Related papers: Boundary and shape of binary images
This paper generalizes and unifies the existing spectral bounds on the $k$-independence number of a graph, which is the maximum size of a set of vertices at pairwise distance greater than $k$. The previous bounds known in the literature…
We study differential geometric properties of cuspidal edges with boundary. There are several differential geometric invariants which are related with the behavior of the boundary in addition to usual differential geometric invariants of…
We give a combinatorial description of shape theory using finite topological $T_0$-spaces (finite partially ordered sets). This description may lead to a sort of computational shape theory. Then we introduce the notion of core for inverse…
The polygon $P$ is small if its diameter equals one. When $n=2^s$, it is still an open problem to find the maximum perimeter or the maximum width of a small $n$-gon. Motivated by Bingane's series of works, we improve the lower bounds for…
We give a short and self-contained proof of the Boundary Harnack inequality for a class of domains satisfying some geometric conditions given in terms of a state function that behaves as the distance function to the boundary, is subharmonic…
This work aims to define the concept of manifold, which has a very important place in the topology, on digital images. So, a general perspective is provided for two and three-dimensional imaging studies on digital curves and digital…
The relational width of a finite structure, if bounded, is always (1,1) or (2,3). In this paper we study the relational width of first-order expansions of finitely bounded homogeneous binary cores where binary cores are structures with…
Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve…
This study revisits the problem of identifying the unknown interior Robin boundary of a connected domain using Cauchy data from the exterior region of a harmonic function. It investigates two shape optimization reformulations employing…
Existence of a photon circular orbit can tell us a lot about the nature of the underlying spacetime, since it plays a pivotal role in the understanding of the characteristic signatures of compact objects, namely the quasi-normal modes and…
The phenomenological boundary conditions for the envelope wave function, which is applicable for contacts of semiconductors with the rather different crystal symmetry are proposed. It is shown that the boundary conditions are determined by…
We give a sharp lower bound on the area of the domain enclosed by an embedded curve lying on a two-dimensional sphere, provided that geodesic curvature of this curve is bounded from below. Furthermore, we prove some dual inequalities for…
A body moves in a medium composed of noninteracting point particles; interaction of particles with the body is absolutely elastic. It is required to find the body's shape minimizing or maximizing resistance of the medium to its motion. This…
The success of deep neural networks in image classification and learning can be partly attributed to the features they extract from images. It is often speculated about the properties of a low-dimensional manifold that models extract and…
We consider the motion of a rigid body due to the pressure of a surrounded two-dimensional irrotational perfect incompressible fluid, the whole system being confined in a bounded domain with an impermeable condition on a part of the…
Invariants underlying shape inference are elusive: a variety of shapes can give rise to the same image, and a variety of images can be rendered from the same shape. The occluding contour is a rare exception: it has both image salience, in…
The metric dimension of a graph is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. Bailey and Meagher obtained an upper bound on the…
We describe how the large scale geometry of the circumstellar envelopes of asymptotic giant branch stars can be used to probe the presence of unseen stellar companions. A nearby companion modifies the mass loss by gravitationally focusing…
We present a novel and effective binary representation for convex shapes. We show the equivalence between the shape convexity and some properties of the associated indicator function. The proposed method has two advantages. Firstly, the…
This paper provides the currently best known upper bound on the density of a packing in three-dimensional Euclidean space of two types of spheres whose size ratio is the largest one that allows the insertion of a small sphere in each…