Advertisement

Reflection Symmetry

  • Eckart Michaelsen
  • Jochen Meidow
Chapter
Part of the Advances in Computer Vision and Pattern Recognition book series (ACVPR)

Abstract

Reflection symmetry is a standard example for the role of perceptual grouping in foreground/background discrimination. The basic relations of reflection symmetric arrangements of oriented parts are given. Hard constraints are replaced by continuous membership assessments. Next to the reflection law, the parts always also need to be in proximity, for which specific continuous assessment functions are discussed. Furthermore, the symmetry is stronger when additionally other features of the parts are similar, such as size, colors, or descriptors. If smaller parts are further away from each other, nested hierarchies of symmetries should be considered. Examples for this are given. Most reflection symmetry recognition procedures use clustering, often implemented in accumulators. A theory for this accumulation is based on a contrario testing. In practice, the reflection symmetry is often distorted due to perspective projection. For this case an algebraic solution using homogeneous coordinates is presented.

References

  1. 1.
    Yang Q, Ding X (2002) Symmetrical PCA in face recognition. In: Image processing—2002. Institute of Electrical and Electronics Engineers (IEEE)Google Scholar
  2. 2.
    Harguess J, Aggarwal JK (2011) Is there a connection between face symmetry and face recognition? In: Computer vision and pattern recognition workshops—CVPRW 2011. Institute of Electrical and Electronics Engineers (IEEE)Google Scholar
  3. 3.
    Liu J, Slota G, Zheng G, Wu Z, Park M, Lee S, Rauschert I, Liu Y (2013) Symmetry detection from realworld images competition 2013: summary and results. In: CVPR 2013, WorkshopsGoogle Scholar
  4. 4.
    Funk C, Lee S, Oswald MR, Tsokas S, Shen W, Cohen A, Dickinson S, Liu Y (2017) ICCV challenge: detecting symmetry in the wild. In: ICCV 2017, WorkshopsGoogle Scholar
  5. 5.
    Pizlo Z, Li Y, Sawada T, Steinman RM (2014) Making a machine that sees like us. Oxford University PressGoogle Scholar
  6. 6.
    Wertheimer M (1923) Untersuchungen zur Lehre der Gestalt II. Psychologische Forschung 4:301–350CrossRefGoogle Scholar
  7. 7.
    Kanizsa G (1980) Grammatica del vedere. Saggi su percezione e gestalt. Il MulinoGoogle Scholar
  8. 8.
    Michaelsen E, Yashina VV (2014) Simple gestalt algebra. Pattern Recognit Image Anal 24(4):542–551CrossRefGoogle Scholar
  9. 9.
    Desolneux A, Moisan L, Morel J-M (2008) From Gestalt theory to image analysis: a probabilistic approach. SpringerGoogle Scholar
  10. 10.
    Reisfeld D, Wolfson H, Yeshurun Y (1990) Detection of interest points using symmetry. In: International conference on computer vision (ICCV 1990), pp 62–65Google Scholar
  11. 11.
    Michaelsen E, Münch D, Arens M (2013) Recognition of symmetry structure by use of gestalt algebra. In: CVPR 2013 competition on symmetry detectionGoogle Scholar
  12. 12.
    Michaelsen E (2014) Gestalt algebra—a proposal for the formalization of gestalt perception and rendering. Symmetry 6(3):566–577MathSciNetCrossRefGoogle Scholar
  13. 13.
    Michaelsen E, Arens M (2017) Hierarchical grouping using gestalt assessments. In: CVPR 2017, Workshops, detecting symmetry in the wildGoogle Scholar
  14. 14.
    Fisher NI (1995) Statistical analysis of circular data. Cambridge University PressGoogle Scholar
  15. 15.
    Michaelsen E, Münch D, Arens M (2016) Searching remotely sensed images for meaningful nested Gestalten. In: XXII ISPRS Congress, (ISPRS Archives XLI-B3), pp 899–903CrossRefGoogle Scholar
  16. 16.
    Loy G, Eklundh J (2006) Detecting symmetry and symmetric constellations of features. In: European conference on computer vision (ECCV), pp 508–521CrossRefGoogle Scholar
  17. 17.
    Kondra S, Petrosino A, Iodice S (2013) Multi-scale kernel operators for reflection and rotation symmetry: further achievements. In: CVPR 2013 competition on symmetry detectionGoogle Scholar
  18. 18.
    Achanta R, Shaji A, Smith K, Lucchi A, Fua P, Susstrunk S (2012) SLIC superpixels compared to state-of-the-art superpixel, methods. Trans Pattern Anal Mach Intell 34(11):2274–2281CrossRefGoogle Scholar
  19. 19.
    Hartley R, Zisserman A (2000) Multiple view geometry in computer vision. Cambridge University PressGoogle Scholar
  20. 20.
    Pătrăucean V, von Gioi RG, Ovsjanikov M (2013) Detection of mirror-symmetric image patches. In: 2013 IEEE conference on computer vision and pattern recognition workshops, pp 211–216Google Scholar
  21. 21.
    Tang Z, Monasse P, Morel J-M (2014) Reflexive symmetry detection in single image. In Boissonnat J-D, Cohen A, Gibaru O, Gout C, Lyche T, Mazure M-L, Schumaker LL (eds) Curves and surfaces. Proceedings of the 8th international conference curves and surfaces, Lecture notes in computer science, vol 9213. Springer, pp 452–460Google Scholar
  22. 22.
    Toldo R, Fusiello A (2008) Robust multiple structures estimation with j-linkage. In: European conference on computer vision (ECCV 2008). Springer, pp 537–547Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Fraunhofer IOSBEttlingenGermany

Personalised recommendations