Abstract
Abstract. In this paper we solve the problem of finding the symmetry axis of the object in a digital binary image. A new axial symmetry criterion is formulated for a connected discrete object. The problem of determining the symmetry measure and finding the symmetry axes arises in a variety of applications. In discrete images, exact symmetry is possible only in special cases. The disadvantage of the existing methods solving this problem is the high computational complexity. To improve computational efficiency, it is proposed to use the so-called Fourier descriptor. A new method for estimating the asymmetry of a discrete silhouette is proposed. The described algorithm for calculating the measure of asymmetry and determining the axis of symmetry is quadratic by the number of contour points. Methods for reducing the volume of calculations using a convex hull and taking into account the values of the modules of Fourier coefficients are proposed. Computational experiments are conducted with silhouettes of aircraft extracted from earth remote sensing images. The reliability of the described solution is established.
Highlights
We solve the problem of finding the symmetry axis of an object on a digital binary image, and formulate a new axial symmetry criterion of a connected discrete object
The problem of determining the symmetry measure and finding symmetry the axes occurs in a variety of applications, for example, there is a problem of detecting tumors in a digital image in medicine, which is characterized by the presence of the axis of symmetry (1)
We introduce a new symmetry measure of discrete objects based on the use of the so-called Fourier descriptor of the contour (9)
Summary
We solve the problem of finding the symmetry axis of an object on a digital binary image, and formulate a new axial symmetry criterion of a connected discrete object. We introduce a new symmetry measure of discrete objects based on the use of the so-called Fourier descriptor of the contour (9). A method for determining the symmetry based on the Fourier descriptor was proposed earlier in (11), the difference of our method consists in a new symmetry measure numerical evaluation, which proved itself well in experiments with noisy images. The existing methods solving this problem have high computational complexity. The methods in the first class based on the comparison of the two halves of the image (contour, skeleton view). An algorithm for refining the axis of symmetry for binary discrete images is presented in (1). There is a binary matrix M , where the element mij is an indicator that the pixel number (i, j) belongs to the object
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