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ON THE LOCAL PROPERTIES OF DIGITAL CURVES

THANH PHUONG NGUYEN, ISABELLE DEBLED-RENNESSON
2008 International journal of shape modeling  
We propose a geometric approach to extract local properties of digital curves.  ...  A curvature estimator 3 for 2D curves in O(n log 2 n) time is proposed relying on this flexible approach. The notion of 2D blurred segment is extended to 3D space.  ...  Acknowledgements A preliminary version of this work was presented at the International Symposium on Visual Computing, Las Vegas, NV, 2008, Special Track on Discrete and Computational Geometry and their  ... 
doi:10.1142/s0218654308001105 fatcat:rj2zio6dufatbop6qgmc4lfnpm

About Multigrid Convergence of Some Length Estimators [chapter]

Loïc Mazo, Étienne Baudrier
2014 Lecture Notes in Computer Science  
An interesting property for curve length digital estimators is the convergence toward the continuous length and the associate convergence speed when the digitization step h tends to 0.  ...  For this class, the pattern size depends on the resolution but not on the digitized function.  ...  Local Estimators Local length estimators (see [10] for a short review) are based on parallel computations of the length of fixed size segments of a digital curve.  ... 
doi:10.1007/978-3-319-09955-2_18 fatcat:hvwfz2ylx5c6xmdn5e5mxtfn5q

Multi-scale Analysis of Discrete Contours for Unsupervised Noise Detection [chapter]

Bertrand Kerautret, Jacques-Olivier Lachaud
2009 Lecture Notes in Computer Science  
Based on the asymptotic properties of maximal segments, it also detects curved and flat parts of the contour.  ...  To overcome this issue, we propose an original strategy to detect locally both the amount of noise and the meaningful scales of each point of a digital contour.  ...  We are now in position to analyze the local geometry of some point P on a digital contour C.  ... 
doi:10.1007/978-3-642-10210-3_15 fatcat:p5o2qqoewbgbhg7hf5k4fp54ia

Analysis and Comparative Evaluation of Discrete Tangent Estimators [chapter]

Jacques-Olivier Lachaud, Anne Vialard, François de Vieilleville
2005 Lecture Notes in Computer Science  
This paper presents a comparative evaluation of tangent estimators based on digital line recognition on digital curves.  ...  We further propose a new estimator mixing the qualities of existing ones and outperforming them on most mentioned points.  ...  Remark that the complexity of computing the pencil P(k) around C k depends on the local shape of the curve (O(F (k) − B(k))).  ... 
doi:10.1007/978-3-540-31965-8_23 fatcat:newmxoy5vfgchci4wqaicm57ze

Faithful polygonal representation of the convex and concave parts of a digital curve

Tristan Roussillon, Isabelle Sivignon
2011 Pattern Recognition  
It is computed from a given digital curve in linear-time using well-known routines: adding a point at the front of a digital straight segment and removing a point from the back of a digital straight segment  ...  From results about digital convexity, we define a reversible polygon that faithfully represents the maximal convex and concave parts of a digital curve.  ...  Let us focus now on the definition of digital convexity for open digital curves.  ... 
doi:10.1016/j.patcog.2011.03.018 fatcat:igaushkojfb2daux2v7c3cvfti

A comparative evaluation of length estimators of digital curves

D. Coeurjolly, R. Klette
2004 IEEE Transactions on Pattern Analysis and Machine Intelligence  
This paper compares previously published length estimators in image analysis having digitized curves as input.  ...  The evaluation uses multigrid convergence (theoretical results and measured speed of convergence) and further measures as criteria.  ...  ACKNOWLEDGMENTS At the time this research was done, D. Coeurjolly was a member of the ERIC Laboratory (Université Lumière Lyon 2).  ... 
doi:10.1109/tpami.2004.1262194 pmid:15376899 fatcat:psisn6pwwnhofoyvcxyaamjpcu

On Local Definitions of Length of Digital Curves [chapter]

Mohamed Tajine, Alain Daurat
2003 Lecture Notes in Computer Science  
In this paper we investigate the 'local' definitions of length of digital curves in the digital space rZ 2 where r is the resolution of the discrete space.  ...  We prove that if µr is any local definition of the length of digital curves in rZ 2 , then for almost all segments S of R 2 , the measure µr(Sr) does not converge to the length of S when the resolution  ...  The local definition of length is obtained by associating a weight p(w) to each digital curve w of size m, where the size of a digital curve is its cardinality minus one, ie its number of edges between  ... 
doi:10.1007/978-3-540-39966-7_10 fatcat:3zevxuqkl5dihiplb4engmyvze

DIGITAL GEOMETRY [chapter]

AZRIEL ROSENFELD
1979 Picture Languages  
On the other hand: Digital spaces and images allow studies of geometric properties of subsets, either in the context of graph theory or of combinatorial topology.  ...  - Characterizing image operations that preserve the properties -Characterizing digital objects that could be digitizations of Euclidean objects that have given properties segment (DSS) = 8-curve resulting  ...  curves however: -no studies on MLPs in computational geometry for 3D (length estimation for 3D digital curves) -also no studies on relative convex hulls in 3D ( surface area estimation)  ... 
doi:10.1016/b978-0-12-597340-3.50008-6 fatcat:q7fl7ygi5vekpnustsnq4fq5g4

Digital geometry

Azriel Rosenfeld, Reinhard Klette
2002 Information Sciences  
On the other hand: Digital spaces and images allow studies of geometric properties of subsets, either in the context of graph theory or of combinatorial topology.  ...  - Characterizing image operations that preserve the properties -Characterizing digital objects that could be digitizations of Euclidean objects that have given properties segment (DSS) = 8-curve resulting  ...  curves however: -no studies on MLPs in computational geometry for 3D (length estimation for 3D digital curves) -also no studies on relative convex hulls in 3D ( surface area estimation)  ... 
doi:10.1016/s0020-0255(02)00284-0 fatcat:fvluroiil5bztgsevlz7kr6yxe

Properties of Digital n-Dimensional Spheres and Manifolds. Separation of Digital Manifolds [article]

Alexander V. Evako
2017 arXiv   pre-print
In the present paper, we study basic properties of digital n-dimensional manifolds and digital simply connected spaces.  ...  An important property of a digital n-manifold is that M is a digital n-sphere if and only if for any point v of M, M-v is a digital n-disk.  ...  In the present paper, we focus on digital spaces with properties, which closely resemble properties of their continuous counterparts.  ... 
arXiv:1712.06108v1 fatcat:rqdhxbouxzcltmlp3nutkel2ca

Nanostructuring of a Surface Layer as a Way to Improve the Mechanical Properties of Hypoeutectic Silumin

A A Kondratyuk, Yu F Ivanov, A A Klopotov, A M Ustinov, Yu A Abzaev, E A Petrikova, A D Teresov, A S Tolkachev
2020 IOP Conference Series: Materials Science and Engineering  
Features and patterns in the distribution of displacement fields in the deformation process in surface layers of the samples in realtime have been identified by digital image correlation method using the  ...  A significant increase in strength and plastic properties of silumin irradiated with an electron beam has been established.  ...  Acknowledgement The research was financially supported by the RSF (project No. 19-79-10059) .  ... 
doi:10.1088/1757-899x/731/1/012013 fatcat:uuzix67zrvevvckg73lowlnklm

A Comparison of Digital Length Estimators for Image Features [chapter]

V. Toh, C. A. Glasbey, A. J. Gray
2003 Lecture Notes in Computer Science  
by estimating local curve orientation.  ...  in a randomly located 2-D cross-sectional image, counting no. of pixels on the cell boundary, and converting to an estimate of cell surface area using geometrical formulae.  ...  Most length estimators are based on either pixel counts or properties of the chain-code representation of a digital line or curve.  ... 
doi:10.1007/3-540-45103-x_126 fatcat:ck3ewe46sfgvhlnqf23ux2hrqa

Design and Optimization of a Curved-Crease-Folding Process Applied to a Light Metallic Structure

Doina Raducanu, Vasile Danut Cojocaru, Vlad Andrei Raducanu, Anna Nocivin, Nicolae Serban, Ion Cinca, Elisabeta Mirela Cojocaru, Laurentiu Moldovan, Corneliu Trisca-Rusu, Irina Varvara Balkan
2021 Processes  
An integrated research approach was proposed that utilized an algorithmic/digital design applied to the curved-crease-folding method with the study (at different length scales) of the metallic material  ...  The results are useful for enhancing the accuracy of the digital design, the structural simulation programs and the fabrication methods.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/pr9071110 fatcat:gr4ncmxwejbwvnebpvrvocmsme

Fuzzy Digital Topology and Geometry and Their Applications to Medical Imaging [chapter]

Punam K. Saha
2013 Lecture Notes in Computer Science  
The notions of digital topology and geometry are often intertwined in medical imaging applications and sometime it is difficult to draw a dividing line between them.  ...  Digital topology and geometry play important roles in medical image processing either by expanding the scope of target information or by providing a strong theoretical foundation to a process enhancing  ...  This work was supported by the NIH grants R01-AR054439, R01-DE012101, and UL1-RR024979.  ... 
doi:10.1007/978-3-642-45062-4_2 fatcat:ao6o7wuhrvhhrinlxlhdw6zhbu

An elementary algorithm for digital arc segmentation

D. Coeurjolly, Y. Gérard, J.-P. Reveillés, L. Tougne
2004 Discrete Applied Mathematics  
After recalling the geometrical meaning of the separating circle problem, we present an incremental algorithm to segment a discrete curve into digital arcs. ?  ...  This paper concerns the digital circle recognition problem, especially in the form of the circular separation problem.  ...  Quasi-circular digital curve Based on the previous deÿnitions, we can deÿne the quasi-circularity property on digital convex curves.  ... 
doi:10.1016/j.dam.2003.08.003 fatcat:tkxvkuqsdzb4tb5fdgr3nr4y6a
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