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This article introduces a full mathematical and numerical framework for treating functional shapes (or fshapes) following the landmarks of shape spaces and shape analysis. Functional shapes can be described as signal functions supported on…
Universe models with compact spatial sections smaller than the observable universe produce a topological lens effect. Given a catalog of cosmic sources, we estimate the number of topological images in locally hyperbolic and locally elliptic…
We focus on the analysis of planar shapes and solid objects having thin features and propose a new mathematical model to characterize them. Based on our model, that we call an epsilon-shape, we show how thin parts can be effectively and…
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…
Structural quantities such as order parameters and correlation functions are often employed to gain insight into the physical behavior and properties of condensed matter systems. While standard quantities for characterizing structure exist,…
Despite being vastly ignored in the literature, coping with topological noise is an issue of increasing importance, especially as a consequence of the increasing number and diversity of 3D polygonal models that are captured by devices of…
With systems for acquiring 3D surface data being evermore commonplace, it has become important to reliably extract specific shapes from the acquired data. In the presence of noise and occlusions, this can be done through the use of…
In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…
Geometrical model for quantum objects is suggested. It is shown that equations for free material Dirac field and for Maxwell electromagnetic field can be considered as relations describing propagation of the space topological defects. This…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…
Non-rigid 3D mesh matching is a critical step in computer vision and computer graphics pipelines. We tackle matching meshes that contain topological artefacts which can break the assumption made by current approaches. While Functional Maps…
3D city models - which represent in 3 dimensions the geometric elements of a city - are increasingly used for an intended wide range of applications. Such uses are made possible by using semantically enriched 3D city models and by…
Additive manufacturing (AM) enables enormous freedom for design of complex structures. However, the process-dependent limitations that result in discrepancies between as-designed and as-manufactured shapes are not fully understood. The…
Functional 3D scene graphs offer a versatile and flexible representation for 3D scene understanding and robotic manipulation, defined by object nodes, interactive elements, and functional relationship edges. However, their potential remains…
Normally we judge Topological shapes analytically but they hide significant amount of data in them about coordinate planes and ordered & unordered paris. In this article we will build our intuition and find those datas.
With the increasing amount of data being visualized in large information spaces, methods providing data-driven context have become indispensable. Off-screen visualization techniques, therefore, have been extensively researched for their…
Finding correspondences between 3D shapes is an important and long-standing problem in computer vision, graphics and beyond. A prominent challenge are partial-to-partial shape matching settings, which occur when the shapes to match are only…
The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed…
This paper investigates how the inherent quantization of camera sensors introduces uncertainty in the calculated position of an observed feature during 3-D mapping. It is typically assumed that pixels and scene features are points, however,…
Shapes do not define a linear space. This paper explores the linear structure of deformations as a representation of shapes. This transforms shape optimization to a variant of optimal control. The numerical challenges of this point of view…