Revisiting Digital Straight Segment Recognition

This paper presents new results about digital straight segments, their recognition and related properties. They come from the study of the arithmetically based recognition algorithm proposed by I. Debled-Rennesson and J.-P. Reveill\`es in 1995 [Debled95]. We indeed exhibit the relations describing the possible changes in the parameters of the digital straight segment under investigation. This description is achieved by considering new parameters on digital segments: instead of their arithmetic description, we examine the parameters related to their combinatoric description. As a result we have a better understanding of their evolution during recognition and analytical formulas to compute them. We also show how this evolution can be projected onto the Stern-Brocot tree. These new relations have interesting consequences on the geometry of digital curves. We show how they can for instance be used to bound the slope difference between consecutive maximal segments

Maximal digital straight segments and convergence of discrete geometric estimators

Discrete geometric estimators approach geometric quantities on digitized shapes without any knowledge of the continuous shape. A classical yet difficult problem is to show that an estimator asymptotically converges toward the true geometric quantity as the resolution increases. We study here the convergence of local estimators based on Digital Straight Segment (DSS) recognition. It is closely linked to the asymptotic growth of maximal DSS, for which we show bounds both about their number and sizes. These results not only give better insights about digitized curves but indicate that curvature estimators based on local DSS recognition are not likely to converge. We indeed invalidate an hypothesis which was essential in the only known convergence theorem of a discrete curvature estimator. The proof involves results from arithmetic properties of digital lines, digital convexity, combinatorics, continued fractions and random polytopes

Two linear-time algorithms for computing the minimum length polygon of a digital contour

AbstractThe Minimum Length Polygon (MLP) is an interesting first order approximation of a digital contour. For instance, the convexity of the MLP is characteristic of the digital convexity of the shape, its perimeter is a good estimate of the perimeter of the digitized shape. We present here two novel equivalent definitions of MLP, one arithmetic, one combinatorial, and both definitions lead to two different linear time algorithms to compute them. This paper extends the work presented in Provençal and Lachaud (2009) [26], by detailing the algorithms and providing full proofs. It includes also a comparative experimental evaluation of both algorithms showing that the combinatorial algorithm is about 5 times faster than the other. We also checked the multigrid convergence of the length estimator based on the MLP

Courbure discrète : théorie et applications

International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor

View generated database

This document represents the final report for the View Generated Database (VGD) project, NAS7-1066. It documents the work done on the project up to the point at which all project work was terminated due to lack of project funds. The VGD was to provide the capability to accurately represent any real-world object or scene as a computer model. Such models include both an accurate spatial/geometric representation of surfaces of the object or scene, as well as any surface detail present on the object. Applications of such models are numerous, including acquisition and maintenance of work models for tele-autonomous systems, generation of accurate 3-D geometric/photometric models for various 3-D vision systems, and graphical models for realistic rendering of 3-D scenes via computer graphics

Information-theoretic investigation of multi-unit activity properties under different stimulus conditions in mouse primary visual cortex

Primary visual cortex (V1) is the first cortical processing level receiving topographically mapped inputs from the retina, relayed through thalamus. Electrophysiological studies discovered its important role in early sensory processing particularly in edge detection in single cells. To this end, little is investigated how these activities relate on a population level. Orientation tuning in mouse V1 has long been reported as salt-and pepper organised, lacking apparent structure as was found in e.g. cat or primates. This is a novel synthesis of specially designed in-vivo electrophysiological experiments aiming to make certain information-theoretic data analysis approaches viable. Sophisticated state-of-the-art data analysis techniques are applied to answer questions about stimulus information in mouse V1. Multi-unit electrophysiological experiments were devised, performed and evaluated in the anaesthetised and in left hemisphere V1 of the awake behaving, head-fixed mouse. A detailed laboratory and computational analysis is presented validating the use of Multi-Unit-Activity (MUA) and information-theoretic measures. Our results indicate left forward drifting gratings (moving from the temporal to nasal visual field) elicit consistently highest neuronal responses across cortical layers and columns, challenging the common understanding of random organisation. These directional biasses of MUA were also observable on the population level. In addition to individual multi-unit analyses, population responses in terms of binary word distributions appear more similar between spontaneous activity and responses to natural movies than either/both to moving gratings, suggesting that mouse V1 processes natural scenes differently from sinusoidal drifting gratings. Response pattern distributions for different gratings emerge to be spatially but not orientationally clustered. Further computational analysis suggests population firing rates can partially account for these differences. Electrophysiological experiments in the awake behaving mouse indicate V1 to contain information about behavioural outcome in a GO/NOGO task. This, along with other statistical measures is examined with statistical models such as the population tracking model, which suggest that population interactions are required to explain these observations.Open Acces

Virtual Morphology and Evolutionary Morphometrics in the new millenium.

EDITED VOLUME; abstract N/

Gaining Insight into Determinants of Physical Activity using Bayesian Network Learning

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