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The paper shows that it is expedient to use vector masks for solving some types of digital image processing problems. The main advantage of vector masks compared to matrix masks is that they reduce the computational complexity of algorithms while maintaining, and in some problems even improving, quality indicators. The article demonstrates examples of the use of vector masks in the problem of estimating the level of discrete white noise in an image, forming a basis for constructing a correctly working sigma filter, which are used for obtaining smoothed partial derivative estimates in the problem of edge detection and detecting straight lines in a contour image. The work uses results obtained by the authors in their earlier publications.

The paper considers the task on columns taking into account the properties of a great number of transpositions as domains of possible solutions of this task. We prove and algorithmize the localization method of the linear function value on a combinatorial set of transpositions. We also study the method of values organization of the efficiency function on a great number of transpositions that makes it possible to find the solutions of the task of linear function on transpositions with linear limitations. [ABSTRACT FROM AUTHOR]