# Optoelectronics, Instrumentation and Data Processing (v.46, #1)

Synthesis of gradient algorithms with the minimum systematic error for estimating directional fields by I. S. Gruzman; V. B. Karpushin

*(1-8)*. A method is proposed for constructing noise-resistant mask differentiating filters minimizing systematic errors in estimating directional fields by a gradient algorithm. A comparative analysis of the accuracy of gradient algorithms was performed by computer modeling It is shown that a decrease in the systematic error leads to a considerable increase in the accuracy of directional field estimation

**Keywords:**directional field; gradient algorithm; mask differentiating filter

Discrimination between random signals and impulse noise in images which is optimal according to the criterion of minimum combined losses by E. A. Samoilin

*(9-17)*. An algorithm is proposed for discriminating between random image signals and non-Gaussian impulse noise with a uniform brightness distribution which is based on a new optimality criterion combining the minimization of weighted unconditional probabilities of wrong decisions of the first and second kind and maximization of the probabilities of making correct decisions. Results of numerical studies of the proposed and the well-known Bayes algorithms are given showing that the use of the new algorithm reduces the discrimination error under conditions of complete a priori uncertainty of the image signal distribution.

**Keywords:**optimal discrimination; image signals; impulse noise; combined losses

Application of the algorithm of compensation for linear distortions in solving systems with banded matrices by V. M. Efimov; A. L. Reznik; A. V. Torgov; A. V. Tuzikov

*(18-26)*. A possibility of application of the algorithm of compensation for linear distortions in solving systems of linear algebraic equations with banded matrices is considered. Relations necessary for the procedure of stage-by-stage searching for the solution are derived, and conditions of correctness of their application are determined.

**Keywords:**banded matrix; Töplitz system of equations; recursive filter; sample function; frequency characteristic

Quasi-optimal algorithm of estimating the coefficients of wavelet expansions during signal filtration by Yu. E. Voskoboinikov; A. V. Gochakov

*(27-36)*. The proposed algorithm calculates its own filtration factor for each coefficient of the wavelet expansion of a noisy signal. The optimal filtration factor depends on the signal-to-noise ratio, which is estimated with a specially constructed iterative procedure. The limit points of this procedure are determined. A computational experiment performed shows that the proposed approach can be effectively used in problems of filtration and compression of noisy signals and images.

**Keywords:**filtration; wavelet functions; filtration factors

Inverse problem of rotation of three-dimensional vector signals by Ya. A. Furman; I. L. Egoshina

*(37-45)*. This paper considers the problem of determining the rotation parameters such as the direction vector of the rotation axis and the rotation angle of a three-dimensional image whose surface points are specified by vectors. The initial and rotated vectors are considered known. An approach using a quaternion representation of vectors is proposed, whose computational efficiency is severalfold higher than the efficiency of known approaches. The mechanism of the effect of noise on the accuracy of determination of the parameters is studied, and recommendations on error minimization are given. Features of the solution of the inverse problem of rotation as applied to the image recognition system are considered.

**Keywords:**rotation matrix; rotating quaternions; quaternion signal; rotation angle corrector; similarity measure generator

Estimation of parameters and recognition of images of three-dimensional objects with disordered samples by A. A. Rozhentsov; A. A. Baev; A. S. Naumov

*(46-55)*. An approach to processing images of three-dimensional objects which does not require knowledge of the ordering of the samples specifying the coordinates of points on the object surface is considered. The approach is based on obtaining a secondary analytical description of an object in the form of a polynomial function of a hypercomplex variable that projects samples of the object surface onto a sphere. It is shown that the method allows one to estimate scaling and rotation parameters and to recognize three-dimensional objects from polynomial coefficients. The performance of the proposed algorithms was estimated in experiments using images of real objects and mathematical models.

**Keywords:**quaternions; recognition; contours of three-dimensional images; functions of a hypercomplex variable; invariance to ordering

Development and investigation of two-level non-parametric estimators by A. V. Lapko; V. A. Lapko

*(56-63)*. A method of synthesis of two-level non-parametric pattern recognition systems based on the principles of decomposition of learning samples in terms of their volume and on using the technology of parallel computations is proposed. The properties of these systems are analyzed on the basis of computational experiments performed.

**Keywords:**non-parametric statistics; pattern recognition systems; decomposition of the learning sample; asymptotic properties

Modeling and analysis of motion of biological objects on the basis of a sequence of images obtained in studying the motion activity by V. A. Kulikov; V. A. Ivanov; V. S. Kirichuk

*(64-69)*. A new approach to analyzing the data obtained by tracking biological objects in studying the motion activity is considered. The approach is based on a proposed mathematical model of motion of a biological object. The object behavior observed during the experiment can be described in the form of model parameters. A numerical experiment with model data is performed, which shows that the estimates predicted by the proposed method ensure a smaller root-mean-square deviation of the object state classification than other available methods.

**Keywords:**testing; trajectory; tracking; biological object; motion activity

Use of the theory of fractals in image analysis tasks by V. S. Pleshanov; A. A. Napryushkin; V. V. Kibitkin

*(70-78)*. A detailed review of the best-known methods for estimating fractal dimension (FD) is given, and their accuracy and computational complexity are demonstrated by estimating the FD of model images with a high degree of self-similarity. A new algorithm for estimating FD by linear transformations is proposed which gives much lower error without significantly increasing the computational complexity.

**Keywords:**fractal; fractal dimension; image; algorithm; generation; error

Specific features of controlling laser systems for micromachining of moving carriers by V. P. Bessmeltsev; N. V. Goloshevsky; K. K. Smirnov

*(79-86)*. One possible approach of controlling laser systems based on galvanometric scanners for precision micromachining of continuously moving materials is considered. A variant of implementation of the system with sensors of relative displacements of the material and real-time correction algorithms is demonstrated, which ensures the micromachining velocity close to the maximum possible value for these scanners. Experimental results of micromachining of polymer tapes are given.

**Keywords:**laser micromachining of moving carriers; complementary scanners; galvanometric scanners; CO

_{2}laser

Methods of improving the accuracy of operation of an autofocus in a circular laser writing system by D. E. Denk; A. G. Poleshchuk

*(87-95)*. Specific features of operation of an autofocus in a CLWS-300IAE circular laser writing system are considered. The influence of the focus error on the process of direct laser writing of diffraction structures is considered. A digital adaptive controller for the system of autofocus control is described and studied in experiments. Algorithms of controller operation, a technique for its tuning, and experimental results are described.

**Keywords:**laser writing; autofocus; diffraction optics; automatic control system

Analysis of design principles of silicon multiplexer circuits for multielement infrared focal plane arrays by A. I. Kozlov

*(96-105)*. Design principles of silicon multiplexers for linear and matrix infrared (IR) focal plane arrays (FPAs) are considered. Silicon multiplexers intended for operation with multielement mercury-cadmium-tellurium (MCT) photodiode detectors, with multielement photoresistor detectors based on multilayer structures with quantum wells, and with other types of photodetectors sensitive to radiation in the IR ranges from 3 to 5 and from 8 to 16 µm, are discussed. The type and size range of the multiplexers includes 19 models that differ in frame sizes, input circuits, charge capacity, and cell pitch. Around the designed multiplexers, hybrid and monolithic FPAs of various formats for medium and far IR ranges with a rather high temperature resolution (< 0.02 K) have been developed.

**Keywords:**infrared focal plane arrays; photocurrent readout circuit; silicon multiplexers