Related papers: An Algebraic Geometry Approach to Viewing Graph So…
The Shape From Shading is one of a computer vision field. It studies the 3D reconstruction of an object from a single grayscale image. The difficulty of this field can be expressed in the local ambiguity (convex / concave). J.Shi and Q.Zhu…
The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
The identifiability problem arises naturally in a number of contexts in mathematics and computer science. Specific instances include local or global rigidity of graphs and unique completability of partially-filled tensors subject to rank…
Graph convexity has been used as an important tool to better understand the structure of classes of graphs. Many studies are devoted to determine if a graph equipped with a convexity is a {\em convex geometry}. In this work we survey…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
We investigate an algebraic problem related to the determination of the fundamental group of a class of spaces of configurations on surfaces. The configuration spaces are spaces of points grouped into colors. Whether two points are allowed…
Graph drawing research traditionally focuses on producing geometric embeddings of graphs satisfying various aesthetic constraints. After the geometric embedding is specified, there is an additional step that is often overlooked or ignored:…
It is proposed that the mathematical formalism that is most appropriate for the study of spatially non-integrable cosmological models is the transverse geometry of a one-dimensional foliation (congruence) defined by a physical observer. By…
In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem.…
The Naive Angle Method, used by Geometry Expressions for solving problems which involve only angle constraints, represents a geometrical configuration as a sparse linear system. Linear systems with the same underlying matrix structure…
We consider the problem of classification of an object given multiple observations that possibly include different transformations. The possible transformations of the object generally span a low-dimensional manifold in the original signal…
We present a means of formulating and solving the well known structure-and-motion problem in computer vision with probabilistic graphical models. We model the unknown camera poses and 3D feature coordinates as well as the observed 2D…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
Signed graphs are an emergent way of representing data in a variety of contexts where antagonistic interactions exist. These include data from biological, ecological, and social systems. Here we propose the concept of communicability for…
This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…
Although NP-Complete problems are the most difficult decisional problems, it is possible to discover in them polynomial (or easy) observables. We study the Graph Partitioning Problem showing that it is possible to recognize in it two…
Existing graph layout algorithms are usually not able to optimize all the aesthetic properties desired in a graph layout. To evaluate how well the desired visual features are reflected in a graph layout, many readability metrics have been…
Answering connectivity queries in real algebraic sets is a fundamental problem in effective real algebraic geometry that finds many applications in e.g. robotics where motion planning issues are topical. This computational problem is…