Reflection Symmetry Detection of Shapes Based on Shape Signatures

Thanh Phuong Nguyen1 and Phuoc Hung Truong2 and Thanh Tuan Nguyen 1,3 and Yong-Guk Kim3

1Toulon University, Aix Marseille University, CNRS, LIS, UMR 7020, 13397 Marseille, France
2Department of Computer Engineering, Sejong University, Seoul, Korea
3HCMC University of Technology and Education, Faculty of IT, Thu Duc City, Ho Chi Minh City, Viet Nam

Abstract

We present two novel shape signature-based re ection symmetry detection meth- ods with their theoretical underpinning and empirical evaluation. LIP-signature and R-signature share similar benecial properties allowing to detect re ection symmetry directions in a high-performing manner. Considering a shape signa- ture of a given shape, its merit prole is constructed to detect candidates of symmetry direction. A verication process is utilized to eliminate the false can- didates by addressing Radon projections. The proposed methods can effectively deal with compound shapes which are challenging for traditional contour-based methods. To quantify the symmetric efficiency, a new symmetry measure is proposed over the range [0, 1]. Furthermore, we introduce two symmetry shape datasets with a new evaluation protocol and a lost measure for evaluation of symmetry de- tectors. Experimental results using standard and new datasets suggest that the proposed methods prominently perform compared to state-of-the-art results.

The proposed UTLN-Reflection dataset has two test suites: SRA and MRA.

Existing datasets (i.e. MPEG-7 dataset) for reflection symmetry detection contain shapes which are single contour shapes, thus they are not really challenging. We also need to consider how well a symmetry detector works on complex/compound shapes where traditional methods based on contour approach can not. On the other hand, there is only one symmetrical axes for every shape of this dataset. Therefore, this fails to evaluate how a symmetry detector works on a shape containing several symmetrical axis and how good the detection is when the number of symmetrical axis is unknown.
In order to address those above shortcomings, we introduce in this paper a new dataset, called ``UTLN Reflection dataset'', designed for evaluation of reflectional symmetry detection. The dataset, which is created by collecting free images on the Internet, contains two test suites: SRA (Single Reflection Axis) and MRA (Multiple Reflection Axes). The first one (see Figure 1.a), which contains shapes having a single reflection symmetry, is designed to evaluate the detection of best reflection axis. The second one (see Figure 1.b), which addresses shapes of multiple reflection axes, is served for evaluating the detection of multiple reflection axes . Moreover, SRA and MRA contain both of simple and compound shapes. We asked 5 experts in the Computer Vision field to annotate datasets. The final ground-truth (GT) should be agreed by all experts. The distribution of number of symmetry axes is shown in Table I.

Figure 1: Some samples of UTLN-Reflection dataset: (a) SRA test suite (the first row); (b) MRA test suite (the second row).


UTLN Reflection

Table 1: A summary of UTLN-Reflection dataset
SRA MRA
Number of images 210 100
Number of reflection symmetry axes 210 535

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The following ressources are free used only for research purpose. If you use any of them, please cite the related works [1,2].

References

[1] Thanh Phuong Nguyen and Phuoc Hung Truong and Thanh Tuan Nguyen and Yong-Guk Kim, Reflection Symmetry Detection of Shapes based on Shape Signatures, Pattern Recognition, 2022
[2] Thanh Phuong Nguyen, Projection-based approach for reflection symmetry detection, International Conference on Image Processing, ICIP'19, Taipeh, Taiwan