Symmetrie

Motivation

Symmetrie ist in der Natur sowie im alltäglichen Leben ein in vielfältiger Weise vorhandenes und weitverbreitetes Merkmal. Viele Gegenstände des täglichen Gebrauchs besitzen eine auf die ein oder andere Art symmetrische Struktur. Tiere und Menschen nutzen Symmetrie als Landmarke zur visuellen Exploration von Objekten und Umgebungen. Bis heute wurden viele unterschiedliche Aspekte der Symmetrie in verschiedenen Domänen erforscht, angefangen in der Biologie, wo Tiere Präferenzen bei der Paarung durch symmetrische Eigenschaften des Partners ziehen [KirkpatrickR'94, EnquistA'94], oder Tauben erfolgreich darauf getestet wurden, achsensymmetrische Muster von asymmetrischen zu unterscheiden [DeliusN'82]. Aspekte der Symmetrie wurden weiterhin auch auf den Gebieten der Psychologie und Psychophysik [PalmerH'78, LocherN'89] und der Mathematik, sowie auch in der maschinellen Bildverarbeitung ergründet. Viele Aspekte, die sich auf Natur und Mathematik beziehen, finden sich z.B. im Buch "Denkt Gott symmetrisch? - Das Ebenmaß in Mathematik und Natur" von Stewart und Golubitsky [StewartG'92]. Auf dem Gebiet der maschinellen Bildverarbeitung beschreibt die Symmetrie im Gegensatz zu bekannteren Verfahren der Merkmalsextraktion wie der Kantenerkennung ein regionales Merkmal, dessen Aussagekraft mit der betrachteten Region wächst. Der daraus entstehende Nachteil vieler Ansätze ist daher im hohen Aufwand an Rechenzeit zu sehen, begründet durch die notwendigerweise weitreichenderen Operatoren zur Symmetrieerkennung.

Referenzen

Eigene und kooperative Arbeiten [HuebnerVI'03] K. Huebner, "A 1-Dimensional Symmetry Operator for Image Feature Extraction in Robot Applications", 16th International Conference on Vision Interface (VI'03), S. 286-291, 2003. [HuebnerRC'03] K. Huebner, "A Symmetry Operator and its Application to the RoboCup", RoboCup 2003: Robot Soccer World Cup VII, S. 274-283, 2004. [Huebner'04] K. Huebner, "Symmetrie als kognitives Bildmerkmal", 10. Workshop Farbbildverarbeitung, 2004. Im Erscheinen. [PopescuHZ'02] D. Popescu and K. Huebner and J. Zhang, "Real-time Intelligent Vision Sensor for Robot Navigation Using Symmetry Features", 5th International FLINS Conference on Computational Intelligent System for Applied Research, S. 421-428, 2002. [PopescuZ'03] D. Popescu and J. Zhang, "Fuzzy expert system based on symmetry features for range estimations,", Proceedings of the 6th International Conference on Climbing and Walking Robots, S. 1007-1014, 2003. [PopescuZ'04] D. Popescu and J. Zhang, "Hardware implementation of an improved symmetry feature point extraction algorithm", Proceedings of the 6th International FLINS Conference on Computational Intelligent Systems for Applied Research, 2004. [WagnerH'04] T. Wagner and K. Huebner, "An Egocentric Qualitative Spatial Knowledge Representation Based on Ordering Information for Physical Robot Navigation", 8th International Workshop on RoboCup 2004 (Robot World Cup Soccer Games and Conferences). Lecture Notes in Computer Science, 2004. Im Erscheinen. [ZhangH'02] J. Zhang and K. Huebner, "Using Symmetry as a Feature in Panoramic Images for Mobile Robot Applications", Proceedings of Robotik 2002, VDI-Berichte 1679, S. 263-268, 2002. Symmetrie in Biologie und Psychologie [BarlowR'79] H.B. Barlow and B.C. Reeves, "The Versatility and Absolute Efficiency of Detecting Mirror Symmetry in Random Dot Displays", Vision Research 19, S. 783-793, 1979. [CsathoVH'03] Á. Csathó and G. van der Vloed and P.A. van der Helm,"Blobs strengthen repetition but weaken symmetry", Vision Research 43, S. 993-1007, 2003. [DeliusN'82] J.D. Delius and B. Nowak, "Visual Symmetry Recognition by Pigeons", Psychological Research 44, S. 199-212, 1982. [EnquistA'94] M. Enquist and A. Arak, "Symmetry, beauty and evolution", Nature 372, S. 169-172, 1994. [KirkpatrickR'94] M. Kirkpatrick and G.G. Rosenthal, "Symmetry without fear", Nature 372, S. 134-135, 1994. [LocherN'89] P. Locher and C. Nodine, "The Perceptual Value of Symmetry", Comput. Math. Applic. 17, S. 475-484, 1989. [PalmerH'78] S.E. Palmer and K. Hemenway, "Orientation and Symmetry: Effects of Multiple, Rotational, and Near Symmetries", Journal of Experimental Psychology: Human Perception and Performance 4 (4), S. 691-702, 1978. [Tyler'94] C.W. Tyler (Ed.), Spatial Vision 8 (4): "Special Issue on The Perception of Symmetry", 1994. [vdHelm'02] P.A. van der Helm, "Natural selection of visual symmetries", Behavioral and Brain Sciences 25 (3), S. 422-423, 2002. Symmetrie in der Bildverarbeitung [BigunPhD'88] J. Bigün, "Local Symmetry Features in Image Processing", Linköping University, PhD Thesis No. 179, 1988. [Bolduc'95] M. Bolduc and G. Sela and M.D. Levine and V. Cantoni and L. Lombardi and M. Mosconi and M. Savini and A. Setti, "Fast Computation of Multiscalar Symmetry in Foveated Images", Proceedings of the Conference on Computer Architectures for Machine Perception, S. 2-11, 1995. Nur Kurzform. [BradyA'84] M. Brady and H. Asada, "Smoothed Local Symmetries and Their Implementation", The International Journal of Robotics Research 3 (3), S. 36-61, 1984. [Chetverikov'99a] D. Chetverikov, "Texture Analysis Using Feature Based Pairwise Interaction Maps,", Pattern Recognition 32, Special Issue on Color and Texture, S.487-502, 1998. [Chetverikov'99] D. Chetverikov, "Fundamental Structural Features in the Visual World", Proceedings of the International Workshop on Fundamental Structural Properties in Image and Pattern Analysis, S. 47-58, 1999. [Chetverikov'03] D. Chetverikov and Z. Jankó, "Skewed Symmetry of Bidirectional Textures", Proceedings of the 27th Workshop of the Austrian Association for Pattern Recognition, S. 97-102, 2003. [DiGesu'95] V. Di Gesù and C. Valenti, "The Discrete Symmetry Transform in Computer Vision", Technical Report DMA Università di Palermo, 1995. [DiGesu'95b] V. Di Gesù and C. Valenti, "Symmetry Operators in Computer Vision", Proceedings of the First CCMA Workshop on Vision Modeling and Information Coding, 1995. [DiGesu'96] V. Di Gesù and C. Valenti, "A New Symmetry Operator for the Analysis of Sequences of Images", 1996. [Ferguson'00] R.W. Ferguson, "Modeling Orientation Effects in Symmetry Detection: The Role of Visual Structure", Proceedings of the 22nd Conference of the Cognitive Science Society, 2000. [JohanssonG'00] B. Johansson and G. Granlund, "Fast Selective Detection of Rotational Symmetries using Normalized Inhibition", Proceedings of the 6th European Conference on Computer Vision I, S. 871-887, 2000. [JohanssonKG'00] B. Johansson and H. Knutsson and G. Granlund, "Detecting Rotational Symmetries using Normalized Convolution", Proceedings of the 15th International Conference on Pattern Recognition 3, S. 500-504, 2000. [Johansson'03] B. Johansson, "Rotational Symmetries - a Quick Tutorial", Dept. EE, Linköping University, 2003. [KellyL'95] M.F. Kelly and M.D. Levine, "Annular Symmetry Operators: A Method for Locating and Describing Objects", Fifth International Conference on Computer Vision, S. 1016-1021, 1995. Nur Kurzform. [Kovesi'97] P.D. Kovesi, "Symmetry and Asymmetry From Local Phase", The 10th Australian Joint Conference on Artificial Intelligence, Poster Proceedings, S. 185-190, 1997. [Liu'00] Y. Liu, "Computational Symmetry", 21 of Symmetry 2000, S. 231-245, 2000. [LoyZ'02] G. Loy and A. Zelinsky, "A Fast Radial Symmetry Transform for Detecting Points of Interest", Proceedings of European Conference on Computer Vision (ECCV2002), S. 358-368, 2002. [ManmathaS'97] R. Manmatha and H.S. Sawhney, "Finding Symmetry in Intensity Images", University of Massachusetts, 1997. [Mukherjee'95] D. Mukherjee and A. Zisserman and J. Brady, "Shape from Symmetry - Detecting and Exploiting Symmetry in Affine Images", Philosophical Transactions of Royal Society of London, Series A (351), S. 77-106, 1995. [ReisfeldWY'95] D. Reisfeld and H. Wolfson and Y. Yeshurun, "Context Free Attentional Operators: the Generalized Symmetry Transform", International Journal of Computer Vision 14, S. 119-130, 1995. [SelaL'97] G. Sela and M.D. Levine, "Real-time Attention for Robotic Vision", Real-Time Imaging 3, S. 173-194, 1997. Nur Kurzform. [Sun'95] C. Sun, "Symmetry detection using gradient information", Pattern Recognition Letters 16, S. 987-996, 1995. [SunS'99] C. Sun and D. Si, "Fast Reflectional Symmetry Detection Using Orientation Histograms", Real-Time Imaging 5 (1), S. 63-74, 1999. [Zabrodsky'90] H. Zabrodsky, "Symmetry - A Review", Department of Computer Science, The Hebrew University of Jerusalem, 1990. [ZabrodskyPA'92] H. Zabrodsky and S. Peleg and D. Avnir, "Hierarchical Symmetry", International Conference on Pattern Recognition C, S. 9-12, 1992. [ZabrodskyPA'95] H. Zabrodsky and S. Peleg and D. Avnir, "Symmetry as a Continuous Feature", IEEE Transactions on Pattern Analysis and Machine Intelligence 17 (12), 1995. Symmetrie in speziellen Domänen [DiPrimio'97] F. Di Primio, "Symmetry and Symmetry-Breaking in Multi-Agent Behavior", In: Proceedings of International Symposium on Artificial Life and Robotics (AROB '97), S. 28-33, 1997. [Wong'00] K.-Y. K. Wong and P. R. S. Mendonca and R. Cipolla, "Camera Calibration from Symmetry", In: Proc. 9th IMA Conference on the Mathematics of Surfaces, S. 214-226, 2000. Bücher über Symmetrie [Hargittai'94] I. Hargittai and M. Hargittai, "Symmetry - A Unifying Concept", Shelter Publications, ISBN 0-936070-17-X, 1994. [StewartG'92] I. Stewart and M. Golubitsky, "Denkt Gott symmetrisch ?" (Deutsche Übersetzung des Buches "Fearful Symmetry: Is God a Geometer?", 1992.