Symmetry Detection Algorithm Research Articles

Skewed Rotation Symmetry Group Detection

We present a novel and effective algorithm for affinely skewed rotation symmetry group detection from real-world images. We define a complete skewed rotation symmetry detection problem as discovering five independent properties of a skewed rotation symmetry group: 1) the center of rotation, 2) the affine deformation, 3) the type of the symmetry group, 4) the cardinality of the symmetry group, and 5) the supporting region of the symmetry group in the image. We propose a frieze-expansion (FE) method that transforms rotation symmetry group detection into a simple, 1D translation symmetry detection problem. We define and construct a pair of rotational symmetry saliency maps, complemented by a local feature method. Frequency analysis, using Discrete Fourier Transform (DFT), is applied to the frieze-expansion patterns (FEPs) to uncover the types (cyclic, dihedral, and O2), the cardinalities, and the corresponding supporting regions, concentric or otherwise, of multiple rotation symmetry groups in an image. The phase information of the FEP is used to rectify affinely skewed rotation symmetry groups. Our result advances the state of the art in symmetry detection by offering a unique combination of region-based, feature-based, and frequency-based approaches. Experimental results on 170 synthetic and natural images demonstrate superior performance of our rotation symmetry detection algorithm over existing methods.

Learning‐based 3D face detection using geometric context

AbstractIn computer graphics community, face model is one of the most useful entities. The automatic detection of 3D face model has special significance to computer graphics, vision, and human‐computer interaction. However, few methods have been dedicated to this task. This paper proposes a machine learning approach for fully automatic 3D face detection. To exploit the facial features, we introduce geometric context, a novel shape descriptor which can compactly encode the distribution of local geometry and can be evaluated efficiently by using a new volume encoding form, named integral volume. Geometric contexts over 3D face offer the rich and discriminative representation of facial shapes and hence are quite suitable to classification. We adopt an AdaBoost learning algorithm to select the most effective geometric context‐based classifiers and to combine them into a strong classifier. Given an arbitrary 3D model, our method first identifies the symmetric parts as candidates with a new reflective symmetry detection algorithm. Then uses the learned classifier to judge whether the face part exists. Experiments are performed on a large set of 3D face and non‐face models and the results demonstrate high performance of our method. Copyright © 2007 John Wiley & Sons, Ltd.

Predicting and Detecting Symmetries in FOL Finite Model Search

Symmetries abound in logically formulated problems where many axioms are universally quantified, as this is the case in equational theories. Two complementary approaches have been used so far to dynamically tackle those symmetries: prediction and detection. The best-known predictive symmetry elimination method is the least number heuristic (lnh). A more recent predictive method, the extended least number heuristic (xlnh), focuses first on the enumeration of a bijection in the problem and easily exploits in the sequel the remaining isomorphisms. On the other hand, dynamic symmetry detection is costly in the general case (the problem is Graph Iso complete) but allows one to exploit more symmetries, and efficient (polytime) yet incomplete detection algorithms can be used on each node. This paper presents a generalization of xlnh that focuses on the enumeration of a unary function that does not require the function to be bijective, a general notion of symmetry for finite-model search in first-order logic together with an efficient symmetry detection algorithm, and a function-ordering heuristic that exploits the inherent structure of first-order logic theories to improve the search when using function-centric methods. A comprehensive study of the compared efficiency of all methods, in isolation and in combination, demonstrates the acceleration that can be expected in all cases. These ideas are implemented by using the known system SEM as an experimentation framework, to allow for accurate comparisons.

Using phase information for symmetry detection

Symmetry exists widely in the real world and plays a remarkable role in perception problems. The existing symmetry detection algorithms are mainly based on luminance or gradient information. Upon analyzing the relationship between symmetry and phase, based on phase congruency, we propose a phase-based symmetry detection (PSD) algorithm. PSD is calculated based on log Gabor wavelet. The symmetric points of objects are obtained by inspecting the phase information. The feasibility analysis, phase-based symmetry detection definition, and rationality demonstrations established the theoretic foundation for this algorithm. The experiments show that this algorithm can be applied directly to original images without segmentation—it is invariant to rotation, luminance and contrast—and it can detect several types of symmetries at the same time and it is compared with several other methods.

Detecting symmetries by branch & cut

The NP-hard problem of finding symmetries in an abstract graph plays an important role in automatic graph drawing and other applications. In this paper, we present an exact algorithm for automorphism and symmetry detection based on the branch & cut technique. We introduce IP-models for these problems and investigate the structure of the corresponding polytopes. For automorphisms, a complete description of the polytope is derived from a given set of generators of the automorphism group. The rotation polytopes are shown to be related to the asymmetric traveling salesman polytope, while the reflection polytope is related to the matching polytope. The algorithm was implemented within the ABACUS-framework and proves to run fast in practice.

Fast Reflectional Symmetry Detection Using Orientation Histograms

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.

Parallelization of symmetry detection algorithms on a network of workstations

Detection of spatial symmetry is useful in several computer vision applications. Due to the real-time nature of the applications, it is important that symmetry detection algorithms be computationally efficient. Sequential algorithms for finding various types of planar symmetries in images are CPU-intensive, prompting us to look for fast parallel implementations. In this paper, we propose parallel algorithms for symmetry detection, and report an implementation on a distributed computing environment consisting of a network of Sun workstations. Experiments revealed close-to-linear speedup on a number of test images which we considered.

3D symmetry detection using the extended Gaussian image

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.

Detection of rotational and involutional symmetries and congruity of polyhedra

We propose a simple and efficient general algorithm for determining both rotational and involutional symmetries of polyhedra. It requiresO(m2) time and usesO(m) space, wherem is the number of edges of the polyhedron. As this is the lower bound of the symmetry detection problem for the considered output form, our algorithm is optimal. We show that a slight modification of our symmetry detection algorithm can be used to solve the related conguity problem of polyhedra.

Symmetry detection using gradient information

Symmetry detection is important in the area of computer vision. A simple and fast symmetry detection algorithm has been developed in this paper. The algorithm employs only the original image and the gradient information. The direction of the symmetry axis is obtained from the gradient orientation histogram; and the position of this symmetry axis is decided either by the center of gravity or by the profile of the image projection along the direction of the symmetry axis. This method works directly on the grey-scale image and does not require any prior segmentation of the input image. Both simulated and real images have been tested and the results are very convincing.

Symmetry detection through local skewed symmetries

We explore how global symmetry can be detected prior to segmentation and under noise and occlusion. The definition of local symmetries is extended to affine geometries by considering the tangents and curvatures of local structures, and a quantitative measure of local symmetry known as symmetricity is introduced, which is based on Mahalanobis distances from the tangent-curvature states of local structures to the local skewed symmetry state-subspace. These symmetricity values, together with the associated local axes of symmetry, are spatially related in the local skewed symmetry field (LSSF). In the implementation, a fast, local symmetry detection algorithm allows initial hypotheses for the symmetry axis to be generated through the use of a modified Hough transform. This is then improved upon by maximizing a global symmetry measure based on accumulated local support in the LSSF-a straight active contour model is used for this purpose. This produced useful estimates for the axis of symmetry and the angle of skew in the presence of contour fragmentation, artifacts and occlusion.