Abstract

Detecting an object using rotation symmetry property is widely applicable as most artificial objects have this property. However, current known techniques often fail due to using single symmetry energy. To tackle this problem, this paper proposes a novel method which consists of two steps: 1) Based on an optical image, two independent symmetry energies are extracted from the optical frequency space (RSS – Rotation Symmetry Strength) and phase space (SSD – Symmetry Shape Density). And, an optimized symmetry-energy-based fusion algorithm is creatively applied to these two energies to achieve a more comprehensive reflection of symmetry information. 2) In the fused symmetry energy map, the local region detection algorithm is used to realize the detection of multi-scale symmetry targets. Compared with known methods, the proposed method can get more multiple-scale (skewed, small-scale, and regular) rotation symmetry centers, and can significantly boost the performance of detecting symmetry properties with better accuracy. Experimental results confirm the performance of the proposed method, which is superior to the state-of-the-art methods.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (3)

X. Xu, Q. Huang, Y. Ren, D.-Y. Zhao, and J. Yang, “Sensor fault diagnosis for bridge monitoring system using similarity of symmetric responses,” Smart Struct. Syst. 23(3), 279–293 (2019).
[Crossref]

S. Wentao, H. Yong, G. Cailan, and K. Dingbo, “Spatial characteristics analysis of multi-scale ship target in scanning detection system,” Acta Opt. Sin. 39(7), 0728010 (2019).
[Crossref]

R. Huang, Y. Liu, X. Shi, Y. Zheng, Y. Wang, and B. Zhai, “A mathematical analysis method of the relationship between dft magnitude and periodic feature of a signal,” Sens. Imaging 20(1), 8 (2019).
[Crossref]

2018 (4)

R. Huang, Y. Liu, Z. Xu, P. Wu, and Y. Shi, “Multiple rotation symmetry group detection via saliency-based visual attention and frieze expansion pattern,” Signal Process. Image Commun. 60, 91–99 (2018).
[Crossref]

I. R. Atadjanov and S. Lee, “Robustness of reflection symmetry detection methods on visual stresses in human perception perspective,” IEEE Access 6, 63712–63725 (2018).
[Crossref]

Z. He and H. He, “Unsupervised multi-object detection for video surveillance using memory-based recurrent attention networks,” Symmetry 10(9), 375 (2018).
[Crossref]

C. Bartalucci, R. Furferi, L. Governi, and Y. Volpe, “A survey of methods for symmetry detection on 3d high point density models in biomedicine,” Symmetry 10(7), 263 (2018).
[Crossref]

2017 (2)

M. A. Zambrello, M. W. Maciejewski, A. D. Schuyler, G. Weatherby, and J. C. Hoch, “Robust and transferable quantification of nmr spectral quality using iroc analysis,” J. Magn. Reson. 285, 37–46 (2017).
[Crossref]

R. Arya, N. Singh, and R. Agrawal, “A novel combination of second-order statistical features and segmentation using multi-layer superpixels for salient object detection,” Appl. Intell. 46(2), 254–271 (2017).
[Crossref]

2016 (4)

P. Ma, Z. Zhang, X. Zhou, Y. Yun, Y. Liang, and H. Lu, “Feature extraction from resolution perspective for gas chromatography-mass spectrometry datasets,” RSC Adv. 6(115), 113997 (2016).
[Crossref]

K. D. Bemis, A. Harry, L. S. Eberlin, C. R. Ferreira, S. M. van de Ven, P. Mallick, M. Stolowitz, and O. Vitek, “Probabilistic segmentation of mass spectrometry (ms) images helps select important ions and characterize confidence in the resulting segments,” Mol. & Cell. Proteomics 15(5), 1761–1772 (2016).
[Crossref]

P. Cools, E. Ho, K. Vranckx, P. Schelstraete, B. Wurth, H. Franckx, G. Ieven, L. Van Simaey, S. Verhulst, F. De Baets, and M. Vaneechoutte, “Epidemic achromobacter xylosoxidans strain among belgian cystic fibrosis patients and review of literature,” BMC Microbiol. 16(1), 122 (2016).
[Crossref]

G. Pan, D. Sun, Y. Chen, and C. Zhang, “Multiresolution rotational symmetry detection via radius-based frieze-expansion,” J. Electr. Comput. Eng. 2016, 1–8 (2016).
[Crossref]

2015 (4)

S. Ren, A. A. Hinzman, E. L. Kang, R. D. Szczesniak, and L. J. Lu, “Computational and statistical analysis of metabolomics data,” Metabolomics 11(6), 1492–1513 (2015).
[Crossref]

J. Lu, M. J. Trnka, S.-H. Roh, P. J. Robinson, C. Shiau, D. G. Fujimori, W. Chiu, A. L. Burlingame, and S. Guan, “Improved peak detection and deconvolution of native electrospray mass spectra from large protein complexes,” J. The Am. Soc. for Mass Spectrom. 26(12), 2141–2151 (2015).
[Crossref]

K. Gupta and A. P. Chattopadhyay, “Dft studies of small rare-gas clusters,” PARIPEX-Indian J. Res. 4(10), 4 (2015).
[Crossref]

A. El ouaazizi, A. Nasri, and R. Benslimane, “A rotation symmetry group detection technique for the characterization of islamic rosette patterns,” Pattern Recognit. Lett. 68, 111–117 (2015).
[Crossref]

2010 (1)

S. Lee and Y. Liu, “Skewed rotation symmetry group detection,” IEEE Trans. Pattern Analysis Mach. Intell. 32(9), 1659–1672 (2010).
[Crossref]

1999 (1)

Y. Lei and K. C. Wong, “Detection and localisation of reflectional and rotational symmetry under weak perspective projection,” Pattern Recognit. 32(2), 167–180 (1999).
[Crossref]

Agrawal, R.

R. Arya, N. Singh, and R. Agrawal, “A novel combination of second-order statistical features and segmentation using multi-layer superpixels for salient object detection,” Appl. Intell. 46(2), 254–271 (2017).
[Crossref]

Arya, R.

R. Arya, N. Singh, and R. Agrawal, “A novel combination of second-order statistical features and segmentation using multi-layer superpixels for salient object detection,” Appl. Intell. 46(2), 254–271 (2017).
[Crossref]

Atadjanov, I. R.

I. R. Atadjanov and S. Lee, “Robustness of reflection symmetry detection methods on visual stresses in human perception perspective,” IEEE Access 6, 63712–63725 (2018).
[Crossref]

Bartalucci, C.

C. Bartalucci, R. Furferi, L. Governi, and Y. Volpe, “A survey of methods for symmetry detection on 3d high point density models in biomedicine,” Symmetry 10(7), 263 (2018).
[Crossref]

Bemis, K. D.

K. D. Bemis, A. Harry, L. S. Eberlin, C. R. Ferreira, S. M. van de Ven, P. Mallick, M. Stolowitz, and O. Vitek, “Probabilistic segmentation of mass spectrometry (ms) images helps select important ions and characterize confidence in the resulting segments,” Mol. & Cell. Proteomics 15(5), 1761–1772 (2016).
[Crossref]

Benslimane, R.

A. El ouaazizi, A. Nasri, and R. Benslimane, “A rotation symmetry group detection technique for the characterization of islamic rosette patterns,” Pattern Recognit. Lett. 68, 111–117 (2015).
[Crossref]

Boskamp, T.

Y. C. Hernandez, T. Boskamp, R. Casadonte, L. Hauberg-Lotte, J. Oetjen, D. Lachmund, A. Peter, D. Trede, K. Kriegsmann, M. Kriegsmann, J. Kriegsmann, and P. Maass, “Targeted feature extraction in maldi mass spectrometry imaging to discriminate proteomic profiles of breast and ovarian cancer,” PROTEOMICS–Clinical Appl. p. 1700168 (2018).

Burlingame, A. L.

J. Lu, M. J. Trnka, S.-H. Roh, P. J. Robinson, C. Shiau, D. G. Fujimori, W. Chiu, A. L. Burlingame, and S. Guan, “Improved peak detection and deconvolution of native electrospray mass spectra from large protein complexes,” J. The Am. Soc. for Mass Spectrom. 26(12), 2141–2151 (2015).
[Crossref]

Cailan, G.

S. Wentao, H. Yong, G. Cailan, and K. Dingbo, “Spatial characteristics analysis of multi-scale ship target in scanning detection system,” Acta Opt. Sin. 39(7), 0728010 (2019).
[Crossref]

Casadonte, R.

Y. C. Hernandez, T. Boskamp, R. Casadonte, L. Hauberg-Lotte, J. Oetjen, D. Lachmund, A. Peter, D. Trede, K. Kriegsmann, M. Kriegsmann, J. Kriegsmann, and P. Maass, “Targeted feature extraction in maldi mass spectrometry imaging to discriminate proteomic profiles of breast and ovarian cancer,” PROTEOMICS–Clinical Appl. p. 1700168 (2018).

Chattopadhyay, A. P.

K. Gupta and A. P. Chattopadhyay, “Dft studies of small rare-gas clusters,” PARIPEX-Indian J. Res. 4(10), 4 (2015).
[Crossref]

Chen, Y.

G. Pan, D. Sun, Y. Chen, and C. Zhang, “Multiresolution rotational symmetry detection via radius-based frieze-expansion,” J. Electr. Comput. Eng. 2016, 1–8 (2016).
[Crossref]

Chiu, W.

J. Lu, M. J. Trnka, S.-H. Roh, P. J. Robinson, C. Shiau, D. G. Fujimori, W. Chiu, A. L. Burlingame, and S. Guan, “Improved peak detection and deconvolution of native electrospray mass spectra from large protein complexes,” J. The Am. Soc. for Mass Spectrom. 26(12), 2141–2151 (2015).
[Crossref]

Collins, R. T.

S. Lee, R. T. Collins, and Y. Liu, “Rotation symmetry group detection via frequency analysis of frieze-expansions,” in Computer Vision and Pattern Recognition, 2008. CVPR 2008. IEEE Conference on, (IEEE, 2008), pp. 1–8.

Cools, P.

P. Cools, E. Ho, K. Vranckx, P. Schelstraete, B. Wurth, H. Franckx, G. Ieven, L. Van Simaey, S. Verhulst, F. De Baets, and M. Vaneechoutte, “Epidemic achromobacter xylosoxidans strain among belgian cystic fibrosis patients and review of literature,” BMC Microbiol. 16(1), 122 (2016).
[Crossref]

Cornelius, H.

H. Cornelius and G. Loy, “Detecting rotational symmetry under affine projection,” in 18th International Conference on Pattern Recognition (ICPR’06), vol. 2 (IEEE, 2006), pp. 292–295.

De Baets, F.

P. Cools, E. Ho, K. Vranckx, P. Schelstraete, B. Wurth, H. Franckx, G. Ieven, L. Van Simaey, S. Verhulst, F. De Baets, and M. Vaneechoutte, “Epidemic achromobacter xylosoxidans strain among belgian cystic fibrosis patients and review of literature,” BMC Microbiol. 16(1), 122 (2016).
[Crossref]

De Boer, B.

G. Kootstra, A. Nederveen, and B. De Boer, “Paying attention to symmetry,” in British Machine Vision Conference (BMVC2008), (The British Machine Vision Association and Society for Pattern Recognition, 2008), pp. 1115–1125.

Dingbo, K.

S. Wentao, H. Yong, G. Cailan, and K. Dingbo, “Spatial characteristics analysis of multi-scale ship target in scanning detection system,” Acta Opt. Sin. 39(7), 0728010 (2019).
[Crossref]

Eberlin, L. S.

K. D. Bemis, A. Harry, L. S. Eberlin, C. R. Ferreira, S. M. van de Ven, P. Mallick, M. Stolowitz, and O. Vitek, “Probabilistic segmentation of mass spectrometry (ms) images helps select important ions and characterize confidence in the resulting segments,” Mol. & Cell. Proteomics 15(5), 1761–1772 (2016).
[Crossref]

Eklundh, J.-O.

G. Loy and J.-O. Eklundh, “Detecting symmetry and symmetric constellations of features,” in European Conference on Computer Vision, (Springer, 2006), pp. 508–521.

El ouaazizi, A.

A. El ouaazizi, A. Nasri, and R. Benslimane, “A rotation symmetry group detection technique for the characterization of islamic rosette patterns,” Pattern Recognit. Lett. 68, 111–117 (2015).
[Crossref]

Ferreira, C. R.

K. D. Bemis, A. Harry, L. S. Eberlin, C. R. Ferreira, S. M. van de Ven, P. Mallick, M. Stolowitz, and O. Vitek, “Probabilistic segmentation of mass spectrometry (ms) images helps select important ions and characterize confidence in the resulting segments,” Mol. & Cell. Proteomics 15(5), 1761–1772 (2016).
[Crossref]

Franckx, H.

P. Cools, E. Ho, K. Vranckx, P. Schelstraete, B. Wurth, H. Franckx, G. Ieven, L. Van Simaey, S. Verhulst, F. De Baets, and M. Vaneechoutte, “Epidemic achromobacter xylosoxidans strain among belgian cystic fibrosis patients and review of literature,” BMC Microbiol. 16(1), 122 (2016).
[Crossref]

Fujimori, D. G.

J. Lu, M. J. Trnka, S.-H. Roh, P. J. Robinson, C. Shiau, D. G. Fujimori, W. Chiu, A. L. Burlingame, and S. Guan, “Improved peak detection and deconvolution of native electrospray mass spectra from large protein complexes,” J. The Am. Soc. for Mass Spectrom. 26(12), 2141–2151 (2015).
[Crossref]

Furferi, R.

C. Bartalucci, R. Furferi, L. Governi, and Y. Volpe, “A survey of methods for symmetry detection on 3d high point density models in biomedicine,” Symmetry 10(7), 263 (2018).
[Crossref]

R. Furferi, L. Governi, F. Uccheddu, and Y. Volpe, “A rgb-d based instant body-scanning solution for compact box installation,” in Advances on Mechanics, Design Engineering and Manufacturing, (Springer, 2017), pp. 819–828.

Galli, M.

M. Galli, “An easy-to-use software program for the ensemble pixel-by-pixel classification of maldi-msi datasets,” Università degli Studi di Milano-Bicocc (2018).

Governi, L.

C. Bartalucci, R. Furferi, L. Governi, and Y. Volpe, “A survey of methods for symmetry detection on 3d high point density models in biomedicine,” Symmetry 10(7), 263 (2018).
[Crossref]

R. Furferi, L. Governi, F. Uccheddu, and Y. Volpe, “A rgb-d based instant body-scanning solution for compact box installation,” in Advances on Mechanics, Design Engineering and Manufacturing, (Springer, 2017), pp. 819–828.

Guan, S.

J. Lu, M. J. Trnka, S.-H. Roh, P. J. Robinson, C. Shiau, D. G. Fujimori, W. Chiu, A. L. Burlingame, and S. Guan, “Improved peak detection and deconvolution of native electrospray mass spectra from large protein complexes,” J. The Am. Soc. for Mass Spectrom. 26(12), 2141–2151 (2015).
[Crossref]

Gupta, K.

K. Gupta and A. P. Chattopadhyay, “Dft studies of small rare-gas clusters,” PARIPEX-Indian J. Res. 4(10), 4 (2015).
[Crossref]

Hamermesh, M.

M. Hamermesh, Group theory and its application to physical problems (Courier Corporation, 2012).

Harry, A.

K. D. Bemis, A. Harry, L. S. Eberlin, C. R. Ferreira, S. M. van de Ven, P. Mallick, M. Stolowitz, and O. Vitek, “Probabilistic segmentation of mass spectrometry (ms) images helps select important ions and characterize confidence in the resulting segments,” Mol. & Cell. Proteomics 15(5), 1761–1772 (2016).
[Crossref]

Hatipoglu, B.

B. Hatipoglu, C. M. Yilmaz, and C. Kose, “A signal-to-image transformation approach for eeg and meg signal classification,” Signal, Image and Video Process. pp. 1–8 (2018).

Hauberg-Lotte, L.

Y. C. Hernandez, T. Boskamp, R. Casadonte, L. Hauberg-Lotte, J. Oetjen, D. Lachmund, A. Peter, D. Trede, K. Kriegsmann, M. Kriegsmann, J. Kriegsmann, and P. Maass, “Targeted feature extraction in maldi mass spectrometry imaging to discriminate proteomic profiles of breast and ovarian cancer,” PROTEOMICS–Clinical Appl. p. 1700168 (2018).

He, H.

Z. He and H. He, “Unsupervised multi-object detection for video surveillance using memory-based recurrent attention networks,” Symmetry 10(9), 375 (2018).
[Crossref]

He, Z.

Z. He and H. He, “Unsupervised multi-object detection for video surveillance using memory-based recurrent attention networks,” Symmetry 10(9), 375 (2018).
[Crossref]

Hel-Or, H.

Y. Liu, H. Hel-Or, and C. S. Kaplan, Computational symmetry in computer vision and computer graphics (Now publishers Inc, 2010).

Hernandez, Y. C.

Y. C. Hernandez, T. Boskamp, R. Casadonte, L. Hauberg-Lotte, J. Oetjen, D. Lachmund, A. Peter, D. Trede, K. Kriegsmann, M. Kriegsmann, J. Kriegsmann, and P. Maass, “Targeted feature extraction in maldi mass spectrometry imaging to discriminate proteomic profiles of breast and ovarian cancer,” PROTEOMICS–Clinical Appl. p. 1700168 (2018).

Hill, P. L.

P. L. Hill, “Post-processing method for determining peaks in noisy strain gauge data with a low sampling frequency,” Ph.D. thesis, Virginia Tech (2017).

Hinzman, A. A.

S. Ren, A. A. Hinzman, E. L. Kang, R. D. Szczesniak, and L. J. Lu, “Computational and statistical analysis of metabolomics data,” Metabolomics 11(6), 1492–1513 (2015).
[Crossref]

Ho, E.

P. Cools, E. Ho, K. Vranckx, P. Schelstraete, B. Wurth, H. Franckx, G. Ieven, L. Van Simaey, S. Verhulst, F. De Baets, and M. Vaneechoutte, “Epidemic achromobacter xylosoxidans strain among belgian cystic fibrosis patients and review of literature,” BMC Microbiol. 16(1), 122 (2016).
[Crossref]

Hoch, J. C.

M. A. Zambrello, M. W. Maciejewski, A. D. Schuyler, G. Weatherby, and J. C. Hoch, “Robust and transferable quantification of nmr spectral quality using iroc analysis,” J. Magn. Reson. 285, 37–46 (2017).
[Crossref]

Huang, Q.

X. Xu, Q. Huang, Y. Ren, D.-Y. Zhao, and J. Yang, “Sensor fault diagnosis for bridge monitoring system using similarity of symmetric responses,” Smart Struct. Syst. 23(3), 279–293 (2019).
[Crossref]

Huang, R.

R. Huang, Y. Liu, X. Shi, Y. Zheng, Y. Wang, and B. Zhai, “A mathematical analysis method of the relationship between dft magnitude and periodic feature of a signal,” Sens. Imaging 20(1), 8 (2019).
[Crossref]

R. Huang, Y. Liu, Z. Xu, P. Wu, and Y. Shi, “Multiple rotation symmetry group detection via saliency-based visual attention and frieze expansion pattern,” Signal Process. Image Commun. 60, 91–99 (2018).
[Crossref]

Ieven, G.

P. Cools, E. Ho, K. Vranckx, P. Schelstraete, B. Wurth, H. Franckx, G. Ieven, L. Van Simaey, S. Verhulst, F. De Baets, and M. Vaneechoutte, “Epidemic achromobacter xylosoxidans strain among belgian cystic fibrosis patients and review of literature,” BMC Microbiol. 16(1), 122 (2016).
[Crossref]

Itti, L.

L. Itti, C. Koch, and E. Niebur, “A model of saliency-based visual attention for rapid scene analysis,” IEEE Transactions on Pattern Analysis & Machine Intelligence pp. 1254–1259 (1998).

Kang, E. L.

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Acta Opt. Sin. (1)

S. Wentao, H. Yong, G. Cailan, and K. Dingbo, “Spatial characteristics analysis of multi-scale ship target in scanning detection system,” Acta Opt. Sin. 39(7), 0728010 (2019).
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R. Arya, N. Singh, and R. Agrawal, “A novel combination of second-order statistical features and segmentation using multi-layer superpixels for salient object detection,” Appl. Intell. 46(2), 254–271 (2017).
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BMC Microbiol. (1)

P. Cools, E. Ho, K. Vranckx, P. Schelstraete, B. Wurth, H. Franckx, G. Ieven, L. Van Simaey, S. Verhulst, F. De Baets, and M. Vaneechoutte, “Epidemic achromobacter xylosoxidans strain among belgian cystic fibrosis patients and review of literature,” BMC Microbiol. 16(1), 122 (2016).
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IEEE Access (1)

I. R. Atadjanov and S. Lee, “Robustness of reflection symmetry detection methods on visual stresses in human perception perspective,” IEEE Access 6, 63712–63725 (2018).
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IEEE Trans. Pattern Analysis Mach. Intell. (1)

S. Lee and Y. Liu, “Skewed rotation symmetry group detection,” IEEE Trans. Pattern Analysis Mach. Intell. 32(9), 1659–1672 (2010).
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J. Electr. Comput. Eng. (1)

G. Pan, D. Sun, Y. Chen, and C. Zhang, “Multiresolution rotational symmetry detection via radius-based frieze-expansion,” J. Electr. Comput. Eng. 2016, 1–8 (2016).
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J. Magn. Reson. (1)

M. A. Zambrello, M. W. Maciejewski, A. D. Schuyler, G. Weatherby, and J. C. Hoch, “Robust and transferable quantification of nmr spectral quality using iroc analysis,” J. Magn. Reson. 285, 37–46 (2017).
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J. The Am. Soc. for Mass Spectrom. (1)

J. Lu, M. J. Trnka, S.-H. Roh, P. J. Robinson, C. Shiau, D. G. Fujimori, W. Chiu, A. L. Burlingame, and S. Guan, “Improved peak detection and deconvolution of native electrospray mass spectra from large protein complexes,” J. The Am. Soc. for Mass Spectrom. 26(12), 2141–2151 (2015).
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Metabolomics (1)

S. Ren, A. A. Hinzman, E. L. Kang, R. D. Szczesniak, and L. J. Lu, “Computational and statistical analysis of metabolomics data,” Metabolomics 11(6), 1492–1513 (2015).
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Mol. & Cell. Proteomics (1)

K. D. Bemis, A. Harry, L. S. Eberlin, C. R. Ferreira, S. M. van de Ven, P. Mallick, M. Stolowitz, and O. Vitek, “Probabilistic segmentation of mass spectrometry (ms) images helps select important ions and characterize confidence in the resulting segments,” Mol. & Cell. Proteomics 15(5), 1761–1772 (2016).
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Pattern Recognit. (1)

Y. Lei and K. C. Wong, “Detection and localisation of reflectional and rotational symmetry under weak perspective projection,” Pattern Recognit. 32(2), 167–180 (1999).
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Pattern Recognit. Lett. (1)

A. El ouaazizi, A. Nasri, and R. Benslimane, “A rotation symmetry group detection technique for the characterization of islamic rosette patterns,” Pattern Recognit. Lett. 68, 111–117 (2015).
[Crossref]

RSC Adv. (1)

P. Ma, Z. Zhang, X. Zhou, Y. Yun, Y. Liang, and H. Lu, “Feature extraction from resolution perspective for gas chromatography-mass spectrometry datasets,” RSC Adv. 6(115), 113997 (2016).
[Crossref]

Sens. Imaging (1)

R. Huang, Y. Liu, X. Shi, Y. Zheng, Y. Wang, and B. Zhai, “A mathematical analysis method of the relationship between dft magnitude and periodic feature of a signal,” Sens. Imaging 20(1), 8 (2019).
[Crossref]

Signal Process. Image Commun. (1)

R. Huang, Y. Liu, Z. Xu, P. Wu, and Y. Shi, “Multiple rotation symmetry group detection via saliency-based visual attention and frieze expansion pattern,” Signal Process. Image Commun. 60, 91–99 (2018).
[Crossref]

Smart Struct. Syst. (1)

X. Xu, Q. Huang, Y. Ren, D.-Y. Zhao, and J. Yang, “Sensor fault diagnosis for bridge monitoring system using similarity of symmetric responses,” Smart Struct. Syst. 23(3), 279–293 (2019).
[Crossref]

Symmetry (2)

Z. He and H. He, “Unsupervised multi-object detection for video surveillance using memory-based recurrent attention networks,” Symmetry 10(9), 375 (2018).
[Crossref]

C. Bartalucci, R. Furferi, L. Governi, and Y. Volpe, “A survey of methods for symmetry detection on 3d high point density models in biomedicine,” Symmetry 10(7), 263 (2018).
[Crossref]

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R. Furferi, L. Governi, F. Uccheddu, and Y. Volpe, “A rgb-d based instant body-scanning solution for compact box installation,” in Advances on Mechanics, Design Engineering and Manufacturing, (Springer, 2017), pp. 819–828.

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S. Lee, R. T. Collins, and Y. Liu, “Rotation symmetry group detection via frequency analysis of frieze-expansions,” in Computer Vision and Pattern Recognition, 2008. CVPR 2008. IEEE Conference on, (IEEE, 2008), pp. 1–8.

P. L. Hill, “Post-processing method for determining peaks in noisy strain gauge data with a low sampling frequency,” Ph.D. thesis, Virginia Tech (2017).

G. Loy and J.-O. Eklundh, “Detecting symmetry and symmetric constellations of features,” in European Conference on Computer Vision, (Springer, 2006), pp. 508–521.

H. Cornelius and G. Loy, “Detecting rotational symmetry under affine projection,” in 18th International Conference on Pattern Recognition (ICPR’06), vol. 2 (IEEE, 2006), pp. 292–295.

T. O’Haver, A Pragmatic Introduction to Signal Processing (Lulu. com, 2016).

B. Hatipoglu, C. M. Yilmaz, and C. Kose, “A signal-to-image transformation approach for eeg and meg signal classification,” Signal, Image and Video Process. pp. 1–8 (2018).

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M. Galli, “An easy-to-use software program for the ensemble pixel-by-pixel classification of maldi-msi datasets,” Università degli Studi di Milano-Bicocc (2018).

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Figures (11)

Fig. 1.
Fig. 1. Core theory of RSS algorithm based on FEP [23]. (a) Original image (red point is rotation symmetry center). (b) FEP pattern. (c) Row of DFT magnitude results for (b) red dotted line.
Fig. 2.
Fig. 2. Core theory of SSD algorithm based on FEP [24]. (a) Original image with red points. (b) Two lines through (a) red points (slope based on phase value). (c) Red region representing all calculated points. (d) Lines through all points.
Fig. 3.
Fig. 3. Flowchart of RSS and SSD fusion algorithm. (a) Input image. (b) RSS map. (c) SSD map. (d) RSS and SSD fusion map. (e) Attended location. (f) Symmetry center region. (g) Location map. (h) Cartesian space. (i) Polar-transformed space. (j) Symmetry region. (k) Rotation symmetry order, type, regions.
Fig. 4.
Fig. 4. Comparison of various fusion algorithms with non-interval sampling calculations. (a) Original image. (b) Red region where RSS and SSD calculations are performed. (c) RSS result. (d) SSD result. (e) Fusion result of RSS direct addition to SSD. (f) Fusion result of RSS multiplied by SSD. (g) RSS gradient result. (h) SSD gradient result. (i) Numerical result after detecting RSS gradient. (j) Fusion result of proposed method.
Fig. 5.
Fig. 5. Comparison of various fusion algorithms with interval sampling calculation. (a) Original image. (b) Red region where RSS and SSD calculations are performed. (c) RSS result. (d) SSD result. (e) Fusion result of RSS direct addition to SSD. (f) Fusion result of RSS multiplication by SSD. (g) RSS gradient result. (h) SSD gradient result. (i) Numerical result after detecting RSS gradient. (j) Fusion result of proposed method.
Fig. 6.
Fig. 6. Comparison of various fusion algorithms with interval sampling to calculate the whole image. (a) Original image. (b) RSS result. (c) SSD result. (d) Fusion result of RSS direct addition to SSD. (e) Fusion result of RSS multiplication by SSD. (f) Fusion result of proposed method.
Fig. 7.
Fig. 7. Process of proposed fusion algorithm. (a) Original image. (b) Fusion result. (c) SBVA region of interest. (d) Concentrated energy region.
Fig. 8.
Fig. 8. Comparison of SSD algorithm [24] and proposed fusion algorithm under image occlusion. (a), (e) Original image (small portion occluded, half of image occluded). (b), (f) Results of SSD algorithm. (c), (d), (g), (h) Results of proposed fusion algorithm.
Fig. 9.
Fig. 9. Comparison of various rotation symmetry detection algorithms. (a-*) Original image. (b-*) Results of Lee algorithm [23]. (c-*) Results of Lee algorithm [24]. (d-*) Results of Huang algorithm [35]. (e-*) Results of proposed method.
Fig. 10.
Fig. 10. Comparison of various rotation symmetry center detection and recognition algorithms. (a) Original image. (b) Ground truth (GT). (c) Loy algorithm [25]. (d) ~(g) SBVA results with Huang algorithm [35], RSS maps, symmetry center detection results (red +), and symmetry attribute detection results. (h) ~(k) RSS map, SSD map, symmetry center detection results (red x), symmetry attribute detection results with Lee algorithm [24]. (l) ~(o) Proposed RSS and SSD fusion map, SBVA interest region detection results under fusion map, symmetry center detection results (red +), and symmetry attribute detection results.
Fig. 11.
Fig. 11. Comparison of various rotation symmetry center detection and recognition algorithms. (a) Original image. (b) Ground truth (GT). (c) Loy algorithm [25]. (d) ~(g) SBVA results with Huang algorithm [35], RSS maps, symmetry center detection results (red +), and symmetry attribute detection results. (h) ~(k) RSS map, SSD map, symmetry center detection results (red x), symmetry attribute detection results with Lee algorithm [24]. (l) ~(o) Proposed RSS and SSD fusion map, SBVA interest region detection results under fusion map, symmetry center detection results (red +), and symmetry attribute detection results.

Tables (1)

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Table 1. Experimental results. a

Equations (13)

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F ( x , y , λ ) = { F R S S 1 ( x , y ) + F S S D 1 ( x , y ) , F R S S 1 ( x , y ) 1 > λ , F S S D 1 ( x , y ) 1 > λ , min ( F R S S 1 ( x , y ) , F S S D 1 ( x , y ) ) ,     o t h e r .
{ λ s = { arg max λ ( x , y ) S F ( x , y , λ ) | λ = 1 , 2 , , max ( x , y ) S ( F R S S 1 ( x , y ) 1 , F S S D 1 ( x , y ) 1 ) } λ = min { arg min λ λ s ( x , y ) S F ( x , y , λ ) 1 }
{ F R S S 1 ( x , y ) = max ( x , y ) S ( F R S S ( x , y ) , F S S D ( x , y ) ) max ( x , y ) S ( F R S S ( x , y ) ) F R S S ( x , y ) F S S D 1 ( x , y ) = max ( x , y ) S ( F R S S ( x , y ) , F S S D ( x , y ) ) max ( x , y ) S ( F S S D ( x , y ) ) F S S D ( x , y )
{ F ( x , y ) = [ F x ( x , y ) F y ( x , y ) ] T F x ( x , y ) = F ( x + 1 , y ) F ( x 1 , y ) F y ( x , y ) = F ( x , y + 1 ) F ( x , y 1 )
F R S S ( x , y ) = r = 5 δ ρ r m e a n ( S x , y ( r , k p e a k ( r ) ) ) m e a n ( S x , y ( r , k ) ) , δ = 0 , 1 , 2 , , ( R 1 ) / 5 s . t . ρ r = { 1 , i f     M o d ( k p e a k ( r ) , min ( k p e a k ( r ) ) ) = 0 , 0 , o t h e r .
S x , y ( r , k ) = | n = 5 δ f x , y ( r , n ) e i 2 π K n k | 2 , δ = 0 , 1 , 2 , , ( K 1 ) / 5
S x , y ( r , k p e a k ( r ) ) m e a n { S x , y ( r , k ) | k = 1 , 2 , , ( K 1 ) / 5 } + β s t d { S x , y ( r , k ) | k = 1 , 2 , , ( K 1 ) / 5 }
P x i , y i ( r , k ) = n = 5 δ p x i , y i ( r , n ) e i 2 π K n k , δ = 0 , 1 , 2 , , ( K 1 ) / 5
{ ϕ i ( r ) = arctan ( R e ( P x i , y i ( r , 1 ) ) I m ( P x i , y i ( r , 1 ) ) ) Φ i = m e d i a n ( ϕ {i} ( r ) )  
tan Φ i x i + y i tan Φ i y + 1 x i + y i tan Φ i x = 1
C = ( x y ) = ( s i x i s j x j + y j y i s i s j s i s j ( x i x j ) + s j y j s i y i s i s j )
F S S D ( x , y ) = ( x i , y i ) S , ( x j , y j ) S ρ i j ρ i j = { 1 , ( x y ) = ( s i x i s j x j + y j y i s i s j s i s j ( x i x j ) + s j y j s i y i s i s j ) , 0 , o t h e r .
F R S S ( x , y ) = { max ( x , y ) S ( F R S S ( x , y ) ) F R S S ( x , y ) , ( ( x , y ) S ( ( [ 1 1 ] F R S S ( x , y ) ) < δ ) ) > α , F R S S ( x , y ) , {o} t h e r .

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