Efficient contour-based shape representation and matching

This paper presents an efficient method for calculating the similarity between 2D closed shape contours. The proposed algorithm is invariant to translation, scale change and rotation. It can be used for database retrieval or for detecting regions with a particular shape in video sequences. The proposed algorithm is suitable for real-time applications. In the first stage of the algorithm, an ordered sequence of contour points approximating the shapes is extracted from the input binary images. The contours are translation and scale-size normalized, and small sets of the most likely starting points for both shapes are extracted. In the second stage, the starting points from both shapes are assigned into pairs and rotation alignment is performed. The dissimilarity measure is based on the geometrical distances between corresponding contour points. A fast sub-optimal method for solving the correspondence problem between contour points from two shapes is proposed. The dissimilarity measure is calculated for each pair of starting points. The lowest dissimilarity is taken as the final dissimilarity measure between two shapes. Three different experiments are carried out using the proposed approach: letter recognition using a web camera, our own simulation of Part B of the MPEG-7 core experiment “CE-Shape1” and detection of characters in cartoon video sequences. Results indicate that the proposed dissimilarity measure is aligned with human intuition

Interactive object contour extraction for shape modeling

In this paper we present a semi-automatic segmentation approach suitable for extracting object contours as a precursor to 2D shape modeling. The approach is a modified and extended version of an existing state-of-the-art approach based on the concept of a Binary Partition Tree (BPT) [1]. The resulting segmentation tool facilitates quick and easy extraction of an object’s contour via a small amount of user interaction that is easy to perform, even in complicated scenes. Illustrative segmentation results are presented and the usefulness of the approach in generating object shape models is discussed

Using dempster-shafer theory to fuse multiple information sources in region-based segmentation

This paper presents a new method for segmentation of images into large regions that reflect the real world objects present in a scene. It explores the feasibility of utilizing spatial configuration of regions and their geometric properties (the so-called Syntactic Visual Features [1]) for improving the correspondence of segmentation results produced by the well-known Recursive Shortest Spanning Tree (RSST) algorithm [2] to semantic objects present in the scene. The main contribution of this paper is a novel framework for integration of evidence from multiple sources with the region merging process based on the Dempster-Shafer (DS) theory [3] that allows integration of sources providing evidence with different accuracy and reliability. Extensive experiments indicate that the proposed solution limits formation of regions spanning more than one semantic object

Kan injectivity in order-enriched categories

Continuous lattices were characterised by Martin Escardo as precisely the objects that are Kan-injective w.r.t. a certain class of morphisms. We study Kan-injectivity in general categories enriched in posets. For every class H of morphisms we study the subcategory of all objects Kan-injective w.r.t. H and all morphisms preserving Kan-extensions. For categories such as Top_0 and Pos we prove that whenever H is a set of morphisms, the above subcategory is monadic, and the monad it creates is a Kock-Zoeberlein monad. However, this does not generalise to proper classes: we present a class of continuous mappings in Top_0 for which Kan-injectivity does not yield a monadic category.Comment: 23 page

Dissipative fields in de Sitter and black hole spacetimes: Quantum entanglement due to pair production and dissipation

For free fields, pair creation in expanding universes is associated with the building up of correlations that lead to nonseparable states, i.e., quantum mechanically entangled ones. For dissipative fields, i.e., fields coupled to an environment, there is a competition between the squeezing of the state and the coupling to the external bath. We compute the final coherence level for dissipative fields that propagate in a two-dimensional de Sitter space, and we characterize the domain in parameter space where the state remains nonseparable. We then apply our analysis to (analogue) Hawking radiation by exploiting the close relationship between Lorentz violating theories propagating in de Sitter and black hole metrics. We establish the robustness of the spectrum and find that the entanglement among Hawking pairs is generally much stronger than that among pairs of quanta with opposite momenta.Comment: Final version published in prd, 22 page

Syntactic Monoids in a Category

The syntactic monoid of a language is generalized to the level of a symmetric monoidal closed category D. This allows for a uniform treatment of several notions of syntactic algebras known in the literature, including the syntactic monoids of Rabin and Scott (D = sets), the syntactic semirings of Polak (D = semilattices), and the syntactic associative algebras of Reutenauer (D = vector spaces). Assuming that D is an entropic variety of algebras, we prove that the syntactic D-monoid of a language L can be constructed as a quotient of a free D-monoid modulo the syntactic congruence of L, and that it is isomorphic to the transition D-monoid of the minimal automaton for L in D. Furthermore, in case the variety D is locally finite, we characterize the regular languages as precisely the languages with finite syntactic D-monoids

N-body methods for relativistic cosmology

We present a framework for general relativistic N-body simulations in the regime of weak gravitational fields. In this approach, Einstein's equations are expanded in terms of metric perturbations about a Friedmann-Lema\^itre background, which are assumed to remain small. The metric perturbations themselves are only kept to linear order, but we keep their first spatial derivatives to second order and treat their second spatial derivatives as well as sources of stress-energy fully non-perturbatively. The evolution of matter is modelled by an N-body ensemble which can consist of free-streaming nonrelativistic (e.g. cold dark matter) or relativistic particle species (e.g. cosmic neutrinos), but the framework is fully general and also allows for other sources of stress-energy, in particular additional relativistic sources like modified-gravity models or topological defects. We compare our method with the traditional Newtonian approach and argue that relativistic methods are conceptually more robust and flexible, at the cost of a moderate increase of numerical difficulty. However, for a LambdaCDM cosmology, where nonrelativistic matter is the only source of perturbations, the relativistic corrections are expected to be small. We quantify this statement by extracting post-Newtonian estimates from Newtonian N-body simulations.Comment: 30 pages, 3 figures. Invited contribution to a Classical and Quantum Gravity focus issue on "Relativistic Effects in Cosmology", edited by Kazuya Koyam