__Keywords:__edge detection wavelet transform

D.A. Bezuglov, S.Yu. Rytikov, S.A. Shvidchenko, M.S. Gavrin, D.S. Gavrin

Edge detection a key initial step in solving a large class of image processing. This problem also applies to the problem of using different two-dimensional derivatives. In many cases, this is analogous to the allocation of sites, some of the critical points of the derivative, for example, such as its maximum or zero. The problem, commonly referred to allocation of units, consists of selecting a differential operator, suitable for further image processing.
The currently known methods for isolating circuits require actual computation of the derivatives of images with different masks. They are based on one of the basic properties of the luminance signal - the discontinuity. The most common way to find gaps is to process the image using a sliding mask, also called the filter kernel, window or template, which is a square matrix corresponding to the specified group of pixels of the image. There are masks Prewitt, Roberts, Sobel, Sobel with a Gaussian smoothing and others. However, since all of these methods actually realize the difference scheme computation of derivatives, they are ineffective in solving the problem of allocation of contours very noisy images. This is due to the fact that the numerical differentiation of signals and images on the background noise increases the error of calculating the derivative and often leads to a significant, unacceptable for practical use errors.
Thus, a new approach to the allocation of contours of images may be the use of other numerical methods for calculating the derivatives of signals and images that are resistant to noise, such as methods of wavelet differentiation.
The proposed method of image processing based on the mathematical apparatus of wavelet differentiation can effectively highlight the contours of images distorted by noise. In this case, the properties of the wavelet transform eliminates the use of various masks, that is, in fact, abandon the inefficient methods of numerical differentiation. On the basis of the proposed method can be implemented and the other edge detection algorithms based on wavelet differentiation using other wavelet bases.

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