Related papers: Nonparametric Continuous Sensor Registration
This paper reports on a novel nonparametric rigid point cloud registration framework that jointly integrates geometric and semantic measurements such as color or semantic labels into the alignment process and does not require explicit data…
In this paper, we propose a novel mathematical framework for piecewise diffeomorphic image registration that involves discontinuous sliding motion using a diffeomorphism groupoid and algebroid approach. The traditional Large Deformation…
We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special…
In computational anatomy, the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework has become a central tool for modeling smooth, invertible transformations between shapes such as curves or landmarks. In this paper, we extend…
Let $G=NH$ be a Lie group where $N,H$ are closed connected subgroups of $G,$ and $N$ is an exponential solvable Lie group which is normal in $G.$ Suppose furthermore that $N$ admits a unitary character $\chi_{\lambda}$ corresponding to a…
In machine learning, data is usually represented in a (flat) Euclidean space where distances between points are along straight lines. Researchers have recently considered more exotic (non-Euclidean) Riemannian manifolds such as hyperbolic…
Graph embedding techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools.…
Let $G$ be a simply connected, connected completely solvable Lie group with Lie algebra $\mathfrak{g}=\mathfrak{p}+\mathfrak{m}.$ Next, let $\pi$ be an infinite-dimensional unitary irreducible representation of $G$ obtained by inducing a…
We propose Lie group embedded dynamical neural networks (LieEDNN) and the corresponding learning algorithms based on gradient descent and metric projection on smooth manifold, where we treat Lie group as an intrinsic representation for…
In the last decades, some literature appeared using the Lie groups theory to solve problems in computer vision. On the other hand, Lie algebraic representations of the transformations therein were introduced to overcome the difficulties…
The ability to build maps is a key functionality for the majority of mobile robots. A central ingredient to most mapping systems is the registration or alignment of the recorded sensor data. In this paper, we present a general methodology…
Riemannian manifolds have been widely employed for video representations in visual classification tasks including video-based face recognition. The success mainly derives from learning a discriminant Riemannian metric which encodes the…
Human motion generation is often learned in Euclidean spaces, although valid motions follow structured non-Euclidean geometry. We present Riemannian Motion Generation (RMG), a unified framework that represents motion on a product manifold…
This paper reports on a novel formulation and evaluation of visual odometry from RGB-D images. Assuming a static scene, the developed theoretical framework generalizes the widely used direct energy formulation (photometric error…
This paper presents a framework for rigid point-set registration and merging using a robust continuous data representation. Our point-set representation is constructed by training a one-class support vector machine with a Gaussian radial…
Many phenomena are naturally characterized by measuring continuous transformations such as shape changes in medicine or articulated systems in robotics. Modeling the variability in such datasets requires performing statistics on Lie groups,…
Geometric representation learning in preserving the intrinsic geometric and topological properties for discrete non-Euclidean data is crucial in scientific applications. Previous research generally mapped non-Euclidean discrete data into…
Modeling 4D scenes requires capturing both spatial structure and temporal motion, which is challenging due to the need for physically consistent representations of complex rigid and non-rigid motions. Existing approaches mainly rely on…
We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The…
We present an accurate, robust and fast method for registration of 3D scans. Our motion estimation optimizes a robust cost function on the intrinsic representation of rigid motions, i.e., the Special Euclidean group $\mathbb{SE}(3)$. We…