Topological maps and robust hierarchical Euclidean skeletons in cubical complexes
نویسنده
چکیده
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Topological maps and robust hierarchical Euclidean skeletons in cubical complexes Michel Couprie
منابع مشابه
Topological maps and robust Euclidean skeletons in cubical complexes
In the 90s, several authors introduced the notion of a hierarchic family of 2D Euclidean skeletons, evolving smoothly under the control of a filtering parameter. We provide in this paper a discrete framework which formalizes and generalizes this notion, in particular to higher dimensions. This framework allows us to propose a new skeletonization scheme and to prove several important properties,...
متن کاملOn simplicial and cubical complexes with short links
We consider closed simplicial and cubical n-complexes in terms of link of their (n−2)faces. Especially, we consider the case, when this link has size 3 or 4, i.e., every (n − 2)face is contained in 3 or 4 n-faces. Such simplicial complexes with short (i.e. of length 3 or 4) links are completely classified by their characteristic partition. We consider also embedding into hypercubes of the skele...
متن کاملGraphs of Some CAT(0) Complexes
In this note, we characterize the graphs (1-skeletons) of some piecewise Euclidean simplicial and cubical complexes having nonpositive curvature in the sense of Gromov’s CAT(0) inequality. Each such cell complex K is simply connected and obeys a certain flag condition. It turns out that if, in addition, all maximal cells are either regular Euclidean cubes or right Euclidean triangles glued in a...
متن کاملGeometric & Topological Representations of Maximum Classes with Applications to Sample Compression
We systematically investigate finite maximum classes, which play an important role in machine learning as concept classes meeting Sauer’s Lemma with equality. Simple arrangements of hyperplanes in Hyperbolic space are shown to represent maximum classes, generalizing the corresponding Euclidean result. We show that sweeping a generic hyperplane across such arrangements forms an unlabeled compres...
متن کاملCombinatorial Groupoids, Cubical Complexes, and the Lovász Conjecture
A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like “holonomy”, “parallel transport”, “bundles”, “combinatorial curvature” etc. in the context of simplicial (polyhedral) complexes, posets, graphs, polytopes and other combinatorial objects. A new, holonomy-type invariant for cubical complexes is introduced, leading to a combinatorial “Theorema Egregium”...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Computer Vision and Image Understanding
دوره 117 شماره
صفحات -
تاریخ انتشار 2013