Related papers: Measuring shape relations using r-parallel sets
An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape…
In previous work, we introduced a method for modeling a configuration of objects in 2D and 3D images using a mathematical "medial/skeletal linking structure." In this paper, we show how these structures allow us to capture positional…
Understanding physical relations between objects, especially their support relations, is crucial for robotic manipulation. There has been work on reasoning about support relations and structural stability of simple configurations in RGB-D…
In this paper we compare the different phenomena that occur when intersecting geometric objects with random geodesics on the unit sphere and inside convex bodies. On the high dimensional sphere we see that with probability bounded away from…
Object data analysis is concerned with statistical methodology for datasets whose elements reside in an arbitrary, unspecified metric space. In this work we propose the object shape, a novel measure of shape/symmetry for object data. The…
Understanding human interaction with objects is an important research topic for embodied Artificial Intelligence and identifying the objects that humans are interacting with is a primary problem for interaction understanding. Existing…
When matching parts of a surface to its whole, a fundamental question arises: Which points should be included in the matching process? The issue is intensified when using isometry to measure similarity, as it requires the validation of…
In this position paper we suggest a possible metric approach to shape comparison that is based on a mathematical formalization of the concept of observer, seen as a collection of suitable operators acting on a metric space of functions.…
The previously described methodology for hierarchical grouping of objects through iterative averaging has been used for simulation of cooperative interactions between objects of a system with the purpose of investigation of the…
Appearance-based generic object recognition is a challenging problem because all possible appearances of objects cannot be registered, especially as new objects are produced every day. Function of objects, however, has a comparatively small…
Statistical mechanics explains the properties of macroscopic phenomena based on the movements of microscopic particles such as atoms and molecules. Movements of microscopic particles can be represented by large-scale interacting systems. In…
Most (3D) multi-object tracking methods rely on appearance-based cues for data association. By contrast, we investigate how far we can get by only encoding geometric relationships between objects in 3D space as cues for data-driven data…
Humans regularly interact with their surrounding objects. Such interactions often result in strongly correlated motion between humans and the interacting objects. We thus ask: "Is it possible to infer object properties from skeletal motion…
Geometric mechanics provides valuable insights into how biological and robotic systems use changes in shape to move by mechanically interacting with their environment. In high-friction environments it provides that the entire interaction is…
In this work we reproduce the characterization of $\Gg^s$-sets from the euclidean setting [J. London Math. Soc. 49:267-280,1994] to more general metric spaces. These sets have Hausdorff dimension at least $s$ and are closed by countable…
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…
In the series of models with interacting particles in stochastic geometry, a new contribution presents the facet process which is defined in arbitrary Euclidean dimension. In 2D, 3D specially it is a process of interacting segments, flat…
We often wish to classify objects by their shapes. Indeed, the study of shapes is an important part of many scientific fields such as evolutionary biology, structural biology, image processing, and archaeology. The most widely-used method…
We completely describe in terms of Hausdorff measures the size of the set of points of the circle that are covered infinitely often by a sequence of random arcs with given lengths. We also show that this set is a set with large…
Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual…