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.
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References
Yang Q, Ding X (2002) Symmetrical PCA in face recognition. In: Image processing—2002. Institute of Electrical and Electronics Engineers (IEEE)
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)
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, Workshops
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, Workshops
Pizlo Z, Li Y, Sawada T, Steinman RM (2014) Making a machine that sees like us. Oxford University Press
Wertheimer M (1923) Untersuchungen zur Lehre der Gestalt II. Psychologische Forschung 4:301–350
Kanizsa G (1980) Grammatica del vedere. Saggi su percezione e gestalt. Il Mulino
Michaelsen E, Yashina VV (2014) Simple gestalt algebra. Pattern Recognit Image Anal 24(4):542–551
Desolneux A, Moisan L, Morel J-M (2008) From Gestalt theory to image analysis: a probabilistic approach. Springer
Reisfeld D, Wolfson H, Yeshurun Y (1990) Detection of interest points using symmetry. In: International conference on computer vision (ICCV 1990), pp 62–65
Michaelsen E, Münch D, Arens M (2013) Recognition of symmetry structure by use of gestalt algebra. In: CVPR 2013 competition on symmetry detection
Michaelsen E (2014) Gestalt algebra—a proposal for the formalization of gestalt perception and rendering. Symmetry 6(3):566–577
Michaelsen E, Arens M (2017) Hierarchical grouping using gestalt assessments. In: CVPR 2017, Workshops, detecting symmetry in the wild
Fisher NI (1995) Statistical analysis of circular data. Cambridge University Press
Michaelsen E, Münch D, Arens M (2016) Searching remotely sensed images for meaningful nested Gestalten. In: XXII ISPRS Congress, (ISPRS Archives XLI-B3), pp 899–903
Loy G, Eklundh J (2006) Detecting symmetry and symmetric constellations of features. In: European conference on computer vision (ECCV), pp 508–521
Kondra S, Petrosino A, Iodice S (2013) Multi-scale kernel operators for reflection and rotation symmetry: further achievements. In: CVPR 2013 competition on symmetry detection
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):2274–2281
Hartley R, Zisserman A (2000) Multiple view geometry in computer vision. Cambridge University Press
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 211–216
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 452–460
Toldo R, Fusiello A (2008) Robust multiple structures estimation with j-linkage. In: European conference on computer vision (ECCV 2008). Springer, pp 537–547
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Michaelsen, E., Meidow, J. (2019). Reflection Symmetry. In: Hierarchical Perceptual Grouping for Object Recognition. Advances in Computer Vision and Pattern Recognition. Springer, Cham. https://doi.org/10.1007/978-3-030-04040-6_2
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DOI: https://doi.org/10.1007/978-3-030-04040-6_2
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