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Found 25 papers, 5 papers with code
Robust Point Set Registration Using Gaussian Mixture Models
Then, the problem of point set registration is reformulated as the problem of aligning two Gaussian mixtures such that a statistical discrepancy measure between the two corresponding mixtures is minimized.
Computing Diffeomorphic Paths for Large Motion Interpolation
In this paper, we introduce a novel framework for computing a path of diffeomorphisms between a pair of input diffeomorphisms.
Tracking on the Product Manifold of Shape and Orientation for Tractography from Diffusion MRI
In this paper, we propose a new intrinsic recursive filter on the product manifold of shape and orientation.
A Riemannian Framework for Matching Point Clouds Represented by the Schrodinger Distance Transform
In this paper, we use the well known Riemannian framework never before used for point cloud matching, and present a novel matching algorithm.
Recursive Frechet Mean Computation on the Grassmannian and its Applications to Computer Vision
In the limit as the number of samples tends to infinity, we prove that GiFME converges to the FM (this is called the weak consistency result on the Grassmann manifold).
Interpolation on the Manifold of K Component GMMs
Probability density functions (PDFs) are fundamental "objects" in mathematics with numerous applications in computer vision, machine learning and medical imaging.
An efficient Exact-PGA algorithm for constant curvature manifolds
Recently, an alternative called exact PGA was proposed which tries to solve the optimization without any linearization.
An information theoretic formulation of the Dictionary Learning and Sparse Coding Problems on Statistical Manifolds
In this work, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distributions).
A Nonlinear Regression Technique for Manifold Valued Data With Applications to Medical Image Analysis
With the exception of a few, most existing methods of regression for manifold valued data are limited to geodesic regression which is a generalization of the linear regression in vector-spaces.
Intrinsic Grassmann Averages for Online Linear, Robust and Nonlinear Subspace Learning
In this paper, we present a geometric framework for computing the principal linear subspaces in both situations as well as for the robust PCA case, that amounts to computing the intrinsic average on the space of all subspaces: the Grassmann manifold.
Riemannian Nonlinear Mixed Effects Models: Analyzing Longitudinal Deformations in Neuroimaging
Statistical machine learning models that operate on manifold-valued data are being extensively studied in vision, motivated by applications in activity recognition, feature tracking and medical imaging.
Intrinsic Grassmann Averages for Online Linear and Robust Subspace Learning
We have demonstrated competitive performance of our proposed online subspace algorithm method on one synthetic and two real data sets.
Sparse Exact PGA on Riemannian Manifolds
In this paper, we present a novel generalization of SPCA, called sparse exact PGA (SEPGA) that can cope with manifold-valued input data and respect the intrinsic geometry of the underlying manifold.
A Geometric Framework for Statistical Analysis of Trajectories With Distinct Temporal Spans
Finally, by using existing algorithms for recursive Frechet mean and exact principal geodesic analysis on the hypersphere, we present several experiments on synthetic and real (vision and medical) data sets showing how group testing on such diversely sampled longitudinal data is possible by analyzing the reconstructed data in the subspace spanned by the first few PGs.
Dictionary Learning and Sparse Coding on Statistical Manifolds
In this paper, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distributions).
A CNN for homogneous Riemannian manifolds with applications to Neuroimaging
(ii) As a corrolary, we prove the equivariance of the correlation operation to group actions admitted by the input domains which are Riemannian homogeneous manifolds.
A Statistical Recurrent Model on the Manifold of Symmetric Positive Definite Matrices
We show how recurrent statistical recurrent network models can be defined in such spaces.
A mixture model for aggregation of multiple pre-trained weak classifiers
The other alternative to increase the performance is to learn multiple weak classifiers and boost their performance using a boosting algorithm or a variant thereof.
ManifoldNet: A Deep Network Framework for Manifold-valued Data
Thus, there is need to generalize the deep neural networks to cope with input data that reside on curved manifolds where vector space operations are not naturally admissible.
MANIFOLDNET: A DEEP NEURAL NETWORK FOR MANIFOLD-VALUED DATA
To this end, we present a provably convergent recursive computation of the wFM of the given data, where the weights makeup the convolution mask, to be learned.
MVC-Net: A Convolutional Neural Network Architecture for Manifold-Valued Images With Applications
Our goal in this paper is to generalize convolutional neural networks (CNN) to the manifold-valued image case which arises commonly in medical imaging and computer vision applications.
Nested Grassmannians for Dimensionality Reduction with Applications
With the proposed NG structure, we develop algorithms for the supervised and unsupervised dimensionality reduction problems respectively.
VolterraNet: A higher order convolutional network with group equivariance for homogeneous manifolds
In this paper, we present a novel higher order Volterra convolutional neural network (VolterraNet) for data defined as samples of functions on Riemannian homogeneous spaces.
Nested Hyperbolic Spaces for Dimensionality Reduction and Hyperbolic NN Design
In this paper, we present a novel fully hyperbolic neural network which uses the concept of projections (embeddings) followed by an intrinsic aggregation and a nonlinearity all within the hyperbolic space.
Higher Order Gauge Equivariant CNNs on Riemannian Manifolds and Applications
With the advent of group equivariant convolutions in deep networks literature, spherical CNNs with $\mathsf{SO}(3)$-equivariant layers have been developed to cope with data that are samples of signals on the sphere $S^2$.
