 11 of 11)

- [Context Modeling in 3D Human Pose Estimation: A Unified Perspective](https://mlsanity.com/paper/2103.15507/) (2021)
- [Gravity-Aware Monocular 3D Human-Object Reconstruction](https://mlsanity.com/paper/2108.08844/) (2021)
- [Optimal Pose and Shape Estimation for Category-level 3D Object Perception](https://mlsanity.com/paper/2104.08383/) (2021)
- [Estimation Contracts for Outlier-Robust Geometric Perception](https://mlsanity.com/paper/2208.10521/) (2022)
- [Optimal and Robust Category-level Perception: Object Pose and Shape Estimation from 2D and 3D Semantic Keypoints](https://mlsanity.com/paper/2206.12498/) (2022)
- [Dynamical Pose Estimation](https://mlsanity.com/paper/2103.06182/) (2021)
- [A Kendall Shape Space Approach to 3D Shape Estimation from 2D Landmarks](https://mlsanity.com/paper/2207.12687/) (2022)
- [Adapted Human Pose: Monocular 3D Human Pose Estimation with Zero Real 3D Pose Data](https://mlsanity.com/paper/2105.10837/) (2021)
- [Generative Landmarks Guided Eyeglasses Removal 3D Face Reconstruction](https://mlsanity.com/paper/2412.19848/) (2024)
- [Learning Transferable Kinematic Dictionary for 3D Human Pose and Shape Reconstruction](https://mlsanity.com/paper/2104.00953/) (2021)
- [LiP-Flow: Learning Inference-time Priors for Codec Avatars via Normalizing Flows in Latent Space](https://mlsanity.com/paper/2203.07881/) (2022)

## Abstract (arXiv)

We investigate the problem of estimating the 3D shape of an object, given a set of 2D landmarks in a single image. To alleviate the reconstruction ambiguity, a widely-used approach is to confine the unknown 3D shape within a shape space built upon existing shapes. While this approach has proven to be successful in various applications, a challenging issue remains, i.e., the joint estimation of shape parameters and camera-pose parameters requires to solve a nonconvex optimization problem. The existing methods often adopt an alternating minimization scheme to locally update the parameters, and consequently the solution is sensitive to initialization. In this paper, we propose a convex formulation to address this problem and develop an efficient algorithm to solve the proposed convex program. We demonstrate the exact recovery property of the proposed method, its merits compared to alternative methods, and the applicability in human pose and car shape estimation.