We present a new dataset, DENse and DIverse symmetry (DENDI), for reflection and rotation symmetry detection. DENDI contains real-world images with accurate and clean annotations for reflection and rotation symmetries and mitigates limitations of existing benchmarks. First, the reflection symmetry axes are diverse in scale and orientation, while previous datasets mostly focus on the dominant axes of the vertical or horizontal ones. Second, the rotation centers are annotated to the objects in polygon and ellipse shape, not limited to the circular objects. Third, the number of the rotation folds for each rotation center is annotated, which is the first in a large-scale dataset. Finally, the number of images is 1.7x and 2.0x larger than the second-largest reflection and rotation symmetry detection datasets, respectively.

Comparison with the existing datasets

Table 1. Comparison of the symmetry detection datasets.


1. Illustration of the annotating rules.

Figure 1. The images and labels of the objects with generic shapes. (a) and (b) indicate the annotations of the reflection and rotation symmetry, respectively. Best viewed in the electronic version.

2. Examples of the images and labels with generic shapes

Figure 2. Illustration of the generic shapes and their annotations. (a) and (b) indicate the annotation rules of the reflection and rotation symmetry, respectively.


Figure 3. Statistical analysis of DENDI. (a) and (b) represent the reflection symmetry dataset while (c) and (d) indicate the rotation symmetry dataset. In specific, (a) and (b) are histograms for scale and orientation of the reflection axes, (c) and (d) represent the histograms of the rotation fold and the number of the rotation centers.

More examples

1. Reflection symmetry.

Figure 4. The samples with (a) multiple symmetry axes, (b) circular objects, (c) skewed objects, and (d) dense symmetry axes are shown in the figure. Green lines indicate the reflection axes and the yellow lines indicate the '4'-shaped reflection circle annotation. The reflection-circle annotations are then converted to masks.

2. Rotation symmetry

Figure 5. Illustration of the examples in the rotation symmetry dataset. The samples with (a) circular objects, (b) circular objects with folds larger than 2, (c) polygons, and (d) dense symmetries are shown in the figure. Green lines indicate the circular annotations and the yellow polygons indicate the polygon-type annotations. Only the center coordinates are used for evaluation.


This work was supported by Samsung Advanced Institute of Technology (SAIT) and also by the NRF grant (NRF-2021R1A2C3012728) and the IITP grant (No.2021-0-02068: AI Innovation Hub, No.2019-0-01906: Artificial Intelligence Graduate School Program at POSTECH) funded by the Korea government (MSIT). We like to thank Yunseon Choi for her contribution to DENDI.


Reflection and Rotation Symmetry Detection via Equivariant Learning
Ahyun Seo, Byungjin Kim, Suha Kwak, Minsu Cho
CVPR, 2022
[arXiv] [Bibtex]

Code & dataset

Download dataset here [dendi.zip(391.8MB)]

Code are available online. [DENDI] [EquiSym]