A comprehensive framework for detection and characterization of overlapping intrinsic symmetry over 3D shapes is proposed. To identify prominent symmetric regions which overlap in space and vary in form, the proposed framework is decoupled into a Correspondence Space Voting procedure followed by a Transformation Space Mapping procedure. In the correspondence space voting procedure, significant symmetries are first detected by identifying surface point pairs on the input shape that exhibit local similarity in terms of their intrinsic geometry while simultaneously maintaining an intrinsic distance structure at a global level. Since different point pairs can share a common point, the detected symmetric shape regions can potentially overlap. To this end, a global intrinsic distance-based voting technique is employed to ensure the inclusion of only those point pairs that exhibit significant symmetry. In the transformation space mapping procedure, the Functional Map framework is employed to generate the final map of symmetries between point pairs. The transformation space mapping procedure ensures the retrieval of the underlying dense correspondence map throughout the 3D shape that follows a particular symmetry. Additionally, the formulation of a novel cost matrix enables the inner product to succesfully indicate the complexity of the underlying symmetry transformation. The proposed transformation space mapping procedure is shown to result in the formulation of a semi-metric symmetry space where each point in the space represents a specific symmetry transformation and the distance between points represents the complexity between the corresponding transformations. Experimental results show that the proposed framework can successfully process complex 3D shapes that possess rich symmetries.
The research literature on symmetry detection has grown substantially in recent years as shown in the excellent survey by Mitra et. al. @cite_11 . In this paper, we do not attempt to provide an exhaustive exposition of the state of the art in symmetry detection; rather we focus on discussing existing works that are most closely related to our proposed approach.
@cite_11
2003233837 2160306297 174734558 2124574189
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. 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. In this work we propose a learning-based approach to symmetry detection in natural images. We focus on ribbon-like structures, i.e. contours marking local and approximate reflection symmetry and make three contributions to improve their detection. First, we create and make publicly available a ground-truth dataset for this task by building on the Berkeley Segmentation Dataset. Second, we extract features representing multiple complementary cues, such as grayscale structure, color, texture, and spectral clustering information. Third, we use supervised learning to learn how to combine these cues, and employ MIL to accommodate the unknown scale and orientation of the symmetric structures. We systematically evaluate the performance contribution of each individual component in our pipeline, and demonstrate that overall we consistently improve upon results obtained using existing alternatives. Symmetry detection aims at discovering redundancy in the form of reoccurring structures in geometric objects. In this paper, we present a new symmetry detection algorithm for geometry represented as point clouds that is based on analyzing a graph of surface features. We combine a general feature detection scheme with a RANSAC-based randomized subgraph searching algorithm in order to reliably detect reoccurring patterns of locally unique structures. A subsequent segmentation step based on a simultaneous region growing variant of the ICP algorithm is applied to verify that the actual point cloud data supports the pattern detected in the feature graphs. We apply our algorithm to synthetic and real-world 3D scanner data sets, demonstrating robust symmetry detection results in the presence of scanning artifacts and noise. The modular and flexible nature of the graph-based detection scheme allows for easy generalizations of the algorithm, which we demonstrate by applying the same technique to other data modalities such as images or triangle meshes.