Symmetry is an important cue for many applications, including object alignment, recognition, and segmentation. In this paper, we describe a planar reflective symmetry transform (PRST) that captures a continuous measure of the reflectional symmetry of a shape with respect to all possible planes. This transform combines and extends previous work that has focused on global symmetries with respect to the center of mass in 3D meshes and local symmetries with respect to points in 2D images. We provide an efficient Monte Carlo sampling algorithm for computing the transform for surfaces and show that it is stable under common transformations. We also provide an iterative refinement algorithm to find local maxima of the transform precisely. We use the transform to define two new geometric properties, center of symmetry and principal symmetry axes, and show that they are useful for aligning objects in a canonical coordinate system. Finally, we demonstrate that the symmetry transform is useful for several applications in computer graphics, including shape matching, segmentation of meshes into parts, and automatic viewpoint selection.

/pdf/a-planar-reflective-symmetry-transform-for-3d-shapes-2rmlk5h2ys.pdf

A planar-reflective symmetry transform for 3D shapes

Symmetry detection is important in the area of computer vision. A 3D symmetry detection algorithm is presented in this paper. The symmetry detection problem is converted to the correlation of the Gaussian image. Once the Gaussian image of the object has been obtained, the algorithm is independent of the input format. The algorithm can handle different kinds of images or objects. Simulated and real images have been tested in a variety of formats, and the results show that the symmetry can be determined using the Gaussian image.

3D symmetry detection using the extended Gaussian image

We propose an automatic method for finding symmetries of 3D shapes, that is, isometric transforms which leave a shape globally unchanged. These symmetries are deterministically found through the use of an intermediate quantity: the generalized moments. By examining the extrema and spherical harmonic coefficients of these moments, we recover the parameters of the symmetries of the shape. The computation for large composite models is made efficient by using this information in an incremental algorithm capable of recovering the symmetries of a whole shape using the symmetries of its subparts. Applications of this work range from coherent remeshing of geometry with respect to the symmetries of a shape to geometric compression, intelligent mesh editing, and automatic instantiation.

/pdf/accurate-detection-of-symmetries-in-3d-shapes-1jki7qbrmc.pdf

Accurate detection of symmetries in 3D shapes

To reveal and leverage the correlated and complemental information between different views, a great amount of multi-view learning algorithms have been proposed in recent years. However, unsupervised feature selection in multi-view learning is still a challenge due to lack of data labels that could be utilized to select the discriminative features. Moreover, most of the traditional feature selection methods are developed for the single-view data, and are not directly applicable to the multi-view data. Therefore, we propose an unsupervised learning method called Adaptive Unsupervised Multi-view Feature Selection (AUMFS) in this paper. AUMFS attempts to jointly utilize three kinds of vital information, i.e., data cluster structure, data similarity and the correlations between different views, contained in the original data together for feature selection. To achieve this goal, a robust sparse regression model with the l2,1-norm penalty is introduced to predict data cluster labels, and at the same time, multiple view-dependent visual similar graphs are constructed to flexibly model the visual similarity in each view. Then, AUMFS integrates data cluster labels prediction and adaptive multi-view visual similar graph learning into a unified framework. To solve the objective function of AUMFS, a simple yet efficient iterative method is proposed. We apply AUMFS to three visual concept recognition applications (i.e., social image concept recognition, object recognition and video-based human action recognition) on four benchmark datasets. Experimental results show the proposed method significantly outperforms several state-of-the-art feature selection methods. More importantly, our method is not very sensitive to the parameters and the optimization method converges very fast.

/pdf/adaptive-unsupervised-multi-view-feature-selection-for-2de1eytwtp.pdf

Adaptive unsupervised multi-view feature selection for visual concept recognition

The detection of significant local reflectional symmetry in grey level images is considered. Prior segmentation is not assumed, and it is intended that the results could be used for guiding visual attention and for providing side information to segmentation algorithms. A local measure of reflectional symmetry that transforms the symmetry detection problem to a global optimization problem is defined. Reflectional symmetry detection becomes equivalent to finding the global maximum of a complicated multimodal function parameterized by the location of the center of the supporting region, its size, and the orientation of the symmetry axis. Unlike previous approaches, time consuming exhaustive search is avoided. A global optimization algorithm for solving the problem is presented. It is related to genetic algorithms and to adaptive random search techniques. The efficiency of the suggested algorithm is experimentally demonstrated. Just one thousand evaluations of the local symmetry measure are typically needed in order to locate the dominant symmetry in natural test images.

https://link.springer.com/content/pdf/10.1023/A:1008034529558.pdf

Detecting Symmetry in Grey Level Images: The Global Optimization Approach

An algorithm for identifying symmetry of a 3-D object given by its octree is presented, and the symmetry degree (a measure of object symmetry) is proposed. The algorithm is based on traversals of the octree obtained by the principal axis transform of an input octree. An object can be in an arbitrary position and with arbitrary orientation within the octree space, and a wide range of symmetries represented by groups of proper and improper rotations can be identified. It is shown that the octree data structure supports these operations well, especially for objects whose symmetry types are simpler or equal in complexity with a fourfold rotational symmetry. The operation of the algorithm is illustrated using some synthetic test objects. The results, which are composed of identified symmetry types and the corresponding symmetry degrees, were satisfactory. >

Symmetry identification of a 3-D object represented by octree

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Symmetry identification of a 3-D object represented by octree