Related papers: Measuring shape relations using r-parallel sets

In this paper, we propose a new algorithm based on radial symmetry center method to track colloidal particles close to contact, where the optical images of the particles start to overlap in digital video microscopy. This overlapping effect…

We study the Hausdorff measure and dimension of the set of intrinsically simultaneously $\psi$-approximable points on a curve, surface, etc., given as a graph of integer valued polynomials. We obtain complete answers to these questions for…

We demonstrate that, under orthographic projection and with a camera fixated on a point located on a rigid body, the rotation of that body can be analytically obtained by tracking only one other feature in the image. With some exceptions,…

We geometrically analyze the problem of estimating parameters related to the shape and size of a two-dimensional target object on the plane by using randomly distributed distance sensors whose locations are unknown. Based on the analysis…

We combine standard persistent homology with image persistent homology to define a novel way of characterizing shapes and interactions between them. In particular, we introduce: (1) a mixup barcode, which captures geometric-topological…

Given the ensemble of random Gaussian Laplace eigenfunctions on the three-dimensional torus (`3d arithmetic random waves'), we investigate the $1$-dimensional Hausdorff measure of the nodal intersection curve against a compact regular toral…

Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/relational information for structured/relational reasoning, typically in low dimensions.…

We analyze correlation functions in a toy model of a random geometry interacting with matter. We show that in general the connected correlator will contain a long-range scaling part which is in some sense a remnant of the disconnected part.…

Algorithmic fractal dimensions quantify the algorithmic information density of individual points and may be defined in terms of Kolmogorov complexity. This work uses these dimensions to bound the classical Hausdorff and packing dimensions…

This paper presents a real-time solution for collision detection between objects based on the physics properties. Traditional approaches on collision detection often rely on the geometric relationships that computing the intersections…

We propose a deep learning approach for finding dense correspondences between 3D scans of people. Our method requires only partial geometric information in the form of two depth maps or partial reconstructed surfaces, works for humans in…

This paper gives an overview of a theory for modelling the interaction between geometric image transformations and receptive field responses for a visual observer that views objects and spatio-temporal events in the environment. This…

Statistical shape modeling is an essential tool for the quantitative analysis of anatomical populations. Point distribution models (PDMs) represent the anatomical surface via a dense set of correspondences, an intuitive and easy-to-use…

We investigate the problem of pixelwise correspondence for deformable objects, namely cloth and rope, by comparing both classical and learning-based methods. We choose cloth and rope because they are traditionally some of the most difficult…

We study the contact process in a dynamical random environment defined on the vertices and edges of a graph. For a broad class of processes, we establish an asymptotic shape theorem for the set H_t, which represents the vertices that have…

The Human-Object Interaction (HOI) task explores the dynamic interactions between humans and objects in physical environments, providing essential biomechanical and cognitive-behavioral foundations for fields such as robotics, virtual…

We propose an approach to predict the 3D shape and pose for the objects present in a scene. Existing learning based methods that pursue this goal make independent predictions per object, and do not leverage the relationships amongst them.…

Visual relationships capture a wide variety of interactions between pairs of objects in images (e.g. "man riding bicycle" and "man pushing bicycle"). Consequently, the set of possible relationships is extremely large and it is difficult to…

We consider the space of geodesic laminations on a surface, endowed with the Hausdorff metric d_H and with a variation of this metric called the d_log metric. We compute and/or estimate the Hausdorff dimensions of these two metrics. We also…

The geometry around a rotating massive body, which carries charge and electrical currents, could be described by its multipole moments (mass moments, mass-current moments, electric moments, and magnetic moments). When a small body is…