相关论文: Modelling Character Motions on Infinite-Dimensiona…

This paper considers the problem of finding a meaningful template function that represents the common pattern of a sample of curves. To address this issue, a novel algorithm based on a robust version of the isometric featuring mapping…

Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…

An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden…

Metamorphosis is a method for diffeomorphic matching of shapes, with many potential applications for anatomical shape comparison in medical imagery, a problem which is central to the field of computational anatomy. An important tool for the…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms of the functions on the projective Hilbert space, and its Hilbert space analog, with a noncommutative product in terms of explicit…

One of the strategies to detect the pose and shape of unknown objects is their geometric modeling, consisting on fitting known geometric entities. Classical geometric modeling fits simple shapes such as spheres or cylinders, but often those…

Although human reconstruction typically results in human-specific avatars, recent 3D scene reconstruction techniques utilizing pixel-aligned features show promise in generalizing to new scenes. Applying these techniques to human avatar…

The realization space of geometric constraint systems is given by the vanishing locus of polynomials corresponding to natural geometric constraints. Such geometric constraint systems arise in many real-world scenarios such as structural…

We present a novel framework for animating humans in 3D scenes using 3D Gaussian Splatting (3DGS), a neural scene representation that has recently achieved state-of-the-art photorealistic results for novel-view synthesis but remains…

We propose to learn a probabilistic motion model from a sequence of images for spatio-temporal registration. Our model encodes motion in a low-dimensional probabilistic space - the motion matrix - which enables various motion analysis tasks…

Multidimensional unfolding methods are widely used for visualizing item response data. Such methods project respondents and items simultaneously onto a low-dimensional Euclidian space, in which respondents and items are represented by ideal…

The objective function used in trajectory optimization is often non-convex and can have an infinite set of local optima. In such cases, there are diverse solutions to perform a given task. Although there are a few methods to find multiple…

In this paper, we propose a novel object-level mapping system that can simultaneously segment, track, and reconstruct objects in dynamic scenes. It can further predict and complete their full geometries by conditioning on reconstructions…

Crafting a single, versatile physics-based controller that can breathe life into interactive characters across a wide spectrum of scenarios represents an exciting frontier in character animation. An ideal controller should support diverse…

Markerless motion capture algorithms require a 3D body with properly personalized skeleton dimension and/or body shape and appearance to successfully track a person. Unfortunately, many tracking methods consider model personalization a…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

This paper unifies the concept of kinematic mappings by using geometric algebras. We present a method for constructing kinematic mappings for certain Cayley-Klein geometries. These geometries are described in an algebraic setting by the…

Recognizing group activities is challenging due to the difficulties in isolating individual entities, finding the respective roles played by the individuals and representing the complex interactions among the participants. Individual…

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…