Automatic rotational symmetry determination for shape analysis

doi:10.1016/0031-3203(87)90028-8

Pattern Recognition

Volume 20, Issue 6, 1987, Pages 571-582

https://doi.org/10.1016/0031-3203(87)90028-8 Get rights and content

Abstract

The determination of the rotational symmetry of a shape is useful for object recognition and shape analysis in computer vision applications. In this paper, a simple, but effective, algorithm to analyse the rotational symmetry of a given closed-curve shape S is proposed. A circle C with the centroid of S as the circle center and the average radius of S as the circle radius is superimposed on S, resulting in the intersection of C and S at a set of points. By theoretical analysis, the relationship between the order N_s of the rotational symmetry of S and the number of intersection points between C and S is established. All the possible values for N_s are determined. And finally N_s is determined by evaluating the similarity between S and its rotated versions. In the proposed algorithm, only simple pixel operations and second-order moment function computation are involved. Several problems caused by the use of discrete image coordinates are analysed and solved for correct decision-making in the algorithm. Good experimental results are also included.

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A noise-robust algorithm for detection and classification of cyclic and dihedral symmetric images is presented in this paper. For a symmetric image corrupted by an additive white Gaussian noise (AWGN), the proposed algorithm is implemented by converting the symmetry information into the representation of angularly evenly spaced zero-crossing lines in Mexican-hat wavelet domain; in addition, a continuous Mexican-hat ridgelet is applied to detect those zero-crossing lines, which achieves a simple and fast discrimination between cyclic and dihedral symmetries. Experimental results show that the proposed algorithm is very robust against noise and it can automatically classify the cyclic and dihedral symmetric images.
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Furthermore, symmetry information is also useful in ‘beautifying’ the object recovered, so as to produce a properly dimensioned solid model that can be used in a CAD system [2]. Most research on symmetry has been concerned with mirror and rotational symmetry [3–7]. Our work on mirror symmetry has been published elsewhere [8].
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^☆: This work was supported partially by ERSO, ITRI under Grant ITRI-MIST-85-C4.

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Automatic rotational symmetry determination for shape analysis☆

Abstract

CGIP

Pattern Recognition

CGIP

CGIP

Information Process. Lett.

CVGIP

Computer Vision and Sensor-Based Robots

A model-based vision system for industrial parts

IEEE Trans. Comput. C-27

A versatile machine vision system for complex industrial parts

IEEE Trans. Comput. C-26

A versatile computer-controlled assembly system

Probability, Random Variables, and Stochastic Processes