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Membranes holomorphically embedded in flat noncompact space are constructed in terms of the degrees of freedom of an infinite collection of 0-branes. To each holomorphic curve we associate infinite-dimensional matrices which are static…

Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…

A motion taxonomy can encode manipulations as a binary-encoded representation, which we refer to as motion codes. These motion codes innately represent a manipulation action in an embedded space that describes the motion's mechanical…

In animation, style can be considered as a distinctive layer over the content of a motion, allowing a character to achieve the same gesture in various ways. Editing existing animation to modify the style while keeping the same content is an…

The geometry of weight spaces and functional manifolds of neural networks play an important role towards 'understanding' the intricacies of ML. In this paper, we attempt to solve certain open questions in ML, by viewing them through the…

We present an algorithm for producing a seamless animated loop from a single image. The algorithm detects periodic structures, such as the windows of a building or the steps of a staircase, and generates a non-trivial displacement vector…

Face animation aims at creating photo-realistic portrait videos with animated poses and expressions. A common practice is to generate displacement fields that are used to warp pixels and features from source to target. However, prior…

We present a new approach for understanding the periodicity structure and semantics of motion datasets, independently of the morphology and skeletal structure of characters. Unlike existing methods using an overly sparse high-dimensional…

We introduce an algorithm for computing geodesics on sampled manifolds that relies on simulation of quantum dynamics on a graph embedding of the sampled data. Our approach exploits classic results in semiclassical analysis and the…

This paper proposes a geodesic-distance-based feature that encodes global information for improved video segmentation algorithms. The feature is a joint histogram of intensity and geodesic distances, where the geodesic distances are…

Current approaches to video analysis of human motion focus on raw pixels or keypoints as the basic units of reasoning. We posit that adding higher-level motion primitives, which can capture natural coarser units of motion such as backswing…

We propose an optimization algorithm for computing geodesics on the universal Teichm\"uller space T(1) in the Weil-Petersson ($W P$) metric. Another realization for T(1) is the space of planar shapes, modulo translation and scale, and thus…

Computing the epipolar geometry between cameras with very different viewpoints is often very difficult. The appearance of objects can vary greatly, and it is difficult to find corresponding feature points. Prior methods searched for…

We propose a numerical scheme based on the principles of Isogeometric Analysis (IgA) for a geometrical pattern formation induced evolution of manifolds. The development is modelled by the use of the Gray-Scott equations for pattern…

This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…

It is shown that a covariant derivative on any d-dimensional manifold M can be mapped to a set of d operators acting on the space of functions on the principal Spin(d)-bundle over M. In other words, any d-dimensional manifold can be…

In this paper, we construct rotating frames for curves, including plane curves, space curves and curves on surfaces. Hence, the behaviour of an arbitrary moving point on a curve can be seen as the composite of linear motion and rotation.…

Neuroscientific studies of drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole. This…

Character image animation, which synthesizes videos of reference characters driven by pose sequences, has advanced rapidly but remains largely limited to single-human settings. Existing methods struggle to generalize to multi-humanoid…

In this paper we address the task of the comparison and the classification of 3D shape sequences of human. The non-linear dynamics of the human motion and the changing of the surface parametrization over the time make this task very…