Curved Glide-Reflection Symmetry Detection

We generalize reflection symmetry detection to a curved glide reflection symmetry detection problem. We propose a unifying, local feature based approach for curved glide reflection symmetry detection from real, unsegmented images, where the classic reflection symmetry becomes one of four special cases. Our method detects and groups statistically dominant local reflection axes in a 3D parameter space. A curved glid reflection symmetry axis is estimated by a set of contiguous local straight reflection axes. Experimental results of the proposed algorithm on 40 real world images demonstrate promising performance.

[1]  Jean Ponce,et al.  Computer Vision: A Modern Approach , 2002 .

[2]  Kok Cheong Wong,et al.  Detection and localisation of reflectional and rotational symmetry under weak perspective projection , 1999, Pattern Recognit..

[3]  Kaleem Siddiqi,et al.  Medial Representations: Mathematics, Algorithms and Applications , 2008 .

[4]  Giovanni Marola A technique for finding the symmetry axes of implicit polynomial curves under perspective projection , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Robert C. Bolles,et al.  Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography , 1981, CACM.

[6]  Bayya Yegnanarayana,et al.  Finding axes of symmetry from potential fields , 2004, IEEE Transactions on Image Processing.

[7]  Antti Ylä-Jääski,et al.  Grouping Symmetrical Structures for Object Segmentation and Description , 1996, Comput. Vis. Image Underst..

[8]  Bernard Chazelle,et al.  A Reflective Symmetry Descriptor , 2002, ECCV.

[9]  Oskar Söderkvist,et al.  Computer Vision Classification of Leaves from Swedish Trees , 2001 .

[10]  G LoweDavid,et al.  Distinctive Image Features from Scale-Invariant Keypoints , 2004 .

[11]  Takeo Kanade,et al.  Mapping Image Properties into Shape Constraints: Skewed Symmetry and Affine-Tramsfornable Patterns, and the Shape-from-Texture Paradigm , 1980, AAAI.

[12]  M. Kasper graphics , 1991, Illustrating Mathematics.

[13]  Xiaoou Tang,et al.  Efficient local reflectional symmetries detection , 2005, IEEE International Conference on Image Processing 2005.

[14]  Hagit Hel-Or,et al.  Symmetry as a Continuous Feature , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Harry Shum,et al.  Digital papercutting , 2005, SIGGRAPH '05.

[16]  Larry S. Davis,et al.  Detecting rotational symmetries , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[17]  Alfred M. Bruckstein,et al.  Skew symmetry detection via invariant signatures , 1998, Pattern Recognit..

[18]  Yanxi Liu Symmetry groups in robotic assembly planning , 1991 .

[19]  Mikkel B. Stegmann,et al.  Mid-sagittal plane and mid-sagittal surface optimization in brain MRI using a local symmetry measure , 2005, SPIE Medical Imaging.

[20]  Gert Kootstra,et al.  Paying Attention to Symmetry , 2008, BMVC.

[21]  Takeo Kanade,et al.  Mapping Image Properties into Shape Constraints: Skewed Symmetry, Affine-Transformable Patterns, and the Shape-from-Texture Paradigm , 1983 .

[22]  Jan-Olof Eklundh,et al.  Detecting Symmetry and Symmetric Constellations of Features , 2006, ECCV.

[23]  Changming Sun,et al.  3D Symmetry Detection Using The Extended Gaussian Image , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Andrew Zisserman,et al.  Shape from symmetry: detecting and exploiting symmetry in affine images , 1995, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[25]  Weixin Xie,et al.  Rotation Registration of Medical Images Based on Image Symmetry , 2005, ICIC.

[26]  S Minoshima,et al.  An automated method for rotational correction and centering of three-dimensional functional brain images. , 1992, Journal of nuclear medicine : official publication, Society of Nuclear Medicine.

[27]  Changming Sun,et al.  Fast Reflectional Symmetry Detection Using Orientation Histograms , 1999, Real Time Imaging.

[28]  Yanxi Liu,et al.  Local facial asymmetry for expression classification , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[29]  Luc Van Gool,et al.  Mirror and point symmetry under perspective skewing , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[30]  Sven J. Dickinson,et al.  Multiscale Symmetric Part Detection and Grouping , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[31]  Bin Dai,et al.  A Vehicle Detection Method via Symmetry in Multi-Scale Windows , 2007, 2007 2nd IEEE Conference on Industrial Electronics and Applications.

[32]  P. Locher,et al.  SYMMETRY CATCHES THE EYE , 1987 .

[33]  Lizhen Ji,et al.  Compactifications of Symmetric Spaces , 1998 .

[34]  Gareth Loy,et al.  Detecting Bilateral Symmetry in Perspective , 2006, 2006 Conference on Computer Vision and Pattern Recognition Workshop (CVPRW'06).

[35]  Andreas Kuehnle,et al.  Symmetry-based recognition of vehicle rears , 1991, Pattern Recognit. Lett..

[36]  Yehezkel Yeshurun,et al.  Context-free attentional operators: The generalized symmetry transform , 1995, International Journal of Computer Vision.

[37]  Sébastien Ourselin,et al.  Computation of the mid-sagittal plane in 3-D brain images , 2002, IEEE Transactions on Medical Imaging.

[38]  Takeo Kanade,et al.  Recovery of the Three-Dimensional Shape of an Object from a Single View , 1981, Artif. Intell..

[39]  Benoit M. Macq,et al.  Fast and automatic tumoral area localisation using symmetry , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[40]  Stefan Carlsson,et al.  Symmetry in Perspective , 1998, ECCV.

[41]  Yanxi Liu,et al.  Robust midsagittal plane extraction from normal and pathological 3-D neuroradiology images , 2001, IEEE Transactions on Medical Imaging.

[42]  Yanxi Liu,et al.  Performance evaluation of state-of-the-art discrete symmetry detection algorithms , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[43]  François X. Sillion,et al.  Accurate detection of symmetries in 3D shapes , 2006, TOGS.

[44]  Li Yi,et al.  Bilateral symmetry of object silhouettes under perspective projection , 2008, 2008 19th International Conference on Pattern Recognition.

[45]  Jean Ponce,et al.  On characterizing ribbons and finding skewed symmetries , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[46]  Giovanni Marola,et al.  On the Detection of the Axes of Symmetry of Symmetric and Almost Symmetric Planar Images , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[47]  Yanxi Liu,et al.  A Group Theoretic Formalization of Surface Contact , 1994, Int. J. Robotics Res..

[48]  Yanxi Liu,et al.  A computational model for periodic pattern perception based on frieze and wallpaper groups , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[49]  H. Damasio,et al.  IEEE Transactions on Pattern Analysis and Machine Intelligence: Special Issue on Perceptual Organization in Computer Vision , 1998 .

[50]  Joseph L. Mundy,et al.  Recognition of plane projective symmetry , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[51]  Luc Van Gool,et al.  Computational Symmetry in Computer Vision and Computer Graphics , 2010, Found. Trends Comput. Graph. Vis..

[52]  Yanxi Liu,et al.  Skewed Rotation Symmetry Group Detection , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[53]  Philippe Saint-Marc,et al.  B-spline Contour Representation and Symmetry Detection , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[54]  A. Zisserman,et al.  A three dimensional mid sagittal plane for brain asymmetry measurement , 1996, Schizophrenia Research.

[55]  Gunther Heidemann,et al.  Focus-of-attention from local color symmetries , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[56]  Yoshinobu Sato,et al.  Detecting Planar and Curved Symmetries of 3D Shapes from a Range Image , 1996, Comput. Vis. Image Underst..

[57]  Shmuel Raz,et al.  A new measure of symmetry and its application to classification of bifurcating structures , 2007, Pattern Recognit..

[58]  Richard A. Volz,et al.  Optimal algorithms for symmetry detection in two and three dimensions , 1985, The Visual Computer.

[59]  Francois Labonte,et al.  A perceptually plausible model for global symmetry detection , 1993, 1993 (4th) International Conference on Computer Vision.

[60]  Alexander V. Tuzikov,et al.  Convex Set Symmetry Measurement via Minkowski Addition , 2004, Journal of Mathematical Imaging and Vision.

[61]  Nahum Kiryati,et al.  Detecting Symmetry in Grey Level Images: The Global Optimization Approach , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[62]  Werner von Seelen,et al.  Intensity and Edge-Based Symmetry Detection Applied to Car-Following , 1992, ECCV.

[63]  M. Brady,et al.  Smoothed Local Symmetries and Their Implementation , 1984 .

[64]  John Stillwell,et al.  Symmetry , 2000, Am. Math. Mon..

[65]  James Hays,et al.  A Quantitative Evaluation of Symmetry Detection Algorithms , 2007 .

[66]  Iwao Kanno,et al.  Automatic detection of the mid-sagittal plane in 3-D brain images , 1997, IEEE Transactions on Medical Imaging.

[67]  Nahum Kiryati,et al.  On Symmetry, Perspectivity, and Level-Set-Based Segmentation , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[68]  Dinggang Shen,et al.  Robust detection of skewed symmetries , 2000, Proceedings 15th International Conference on Pattern Recognition. ICPR-2000.

[69]  Philippe Saint-Marc,et al.  B-Spline Contour Representation and Symmetry Detection , 1990, ECCV.

[70]  Leonidas J. Guibas,et al.  Discovering structural regularity in 3D geometry , 2008, ACM Trans. Graph..

[71]  Yanxi Liu,et al.  Curved Reflection Symmetry Detection with Self-validation , 2010, ACCV.