Reconstructions of Noisy Digital Contours with Maximal Primitives Based on Multi-scale/Irregular Geometric Representation and Generalized Linear Programming

The reconstruction of noisy digital shapes is a complex question and a lot of contributions have been proposed to address this problem, including blurred segment decomposition or adaptive tangential covering for instance. In this article, we propose a novel approach combining multi-scale and irregular isothetic representations of the input contour, as an extension of a previous work [Vacavant et al., A Combined MultiScale/Irregular Algorithm for the Vectorization of Noisy Digital Contours, CVIU 2013]. Our new algorithm improves the representation of the contour by 1-D intervals, and achieves afterwards the decomposition of the contour into maximal arcs or segments. Our experiments with synthetic and real images show that our contribution can be employed as a relevant option for noisy shape reconstruction.

[1]  Gongning Luo,et al.  A graph-based method for fitting planar B-spline curves with intersections , 2016, J. Comput. Des. Eng..

[2]  Jacques-Olivier Lachaud,et al.  Accurate Curvature Estimation along Digital Contours with Maximal Digital Circular Arcs , 2011, IWCIA.

[3]  Laure Tougne,et al.  Topological and Geometrical Reconstruction of Complex Objects on Irregular Isothetic Grids , 2006, DGCI.

[4]  Laure Tougne,et al.  Optimal Time Computation of the Tangent of a Discrete Curve: Application to the Curvature , 1999, DGCI.

[5]  Antoine Vacavant,et al.  Arc Recognition on Irregular Isothetic Grids and Its Application to Reconstruction of Noisy Digital Contours , 2013, DGCI.

[6]  Jacques-Olivier Lachaud,et al.  Meaningful Scales Detection along Digital Contours for Unsupervised Local Noise Estimation , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Jean-Michel Morel,et al.  Secrets of image denoising cuisine* , 2012, Acta Numerica.

[8]  Jacques-Olivier Lachaud,et al.  Meaningful Scales Detection: an Unsupervised Noise Detection Algorithm for Digital Contours , 2014, Image Process. Line.

[9]  Geoff A. W. West,et al.  Nonparametric Segmentation of Curves into Various Representations , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Joseph O'Rourke,et al.  An on-line algorithm for fitting straight lines between data ranges , 1981, CACM.

[11]  Antoine Vacavant.  A Novel Definition of Robustness for Image Processing Algorithms , 2016, RRPR@ICPR.

[12]  Kazuhiko Yamamoto,et al.  Structured Document Image Analysis , 1992, Springer Berlin Heidelberg.

[13]  Jacques-Olivier Lachaud,et al.  Espaces non-euclidiens et analyse d'image : modèles déformables riemanniens et discrets, topologie et géométrie discrète. (Non-Euclidean spaces and image analysis : Riemannian and discrete deformable models, discrete topology and geometry) , 2006 .

[14]  Isabelle Debled-Rennesson,et al.  Adaptive Tangential Cover for Noisy Digital Contours , 2016, DGCI.

[15]  Thanh Phuong Nguyen,et al.  Decomposition of a Curve into Arcs and Line Segments Based on Dominant Point Detection , 2011, SCIA.

[16]  Xiaoming Hu,et al.  Contour reconstruction using recursive smoothing splines - Algorithms and experimental validation , 2009, Robotics Auton. Syst..

[17]  Emo Welzl,et al.  Smallest enclosing disks (balls and ellipsoids) , 1991, New Results and New Trends in Computer Science.

[18]  Nina Amenta,et al.  Helly-type theorems and Generalized Linear Programming , 1994, Discret. Comput. Geom..

[19]  Jacques-Olivier Lachaud,et al.  A combined multi-scale/irregular algorithm for the vectorization of noisy digital contours , 2013, Comput. Vis. Image Underst..

[20]  Laure Tougne,et al.  On the min DSS problem of closed discrete curves , 2003, Discret. Appl. Math..

[21]  Alexandre Faure,et al.  Multi-primitive Analysis of Digital Curves , 2009, IWCIA.

[22]  Micha Sharir,et al.  A Combinatorial Bound for Linear Programming and Related Problems , 1992, STACS.

[23]  D. T. Lee,et al.  An optimal algorithm for shortest paths on weighted interval and circular-arc graphs, with applications , 1993, Algorithmica.

[24]  Oliver Wirjadi,et al.  Survey of 3d image segmentation methods , 2007 .

[25]  Karl Tombre,et al.  Robust and accurate vectorization of line drawings , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[26]  A. Ardeshir Goshtasby,et al.  Fitting Parametric Curves to Dense and Noisy Points , 2000 .