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
More filters
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
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
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
More filters
TL;DR: This paper presents Nautilus --- a method for automatically identifying symmetric regions in an image along with their corresponding symmetry transformations that enables a number of automatic symmetry-aware image editing applications including inpainting, rectification, beautification, and segmentation.
Abstract: Natural images often exhibit symmetries that should be taken into account when editing them. In this paper we present Nautilus --- a method for automatically identifying symmetric regions in an image along with their corresponding symmetry transformations. We compute dense local similarity symmetry transformations using a novel variant of the Generalised PatchMatch algorithm that uses Metropolis-Hastings sampling. We combine and refine these local symmetries using an extended Lucas-Kanade algorithm to compute regional transformations and their spatial extents. Our approach produces dense estimates of complex symmetries that are combinations of translation, rotation, scale, and reflection under perspective distortion. This enables a number of automatic symmetry-aware image editing applications including inpainting, rectification, beautification, and segmentation, and we demonstrate state-of-the-art applications for each of them.
25 citations
"Reflection Symmetry Detection by Em..." refers background in this paper
...Symmetry has various applications in computer vision such as image matching and recognition [1], face verification [2], and image editing [3]....
[...]
01 Oct 2017
TL;DR: Using the MSR-computed plane of symmetry, techniques for the optimal symmetric pairwise assignment between axon reconstructions are introduced and visualizations illustrating how neighborhood relationships between nearby axon pairs compare with the relationships between their mirror-reflected counterparts along the anteroposterior axis are provided.
Abstract: We demonstrate that the problem of fitting a plane of mirror symmetry to data in any Euclidian space can be reduced to the problem of registering two datasets. The exactness of the resulting solution depends entirely on the registration accuracy. This new Mirror Symmetry via Registration (MSR) framework involves (1) data reflection with respect to an arbitrary plane, (2) registration of original and reflected datasets, and (3) calculation of the eigenvector of eigenvalue -1 for the transformation matrix representing the reflection and registration mappings. To support MSR, we also introduce a novel 2D registration method based on random sample consensus of an ensemble of normalized cross-correlation matches. With this as its registration back-end, MSR achieves state-of-the-art performance for symmetry line detection in two independent 2D testing databases. We further demonstrate the generality of MSR by testing it on a database of 3D shapes with an iterative closest point registration back-end. We finally explore its applicability to examining symmetry in natural systems by assessing the degree of symmetry present in myelinated axon reconstructions from a larval zebrafish. Using the MSR-computed plane of symmetry, we introduce techniques for the optimal symmetric pairwise assignment between axon reconstructions and provide visualizations illustrating how neighborhood relationships between nearby axon pairs compare with the relationships between their mirror-reflected counterparts along the anteroposterior axis.
23 citations
"Reflection Symmetry Detection by Em..." refers background or methods in this paper
...proposed a registration based approach for single axis detection [26]....
[...]
...We compare our method with the state-of-the-art methods [5], [26], [4], and [18] for single symmetry axis detection and with the methods [5], [4], and [18] for the multiple symmetry axes detection on the dataset in [8]....
[...]
...The method by [26] can only detect a single symmetry axis....
[...]
...[26], Loy and Eklundh [4], Nagar and Raman [18], and the proposed approach on the dataset [8]....
[...]
...Therefore, we do not compare with [26] for the multiple symmetry case....
[...]
01 Sep 2013
TL;DR: A simple but effective model for detecting the symmetric axes of bilaterally symmetric objects in unsegmented natural scene images and can often produce better results for the images containing limited texture.
Abstract: This paper presents a simple but effective model for detecting the symmetric axes of bilaterally symmetric objects in unsegmented natural scene images. Our model constructs a directed graph of symmetry interaction. Every node in the graph represents a matched pair of features, and every directed edge represents the interaction between nodes. The bilateral symmetry detection problem is then formulated as finding the star subgraph with maximal weight. The star structure ensures the consistency between grouped nodes while the optimal star subgraph can be found in polynomial time. Our model makes prediction based on contour cue: each node in the graph represents a pair of edge segments. Compared with the Loy and Eklundh's method which used SIFT feature, our model can often produce better results for the images containing limited texture. This advantage is demonstrated on two natural scene image sets.
13 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]....
[...]
TL;DR: A novel $k-symmetry clustering algorithm is proposed to minimize this energy function in order to efficiently find all the symmetry axes present in the given image.
Abstract: We propose an energy minimization approach to detect multiple reflection symmetry axes present in a given image representing fronto-parallel view of a scene. We perform local feature matching to detect the pairs of mirror symmetric points, and in order to formulate an energy function, we use the geometric characteristics of the symmetry axis. That is, it passes through the midpoint of line segment joining the two mirror symmetric points and is perpendicular to the vector joining two mirror symmetric points. We propose a novel $k$ - symmetry clustering algorithm to minimize this energy function in order to efficiently find all the symmetry axes present in the given image. We evaluate the proposed method on the standard datasets and show that we get comparable and better results than that of the state-of-the-art reflection symmetry detection methods.
12 citations
"Reflection Symmetry Detection by Em..." refers background or methods in this paper
...However, the keypoint detection based methods suffer from the following R. Nagar was supported by a TCS Research Scholarship and S. Raman was supported by a SERB Core Research Grant. issue....
[...]
...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]....
[...]
...[26], Loy and Eklundh [4], Nagar and Raman [18], and the proposed approach on the dataset [8]....
[...]
...We compare our method with the state-of-the-art methods [5], [26], [4], and [18] for single symmetry axis detection and with the methods [5], [4], and [18] for the multiple symmetry axes detection on the dataset in [8]....
[...]
01 Oct 2017
TL;DR: The proposed algorithm detects globally the symmetry axes inside an image plane and constructs a polar-based voting histogram based on the accumulation of the symmetry contribution (local texture and color information), in order to find the maximum peaks presenting as candidates of the primary symmetry axes.
Abstract: The proposed algorithm detects globally the symmetry axes inside an image plane. The main steps are as follows: We firstly extract edge features using Log-Gabor filters with different scales and orientations. Afterwards, we use the edge characteristics associated with the textural and color information as symmetrical weights for voting triangulation. In the end, we construct a polar-based voting histogram based on the accumulation of the symmetry contribution (local texture and color information), in order to find the maximum peaks presenting as candidates of the primary symmetry axes.
7 citations
"Reflection Symmetry Detection by Em..." refers background or methods 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]....
[...]
...We compare our method with the state-of-the-art methods [5], [26], [4], and [18] for single symmetry axis detection and with the methods [5], [4], and [18] for the multiple symmetry axes detection on the dataset in [8]....
[...]
...proposed an efficient voting based method, where they used the edge characteristics in the Log-Gabor wavelet response space [5]....
[...]