We propose an algorithm to detect approximate reflection symmetry present in a set of volumetrically distributed points belonging to @math containing a distorted reflection symmetry pattern. We pose the problem of detecting approximate reflection symmetry as the problem of establishing the correspondences between the points which are reflections of each other and determining the reflection symmetry transformation. We formulate an optimization framework in which the problem of establishing the correspondences amounts to solving a linear assignment problem and the problem of determining the reflection symmetry transformation amounts to an optimization problem on a smooth Riemannian product manifold. The proposed approach estimates the symmetry from the distribution of the points and is descriptor independent. We evaluate the robustness of our approach by varying the amount of distortion in a perfect reflection symmetry pattern where we perturb each point by a different amount of perturbation. We demonstrate the effectiveness of the method by applying it to the problem of 2-D reflection symmetry detection along with relevant comparisons.
These algorithms primarily rely on the local image features such as edge orientations, curvatures, and gradients. The recent works such as ( @cite_49 @cite_40 @cite_28 @cite_31 @cite_51 @cite_52 @cite_11 @cite_27 @cite_18 @cite_12 @cite_26 @cite_42 ) present excellent algorithms for reflection symmetry detection in images. Given the accurate detection of keypoints, the algorithm developed in this work can be used to detect reflection symmetry in images without using local features.
@cite_18 @cite_26 @cite_28 @cite_42 @cite_52 @cite_40 @cite_27 @cite_49 @cite_31 @cite_51 @cite_12 @cite_11
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Reflection symmetry detection receives increasing attentions in recent years. The state-of-the-art algorithms mainly use the matching of intensity-based features (such as the SIFT) within a single image to find symmetry axes. This paper proposes a novel approach by establishing the correspondence of locally affine invariant edge-based features, which are superior to the intensity based in the aspects that it is insensitive to illumination variations, and applicable to textureless objects. The locally affine invariance is achieved by simple linear algebra for efficient and robust computations, making the algorithm suitable for detections under object distortions like perspective projection. Commonly used edge detectors and a voting process are, respectively, used before and after the edge description and matching steps to form a complete reflection detection pipeline. Experiments are performed using synthetic and real-world images with both multiple and single reflection symmetry axis. The test results are compared with existing algorithms to validate the proposed method. A simple and fast reflectional symmetry detection algorithm has been developed in this paper. The algorithm employs only the original gray scale image and the gradient information of the image, and it is able to detect multiple reflectional symmetry axes of an object in the image. The directions of the symmetry axes are obtained from the gradient orientation histogram of the input gray scale image by using the Fourier method. Both synthetic and real images have been tested using the proposed algorithm. Local feature-based symmetry detection algorithms can simultaneously consider symmetries over all locations, scales and orientations and achieve state-of-the-art performance. This paper demonstrates the limitations of these algorithms in case of dealing with background clutters, low contrast and smooth surfaces, and presents an adaptive feature point detection algorithm to overcome those limitations. Quantitative evaluations and subjective comparisons against the state-of-the-art reflection symmetry detection algorithm on the image dataset released by "Symmetry Detection from Real World Images Competition 2013" show a significant improvement in detection accuracy and computation efficiency. Furthermore, the proposed algorithm is also tested on the non-human primates' (NHPs') video surveillance data as a preprocessing step before NHPs' behaviors analysis, and a good performance is obtained as well. Local reflection symmetry detection in nature images is a quite important but challenging task in computer vision. The main obstacle is both the scales and the orientations of symmetric structure are unknown. The multiple instance learning (MIL) framework sheds lights onto this task owing to its capability to well accommodate the unknown scales and orientations of the symmetric structures. However, to differentiate symmetry vs non-symmetry remains to face extreme confusions caused by clutters scenes and ambiguous object structures. In this paper, we propose a novel multiple instance learning framework for local reflection symmetry detection, named multiple instance subspace learning (MISL), which instead learns a group of models respectively on well partitioned subspaces. To obtain such subspaces, we propose an efficient dividing strategy under MIL setting, named partial random projection tree (PRPT), by taking advantage of the fact that each sample (bag) is represented by the proposed symmetry features computed at specific scale and orientation combinations (instances). Encouraging experimental results on two datasets demonstrate that the proposed local reflection symmetry detection method outperforms current state-of-the-arts. HighlightsWe perform clustering on samples represented by multiple instances.We learn a group of MIL classifiers on subspaces.We report state-of-the-arts results on the symmetry detection benchmark.