Related papers: Modelling Character Motions on Infinite-Dimensiona…

Motions of virtual characters in movies or video games are typically generated by recording actors using motion capturing methods. Animations generated this way often need postprocessing, such as improving the periodicity of cyclic…

Human motion generation involves creating natural sequences of human body poses, widely used in gaming, virtual reality, and human-computer interaction. It aims to produce lifelike virtual characters with realistic movements, enhancing…

In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…

For robots to work alongside humans and perform in unstructured environments, they must learn new motion skills and adapt them to unseen situations on the fly. This demands learning models that capture relevant motion patterns, while…

Shape analysis methods have in the past few years become very popular, both for theoretical exploration as well as from an application point of view. Originally developed for planar curves, these methods have been expanded to higher…

Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…

In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform…

In the elastic shape analysis approach to shape matching and object classification, plane curves are represented as points in an infinite-dimensional Riemannian manifold, wherein shape dissimilarity is measured by geodesic distance. A…

We use some fundamental ideas from complex analysis to create symmetric images and animations. Using a domain coloring algorithm, we generate mappings to the entire complex plane or the hyperbolic upper half-plane. The resulting designs can…

In recent decades, advancements in motion learning have enabled robots to acquire new skills and adapt to unseen conditions in both structured and unstructured environments. In practice, motion learning methods capture relevant patterns and…

Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…

In this paper we present a new deep learning-driven approach to image-based synthesis of animations involving humanoid characters. Unlike previous deep approaches to image-based animation our method makes no assumptions on the type of…

We propose a novel deep learning framework for animation video resequencing. Our system produces new video sequences by minimizing a perceptual distance of images from an existing animation video clip. To measure perceptual distance, we…

We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably…

Focus of this study is to explore some aspects of mathematical foundations for using complex manifolds as a model for space-time. More specifically, certain equations of motions have been derived as a Projective geodesic on a real manifold…

Let $V$ be a separable Hilbert space, possibly infinite dimensional. Let $\St(p,V)$ be the Stiefel manifold of orthonormal frames of $p$ vectors in $V$, and let $\Gr(p,V)$ be the Grassmann manifold of $p$ dimensional subspaces of $V$. We…

We propose novel motion representations for animating articulated objects consisting of distinct parts. In a completely unsupervised manner, our method identifies object parts, tracks them in a driving video, and infers their motions by…

In this study, we present and analyze a framework for geometric and topological estimation for mapping of unknown environments. We consider agents mimicking motion behaviors of cyborg insects, known as biobots, and exploit coordinate-free…

Infinite-dimensional manifolds modelled on arbitrary Hilbert spaces of functions are considered. It is shown that changes in model rather than changes of charts within the same model make coordinate formalisms on finite and…

The morphological classification of galaxies is considered a relevant issue and can be approached from different points of view. The increasing growth in the size and accuracy of astronomical data sets brings with it the need for the use of…