# Gaussian Process Morphable Models

arXiv: https://arxiv.org/abs/1603.07254 · HTML: https://mlsanity.com/paper/1603.07254/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2016.

## Built on by (most cited first, 30 of 31)

- [Accurate Point Cloud Registration with Robust Optimal Transport](https://mlsanity.com/paper/2111.00648/) (2021)
- [Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flow](https://mlsanity.com/paper/2203.08652/) (2022)
- [Dynamic Point Fields](https://mlsanity.com/paper/2304.02626/) (2023)
- [Learning Parallel Dense Correspondence from Spatio-Temporal Descriptors for Efficient and Robust 4D Reconstruction](https://mlsanity.com/paper/2103.16341/) (2021)
- [Sparse to Dense Dynamic 3D Facial Expression Generation](https://mlsanity.com/paper/2105.07463/) (2021)
- [Deep Deformable 3D Caricatures with Learned Shape Control](https://mlsanity.com/paper/2207.14593/) (2022)
- [Generating Multiple 4D Expression Transitions by Learning Face Landmark Trajectories](https://mlsanity.com/paper/2208.00050/) (2022)
- [Neuromorphic Facial Analysis with Cross-Modal Supervision](https://mlsanity.com/paper/2409.10213/) (2024)
- [RFNet-4D++: Joint Object Reconstruction and Flow Estimation from 4D Point Clouds with Cross-Attention Spatio-Temporal Features](https://mlsanity.com/paper/2203.16482/) (2022)
- [InstaFace: Identity-Preserving Facial Editing with Single Image Inference](https://mlsanity.com/paper/2502.20577/) (2025)
- [Uncertainty-Aware Annotation Protocol to Evaluate Deformable Registration Algorithms](https://mlsanity.com/paper/2104.01217/) (2021)
- [Learning the shape of female breasts: an open-access 3D statistical shape model of the female breast built from 110 breast scans](https://mlsanity.com/paper/2107.13463/) (2021)
- [MIRACLE3D: Memory-efficient Integrated Robust Approach for Continual Learning on Point Clouds via Shape Model Construction](https://mlsanity.com/paper/2410.06418/) (2024)
- [Approximating Intersections and Differences Between Linear Statistical Shape Models Using Markov Chain Monte Carlo](https://mlsanity.com/paper/2211.16314/) (2022)
- [Spatio-temporal Transformers for Action Unit Classification with Event Cameras](https://mlsanity.com/paper/2410.21958/) (2024)
- [Bone Surface Reconstruction and Clinical Features Estimation from Sparse Landmarks and Statistical Shape Models: A feasibility study on the femur](https://mlsanity.com/paper/2107.03292/) (2021)
- [3D Face Recognition: A Survey](https://mlsanity.com/paper/2108.11082/) (2021)
- [Beyond Flatland: Pre-training with a Strong 3D Inductive Bias](https://mlsanity.com/paper/2112.00113/) (2021)
- [Geodesic squared exponential kernel for non-rigid shape registration](https://mlsanity.com/paper/2112.11853/) (2021)
- [A statistical shape model for radiation-free assessment and classification of craniosynostosis](https://mlsanity.com/paper/2201.03288/) (2022)
- [Anatomically Parameterized Statistical Shape Model: Explaining Morphometry through Statistical Learning](https://mlsanity.com/paper/2202.08580/) (2022)
- [Building 3D Generative Models from Minimal Data](https://mlsanity.com/paper/2203.02554/) (2022)
- [High-Fidelity Single-Image Head Modeling with Industry-Grade Topology](https://mlsanity.com/paper/2605.04524/) (2026)
- [Few-Data Guided Learning Upon End-to-End Point Cloud Network for 3D Face Recognition](https://mlsanity.com/paper/2103.16927/) (2021)
- [Dynamic multi feature-class Gaussian process models](https://mlsanity.com/paper/2112.04495/) (2021)
- [GiNGR: Generalized Iterative Non-Rigid Point Cloud and Surface Registration Using Gaussian Process Regression](https://mlsanity.com/paper/2203.09986/) (2022)
- [Probabilistic Registration for Gaussian Process 3D shape modelling in the presence of extensive missing data](https://mlsanity.com/paper/2203.14113/) (2022)
- [exploreCOSMOS: Interactive Exploration of Conditional Statistical Shape Models in the Web-Browser](https://mlsanity.com/paper/2402.13131/) (2024)
- [Posterior shape models revisited: Improving 3D reconstructions from partial data using target specific models](https://mlsanity.com/paper/2509.05776/) (2025)
- [PRISM: A 3D Probabilistic Neural Representation for Interpretable Shape Modeling](https://mlsanity.com/paper/2602.11467/) (2026)

## Abstract (arXiv)

Statistical shape models (SSMs) represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional representation of the shape variation in terms of the leading principal components. In this paper, we propose a generalization of SSMs, called Gaussian Process Morphable Models (GPMMs). We model the shape variations with a Gaussian process, which we represent using the leading components of its Karhunen-Loeve expansion. To compute the expansion, we make use of an approximation scheme based on the Nystrom method. The resulting model can be seen as a continuous analogon of an SSM. However, while for SSMs the shape variation is restricted to the span of the example data, with GPMMs we can define the shape variation using any Gaussian process. For example, we can build shape models that correspond to classical spline models, and thus do not require any example data. Furthermore, Gaussian processes make it possible to combine different models. For example, an SSM can be extended with a spline model, to obtain a model that incorporates learned shape characteristics, but is flexible enough to explain shapes that cannot be represented by the SSM. We introduce a simple algorithm for fitting a GPMM to a surface or image. This results in a non-rigid registration approach, whose regularization properties are defined by a GPMM. We show how we can obtain different registration schemes,including methods for multi-scale, spatially-varying or hybrid registration, by constructing an appropriate GPMM. As our approach strictly separates modelling from the fitting process, this is all achieved without changes to the fitting algorithm. We show the applicability and versatility of GPMMs on a clinical use case, where the goal is the model-based segmentation of 3D forearm images.