Finding Poly-Curves of Straight Line and Ellipse Segments in Images Segmentierung von Pixelketten in Geraden- und Ellipsenelemente

Simplification of given polygons has attracted many researchers. Especially, finding circular and elliptical structures in images is relevant in many applications. Given pixel chains from edge detection, this paper proposes a method to segment them into straight line and ellipse segments. We propose an adaption of Douglas-Peucker’s polygon simplification algorithm using circle segments instead of straight line segments and partition the sequence of points instead the sequence of edges. It is robust and decreases the complexity of given polygons better than the original algorithm. In a second step, we further simplify the poly-curve by merging neighbouring segments to straight line and ellipse segments. Merging is based on the evaluation of variation of entropy for proposed geometric models, which turns out as a combination of hypothesis testing and model selection. We demonstrate the results of circlePeucker as well as merging on several images of scenes with significant circular structures and compare them with the method of PATRAUCEAN et al. (2012). Zusammenfassung: . ie tion runder und elliptischer Strukturen ist relevant für viele Anwendungen. Die Reduktion der Komplexität gegebener Polygone ist für sich ein interessantes Forschungsthema. Diese Arbeit stellt ein Verfahren zur Segmentierung von Pixelketten einer Kantendetektion in Geradenund Ellipsensegmente vor. Der erste Schritt besteht in einer Adaption des Douglas-Peucker Algorithmus, in der Kreise anstelle von Geraden zur Partitionierung verwendet werden und die Punktstatt der Kantensequenz partitioniert wird. Das Verfahren ist robust und reduziert die Komplexität der gegebenen Polygone stärker als der originale Algorithmus. In einem zweiten Schritt vereinfachen wir diese Vorsegmentierung durch das Verschmelzen benachbarter Segmente zu Geradenund Ellipsensegmenten und stützen uns dabei auf die Entropieänderung. Wir zeigen die Ergebnisse der Vorsegmentierung als auch der folgenden Vereinfachung anhand verschiedener Bilder von Szenen, die signifikante kreisförmige Strukturen aufweisen und vergleichen sie mit dem Algorithmus von PATRAUCEAN et al. (2012).

[1]  Ullrich Köthe,et al.  Edge and Junction Detection with an Improved Structure Tensor , 2003, DAGM-Symposium.

[2]  Antonio Albano,et al.  Representation of Digitized Contours in Terms of Conic Arcs and Straight-Line Segments , 1974, Comput. Graph. Image Process..

[3]  H. Akaike.  A new look at the statistical model identification , 1974 .

[4]  David H. Douglas,et al.  ALGORITHMS FOR THE REDUCTION OF THE NUMBER OF POINTS REQUIRED TO REPRESENT A DIGITIZED LINE OR ITS CARICATURE , 1973 .

[5]  Karl-Friedrich Kraiss,et al.  Ellipse detection in digital image data using geometric features , 2006, VISAPP.

[6]  Andrew W. Fitzgibbon,et al.  Direct least squares fitting of ellipses , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[7]  Wolfgang Förstner,et al.  A Framework for Low Level Feature Extraction , 1994, ECCV.

[8]  Thanh Phuong Nguyen,et al.  Ellipse Detection through Decomposition of Circular Arcs and Line Segments , 2011, ICIAP.

[9]  Pierre Gurdjos,et al.  A Parameterless Line Segment and Elliptical Arc Detector with Enhanced Ellipse Fitting , 2012, ECCV.

[10]  Cordelia Schmid,et al.  Scale-invariant shape features for recognition of object categories , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[11]  John Porrill,et al.  Fitting ellipses and predicting confidence envelopes using a bias corrected Kalman filter , 1990, Image Vis. Comput..

[12]  Theodosios Pavlidis,et al.  Curve Fitting with Conic Splines , 1983, TOGS.

[13]  Paul L. Rosin,et al.  Multistage Combined Ellipse and Line Detection , 1992 .

[14]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[15]  Christian Beder.  Agglomerative Grouping of Observations by Bounding Entropy Variation , 2005, DAGM-Symposium.

[16]  Qiang Ji,et al.  A statistically efficient method for ellipse detection , 1999, Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348).

[17]  Wolfgang Förstner,et al.  Image Preprocessing for Feature Extraction in Digital Intensity, Color and Range Images , 2000 .

[18]  A. Moore,et al.  The Use of the Circle Tree for the Efficient Storage of Polygons , 2003 .

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

[20]  Jianping Wu.  Robust Real-Time Ellipse Detection by Direct Least-Square-Fitting , 2008, 2008 International Conference on Computer Science and Software Engineering.

[21]  Eugene Wong,et al.  Approximating parametric curves with strip trees using affine arithmetic , 2002, Proceedings. XV Brazilian Symposium on Computer Graphics and Image Processing.

[22]  Wolfgang Förstner,et al.  Polymorphic grouping for image segmentation , 1995, Proceedings of IEEE International Conference on Computer Vision.

[23]  Susanto Rahardja,et al.  Object Recognition by Discriminative Combinations of Line Segments, Ellipses, and Appearance Features , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.