# Reflection Symmetry Detection by Embedding Symmetry in a Graph

12 May 2019-pp 2147-2151

TL;DR: This work exploits the estimated boundary of the object and describes a boundary pixel using only the estimated normal of the boundary segment around the pixel to embed the symmetry axes in a graph as cliques to robustly detect the symmetry axis.

Abstract: Reflection symmetry is ubiquitous in nature and plays an important role in object detection and recognition tasks. Most of the existing methods for symmetry detection extract and describe each keypoint using a descriptor and a mirrored descriptor. Two keypoints are said to be mirror symmetric key-points if the original descriptor of one keypoint and the mirrored descriptor of the other keypoint are similar. However, these methods suffer from the following issue. The background pixels around the mirror symmetric pixels lying on the boundary of an object can be different. Therefore, their descriptors can be different. However, the boundary of a symmetric object is a major component of global reflection symmetry. We exploit the estimated boundary of the object and describe a boundary pixel using only the estimated normal of the boundary segment around the pixel. We embed the symmetry axes in a graph as cliques to robustly detect the symmetry axes. We show that this approach achieves state-of-the-art results in a standard dataset.

##### Citations

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TL;DR: Wang et al. as mentioned in this paper presented two shape signature-based reflection symmetry detection methods with their theoretical underpinning and empirical evaluation, which can effectively deal with compound shapes which are challenging for traditional contour-based methods.

Abstract: • A solid theoretical foundation of R-signature and LIP-signature about symmetric properties of a given shape is represented. • A verification process is theoretically justified to remove the false candidates based on an efficient symmetry measure. • Two novel datasets (UTLN-SRA & UTLN-MRA) with single & multiple reflections are designed for evaluating symmetry detectors. • A new evaluation protocol based on a lost measure is presented to evaluate reflectional symmetry detectors. • Comprehensive evaluations have verified that our proposed detectors perform well on binary images compared to state of the art. We present two novel shape signature-based reflection symmetry detection methods with their theoretical underpinning and empirical evaluation. LIP-signature and R-signature share similar beneficial properties allowing to detect reflection symmetry directions in a high-performing manner. For the shape signature of a given shape, its merit profile is constructed to detect candidates of symmetry direction. A verification process is utilized to eliminate the false candidates 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 evaluating symmetry detectors. Experimental results using standard and new datasets suggest that the proposed methods prominently perform compared to state of the art.

8 citations

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TL;DR: In this article, a stable metric is proposed to extract subsets of consistently oriented candidate segments, whenever the underlying 2D signal appearance exhibits definite near symmetric correspondences, and the ranking of such segments on the basis of the surrounding gradient orientation specularity, in order to reflect real symmetric object boundaries.

Abstract: This work addresses the challenging problem of reflection symmetry detection in unconstrained environments. Starting from the understanding on how the visual cortex manages planar symmetry detection, it is proposed to treat the problem in two stages: i) the design of a stable metric that extracts subsets of consistently oriented candidate segments, whenever the underlying 2D signal appearance exhibits definite near symmetric correspondences; ii) the ranking of such segments on the basis of the surrounding gradient orientation specularity, in order to reflect real symmetric object boundaries. Since these operations are related to the way the human brain performs planar symmetry detection, a better correspondence can be established between the outcomes of the proposed algorithm and a human-constructed ground truth. When compared to the testing sets used in recent symmetry detection competitions, a remarkable performance gain can be observed. In additional, further validation has been achieved by conducting perceptual validation experiments with users on a newly built dataset.

6 citations

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01 Oct 2022

TL;DR: This work points out an efficient detector of reflectionally symmetric shapes by addressing a class of projection-based signatures that are structured by a generalized $\mathcal{R}_{fm}$-transform model in accordance with reflectional symmetry detection.

Abstract: Analyzing reflectionally symmetric features inside an image is one of the important processes for recognizing the peculiar appearance of natural and man-made objects, biological patterns, etc. In this work, we will point out an efficient detector of reflectionally symmetric shapes by addressing a class of projection-based signatures that are structured by a generalized $\mathcal{R}_{fm}$-transform model. To this end, we will firstly prove the $\mathcal{R}_{fm^{-}}$transform in accordance with reflectional symmetry detection. Then different corresponding $\mathcal{R}_{fm}$-signatures of binary shapes are evaluated in order to determine which the corresponding exponentiation of the $\mathcal{R}_{fm}$-transform is the best for the detection. Experimental results of detecting on single/compound contour-based shapes have validated that the exponentiation of 10 is the most discriminatory, with over 2.7% better performance on the multiple-axis shapes in comparison with the conventional one. Additionally, the proposed detector also outperforms most of other existing methods. This finding should be recommended for applications in practice.

##### References

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01 Oct 2017TL;DR: The work in this paper starts from super-pixel primitives, and the grouping ends when the Gestalten almost fill the whole image, when the recognition rates are a little better.

Abstract: Real images contain symmetric Gestalten with high probability. I.e. certain parts can be mapped on other certain parts by the usual Gestalt laws and are repeated there with high similarity. Moreover, such mapping comes in nested hierarchies - e.g. a reflection Gestalt that is made of repetition friezes, whose parts are again reflection symmetric compositions. This can be explicitly modelled by continuous assessment functions. Hard decisions on whether or not a law is fulfilled are avoided. Starting from primitive objects extracted from the input image successively aggregates are constructed: reflection pairs, rows, etc., forming a part-of-hierarchy and rising in scale. The work in this paper starts from super-pixel primitives, and the grouping ends when the Gestalten almost fill the whole image. Occasionally the results may not be in accordance with human perception. The parameters have not been adjusted specifically for the data at hand. Previous work only used the compulsory attributes location, scale, orientation and assessment for each object. A way to improve the recognition performance is utilizing additional features such as colors or eccentricity. Thus the recognition rates are a little better.

6 citations

### "Reflection Symmetry Detection by Em..." refers background in this paper

...The approaches for reflection symmetry detection in real-world images can be categorized as voting based approaches [12, 13, 14, 21, 4, 6, 5, 15, 16, 17] and multiple model fitting approaches in [18, 19, 20]....

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01 Oct 2017TL;DR: This work attempts to compute the 2-D reflection symmetry map as an intra-image dense symmetric pixels correspondence problem, which is solved efficiently using a randomized algorithm by observing the reflection symmetry coherency present in the image.

Abstract: Detecting the reflection symmetry axis present in an object has been an active research problem in computer vision and computer graphics due to its various applications such as object recognition, object detection, modelling, and symmetrization of 3D objects. However, the problem of computing the reflection symmetry map for a given image containing objects exhibiting reflection symmetry has received a very little attention. The symmetry map enables us to represent the pixels in the image using a score depending on the probability of each of them having a symmetric counterpart. In this work, we attempt to compute the 2-D reflection symmetry map. We pose the problem of generating the symmetry map as an intra-image dense symmetric pixels correspondence problem, which we solve efficiently using a randomized algorithm by observing the reflection symmetry coherency present in the image. We introduce an application of symmetry map called symmetry preserving image stylization.

5 citations

### "Reflection Symmetry Detection by Em..." refers background in this paper

...The approaches for reflection symmetry detection in real-world images can be categorized as voting based approaches [12, 13, 14, 21, 4, 6, 5, 15, 16, 17] and multiple model fitting approaches in [18, 19, 20]....

[...]