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Found 28 papers, 7 papers with code
Optimization over Geodesics for Exact Principal Geodesic Analysis
In fields ranging from computer vision to signal processing and statistics, increasing computational power allows a move from classical linear models to models that incorporate non-linear phenomena.
Computational Geometry
Higher-order Spatial Accuracy in Diffeomorphic Image Registration
We discretize a cost functional for image registration problems by deriving Taylor expansions for the matching term.
Symmetry in Image Registration and Deformation Modeling
We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data.
Most Likely Separation of Intensity and Warping Effects in Image Registration
This paper introduces a class of mixed-effects models for joint modeling of spatially correlated intensity variation and warping variation in 2D images.
A Stochastic Large Deformation Model for Computational Anatomy
In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise.
A Geometric Framework for Stochastic Shape Analysis
We introduce a stochastic model of diffeomorphisms, whose action on a variety of data types descends to stochastic evolution of shapes, images and landmarks.
A Statistical Model for Simultaneous Template Estimation, Bias Correction, and Registration of 3D Brain Images
Template estimation plays a crucial role in computational anatomy since it provides reference frames for performing statistical analysis of the underlying anatomical population variability.
Bridge Simulation and Metric Estimation on Landmark Manifolds
We present an inference algorithm and connected Monte Carlo based estimation procedures for metric estimation from landmark configurations distributed according to the transition distribution of a Riemannian Brownian motion arising from the Large Deformation Diffeomorphic Metric Mapping (LDDMM) metric.
Computational Anatomy in Theano
To model deformation of anatomical shapes, non-linear statistics are required to take into account the non-linear structure of the data space.
Other Computer Science 53A35
Stochastic metamorphosis with template uncertainties
In this paper, we investigate two stochastic perturbations of the metamorphosis equations of image analysis, in the geometrical context of the Euler-Poincar\'e theory.
Differential geometry and stochastic dynamics with deep learning numerics
In this paper, we demonstrate how deterministic and stochastic dynamics on manifolds, as well as differential geometric constructions can be implemented concisely and efficiently using modern computational frameworks that mix symbolic expressions with efficient numerical computations.
Computational Geometry Computation 53A35, 53C17, 53C44, 70H05, 22E30 G.3; G.4; G.1.4
An Infinitesimal Probabilistic Model for Principal Component Analysis of Manifold Valued Data
We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data.
String Methods for Stochastic Image and Shape Matching
Matching of images and analysis of shape differences is traditionally pursued by energy minimization of paths of deformations acting to match the shape objects.
Latent Space Non-Linear Statistics
Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space.
PADDIT: Probabilistic Augmentation of Data using Diffeomorphic Image Transformation
For proper generalization performance of convolutional neural networks (CNNs) in medical image segmentation, the learnt features should be invariant under particular non-linear shape variations of the input.
An Average of the Human Ear Canal: Recovering Acoustical Properties via Shape Analysis
This is however not the case for the part of the ear canal that is embedded in the skull, until the typanic membrane.
Stochastic Image Deformation in Frequency Domain and Parameter Estimation using Moment Evolutions
We apply a stochastic generalisation of the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework to model differences in the evolution of anatomical objects detected in populations of image data.
Horizontal Flows and Manifold Stochastics in Geometric Deep Learning
We introduce two constructions in geometric deep learning for 1) transporting orientation-dependent convolutional filters over a manifold in a continuous way and thereby defining a convolution operator that naturally incorporates the rotational effect of holonomy; and 2) allowing efficient evaluation of manifold convolution layers by sampling manifold valued random variables that center around a weighted diffusion mean.
Diffusion bridges for stochastic Hamiltonian systems and shape evolutions
Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes.
Numerical Analysis Computational Engineering, Finance, and Science Numerical Analysis Computational Physics
Atlas Generative Models and Geodesic Interpolation
In this work we define the general class of Atlas Generative Models (AGMs), models with hybrid discrete-continuous latent space that estimate an atlas on the underlying data manifold together with a partition of unity on the data space.
Moment evolution equations and moment matching for stochastic image EPDiff
Models of stochastic image deformation allow study of time-continuous stochastic effects transforming images by deforming the image domain.
A Denoising Diffusion Model for Fluid Field Prediction
We propose a novel denoising diffusion generative model for predicting nonlinear fluid fields named FluidDiff.
A function space perspective on stochastic shape evolution
Modelling randomness in shape data, for example, the evolution of shapes of organisms in biology, requires stochastic models of shapes.
Deep Anatomical Federated Network (Dafne): an open client/server framework for the continuous collaborative improvement of deep-learning-based medical image segmentation
Semantic segmentation is a crucial step to extract quantitative information from medical (and, specifically, radiological) images to aid the diagnostic process, clinical follow-up.
Sliding at first order: Higher-order momentum distributions for discontinuous image registration
In this paper, we propose a new approach to deformable image registration that captures sliding motions.
Principal subbundles for dimension reduction
In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to obtain lower dimensional bundles.
Incorporating Riemannian Geometric Features for Learning Coefficient of Pressure Distributions on Airplane Wings
The aerodynamic coefficients of aircrafts are significantly impacted by its geometry, especially when the angle of attack (AoA) is large.
Conditioning non-linear and infinite-dimensional diffusion processes
Generative diffusion models and many stochastic models in science and engineering naturally live in infinite dimensions before discretisation.
