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Multigrid Convergence of Discrete Geometric Estimators [chapter]

David Coeurjolly, Jacques-Olivier Lachaud, Tristan Roussillon
2012 Lecture Notes in Computational Vision and Biomechanics  
Their boundary is by essence discrete and is seen by continuous geometry as a jagged continuous curve, either straight or not derivable.  ...  We present here global geometric estimators of area, length, moments, as well as local geometric estimators of tangent and curvature.  ...  shape is the ellipse digitized at h = 0.1. Fig. 4 4 Plots of tangent directions as a function of the grid edge index for several shapes and several tangent estimators.  ... 
doi:10.1007/978-94-007-4174-4_13 fatcat:ym22kbvxdfh35hz22yqe6yrbem

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.  ...  Introduction In this paper, we address the problem of tangent estimation along contours of digitized 2D objects. Tangent estimation has many applications in discrete geometry.  ... 
doi:10.1007/978-3-540-31965-8_23 fatcat:newmxoy5vfgchci4wqaicm57ze

A Discrete Approach for Decomposing Noisy Digital Contours into Arcs and Segments [chapter]

Phuc Ngo, Hayat Nasser, Isabelle Debled-Rennesson
2017 Lecture Notes in Computer Science  
In the paper, we present a method for decomposing a discrete noisy curve into arcs and segments which are the frequent primitives in digital images.  ...  This method is based on two tools: dominant point detection using adaptive tangential cover and tangent space representation of the polygon issued from detected dominant points.  ...  The sequence of maximal segments along a digital contour is called a tangential cover and used in numerous discrete geometric estimators (see [9] for a state of the art): length, tangent, curvature estimators  ... 
doi:10.1007/978-3-319-54427-4_36 fatcat:27emdlwumzav5gi6gjryd5sdya

Analysis of Noisy Digital Contours with Adaptive Tangential Cover

Phuc Ngo, Isabelle Debled-Rennesson, Bertrand Kerautret, Hayat Nasser
2017 Journal of Mathematical Imaging and Vision  
This study leads to the proposal of several applications of ATC on noisy digital contours: dominant point detection, contour length estimator, tangent/normal estimator, detection of convex and concave  ...  An extension of ATC to 3D curves is also proposed in this paper. The experimental results demonstrate the efficiency of this new notion.  ...  Experimentations and comparisons with other methods show the interest of the proposed framework using ATC.  ... 
doi:10.1007/s10851-017-0723-7 fatcat:gnj7lnfqfrgyvok2tnikvsmkjq

Curvature estimation along noisy digital contours by approximate global optimization

B. Kerautret, J.-O. Lachaud
2009 Pattern Recognition  
The GMC estimator exploits the geometric properties of digital contours by using local bounds on tangent directions defined by the maximal digital straight segments.  ...  Experiments on perfect and damaged digital contours are performed and in both cases, comparisons with other existing methods are presented.  ...  Acknowledgements We would like to thank the anonymous reviewers for their many constructive comments, questions and suggestions.  ... 
doi:10.1016/j.patcog.2008.11.013 fatcat:wrsubb2i6nfmlhk27t5j5mut3y

Multigrid Convergence and Surface Area Estimation [chapter]

David Coeurjolly, Frédéric Flin, Olivier Teytaud, Laure Tougne
2003 Lecture Notes in Computer Science  
In this article, we present a theoretical framework in order to prove multigrid convergence of surface area estimators based on discrete normal vector field integration.  ...  Surface area of discrete objects is an important feature for model-based image analysis.  ...  We have shown experimental results of this estimator on various discrete shapes.  ... 
doi:10.1007/3-540-36586-9_7 fatcat:55ot7eilq5d3jbhyybj4g5nti4

Multigrid convergence for the MDCA-curvature estimator [article]

Andreas Schindele, Peter Massopust, Brigitte Forster
2015 arXiv   pre-print
We consider the problem of estimating the curvature profile along the boundaries of digital objects in segmented black-and-white images.  ...  We start with the curvature estimator proposed by Roussillon et al., which is based on the calculation of \emph{maximal digital circular arcs} (MDCA).  ...  Inner Pixel Outer Pixel DCA -Discrete Circular Arc Continuous curve γ Figure 2 . The digital circular arc (dashed) for the continuous curve γ (dotted) separates into inner and outer pixels.  ... 
arXiv:1510.00678v1 fatcat:vhbgtak5rfgojkmdi7bnpnm7j4

Estimation of the curvature of an interface from a digital 2D image

Olav Inge Frette, George Virnovsky, Dmitriy Silin
2009 Computational materials science  
In this paper a method for the estimation of the curvature along a condensed phase interface is presented.  ...  Modifications of the algorithm are however needed, and with good data smoothing techniques, our method provides good quantitative curvature estimates.  ...  Assuming sufficient smoothness of the curve, we locate the 2D Cartesian coordinate system with origin in P and the x-coordinate axis is placed along the tangent line of the curve.  ... 
doi:10.1016/j.commatsci.2008.06.006 fatcat:4wftxtowvbczxn3rvkejmscjc4

Convergent Tangent Estimator for Discrete Objects Based on Isothetic Covers

Yumnam Surajkanta, Shyamosree Pal
2020 Journal of Computer Science  
Upper bound for the tangent estimator are derived and show that it tends toward the directions of the tangents of the underlying real curve as we reduce the grid size.  ...  In this article, we propose a tangent estimation method for discrete object based on isothetic covers.  ...  Author's Contributions Yumnam Surajkanta: Propose the concept of maximal isothtic straight segment and the isothetic tangent. Shyamosree Pal: Conceptualize and implemented the isotheitc covers.  ... 
doi:10.3844/jcssp.2020.467.478 fatcat:dotbkmj6wjeonkwube3fqfidbu

An effective third-order local fitting patch and its application

Zhong Li, Brian Barsky, Xiaogang Jin
2009 2009 IEEE International Conference on Shape Modeling and Applications  
Compared to other estimation algorithms, this weighted bicubic B zier patch more accurately obtains the normal vector and curvature estimation of a triangular mesh model.  ...  Furthermore, we define the principal geodesic torsion of each vertex on the mesh model and estimate it through this local fitting patch.  ...  ACKNOWLEDGEMENTS The authors gratefully appreciate the anonymous referees for the useful comments and suggestions which improved this paper considerably.  ... 
doi:10.1109/smi.2009.5170157 dblp:conf/smi/LiBJ09 fatcat:gzz332vvxvb57jwj3y45tt6d24

Curve Digitization Variability [chapter]

Étienne Baudrier, Loïc Mazo
2016 Lecture Notes in Computer Science  
This paper presents a study on the set of digitizations generated by the action of a group of transformations on a continuous curve before the digitization step.  ...  Finally, a representation of this digitization set is proposed and an illustration of its potential use is given on a length estimator.  ...  For a given digital curve S, these criteria calculate the minimum of the (continuous) estimator on a family of continuous curves whose digitization at a given resolution is S.  ... 
doi:10.1007/978-3-319-32360-2_5 fatcat:sq7ftitkbnf2jmjk7tmwgpdkkq

Parameter Estimation for the Forest Fire Propagation Model

Martin Ambroz, Karol Mikula, Marek Fraštia, Marián Marčiš
2020 Tatra Mountains Mathematical Publications  
From the data, we are able to estimate the normal velocity of the fire front (rate of spread), dominant wind direction and selected model parameters.  ...  Then, we aim to estimate the optimal model parameters. To achieve this goal, we use data assimilation of the measured data.  ...  Acknowledgementsº We would like to thank RomanČunderlík and Andrea Majlingová for organizing and inviting us to the training of fire-fighting units.  ... 
doi:10.2478/tmmp-2020-0001 fatcat:46rhbnnvo5fyjnmtl7irubn37i

Oscillation mitigation for sliding-mode observers in sensorless control of IPMSMs

Yue Zhao, Wei Qiao, Long Wu
2012 2012 IEEE Transportation Electrification Conference and Expo (ITEC)  
The proposed algorithm can effectively mitigate the oscillation and improve the dynamic performance of the SMO for rotor position estimation.  ...  The feature of high robustness to system structure and parameter uncertainties makes the sliding-mode observer (SMO) a promising candidate for rotor position estimation.  ...  Problem Discription In a continuous-time system, the state trajectory can exactly move along the sliding surface; while in a discrete-time system, due to the use of a finite sampling frequency, the state  ... 
doi:10.1109/itec.2012.6243496 fatcat:zgcphbblprdghp7iuwyuifex54

Robust and Accurate Curvature Estimation Using Adaptive Line Integrals

Wei-Yang Lin, Yen-Lin Chiu, KerryR Widder, YuHen Hu, Nigel Boston
2010 EURASIP Journal on Advances in Signal Processing  
The task of curvature estimation from discrete sampling points along a curve is investigated.  ...  A number of numerical examples using synthetic noisy and noiseless data clearly demonstrated the advantages of this proposed method over state-of-the-art curvature estimation algorithms.  ...  These continuous curves have been discretized by uniformly sampling in the angular variable and curvature is estimated at each sampling point.  ... 
doi:10.1155/2010/240309 fatcat:up3j4pkojfbazd6n5gwzzoqcim

Parameter-Free and Multigrid Convergent Digital Curvature Estimators [chapter]

Jérémy Levallois, David Coeurjolly, Jacques-Olivier Lachaud
2014 Lecture Notes in Computer Science  
In a previous work, we have proposed a new class of estimators on digital shape boundaries based on Integral Invariants.  ...  In this paper, we propose new variants of these estimators which are parameter-free and ensure multigrid convergence in 2D.  ...  For 2D digital curves, tangent estimation from maximal digital straight segments answers these two questions in a nice way.  ... 
doi:10.1007/978-3-319-09955-2_14 fatcat:2pxlp37smjbwjg4yqk3i7c5mna
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