Related papers: Dynamic shape analysis and comparison of leaf grow…
Via circle pattern techniques, random planar triangulations (with angle variables) are mapped onto Delaunay triangulations in the complex plane. The uniform measure on triangulations is mapped onto a conformally invariant spatial point…
Shape is an important physical property of natural and manmade 3D objects that characterizes their external appearances. Understanding differences between shapes and modeling the variability within and across shape classes, hereinafter…
This paper provides theoretical and computational developments in statistical shape analysis of shape graphs, and demonstrates them using analysis of complex data from retinal blood-vessel (RBV) networks. The shape graphs are represented by…
Describing shapes by suitable measures in object segmentation, as proposed in [24], allows to combine the advantages of the representations as parametrized contours and indicator functions. The pseudo-Riemannian structure of optimal…
Dynamic MRI may capture temporal anatomical changes in soft tissue organs with high contrast but the obtained sequences usually suffer from limited volume coverage which makes the high resolution reconstruction of organ shape trajectories a…
We provide a full characterization of geodesic completeness for spaces of configurations of landmarks with smooth Riemannian metrics that satisfy a rotational and translation invariance and which are induced from metrics on subgroups of the…
Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous…
Continual learning aims to efficiently learn from a non-stationary stream of data while avoiding forgetting the knowledge of old data. In many practical applications, data complies with non-Euclidean geometry. As such, the commonly used…
We cast shape matching as metric learning with convolutional networks. We break the end-to-end process of image representation into two parts. Firstly, well established efficient methods are chosen to turn the images into edge maps.…
This article presents certain recent methodologies and some new results for the statistical analysis of probability distributions on manifolds. An important example considered in some detail here is the 2-D shape space of k-ads, comprising…
Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices,…
A complete representation of 3D objects requires characterizing the space of deformations in an interpretable manner, from articulations of a single instance to changes in shape across categories. In this work, we improve on a prior…
Inferring time-varying graph structures from high-dimensional nodal observations is a fundamental problem arising in neuroscience, finance, climatology, and beyond. Two intrinsic challenges govern this problem: maintaining the…
Classical archetypal analysis is appealing for its interpretability, but its linear geometry can limit performance on data with strongly non-linear structure; at the same time, existing neural extensions improve flexibility while often…
Tip-driven growth processes underlie the development of many plants. To date, tip-driven growth processes have been modelled as an elongating path or series of segments without taking into account lateral expansion during elongation.…
A topological shape analysis is proposed and utilized to learn concepts that reflect shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects. Therein constellations…
Shape dynamics is a completely background-independent universal framework of dynamical theories from which all absolute elements have been eliminated. For particles, only the variables that describe the shapes of the instantaneous particle…
For planar landmark based shapes, taking into account the non-Euclidean geometry of the shape space, a statistical test for a common mean first geodesic principal component (GPC) is devised. It rests on one of two asymptotic scenarios, both…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
We express parallel transport for several common matrix Lie groups with a family of pseudo-Riemannian metrics in terms of matrix exponential and exponential actions. The metrics are constructed from a deformation of a bi-invariant metric…