Theoretical methods of optical pattern recognition

The vast majority of modern optical information processing systems are based on the use of Fourier optics methods and integral transformations of convolution type, such as Fourier transform, Hadamard transform etc. The last decade in optics is characterized by intense development of Fractional Fourier Transform (FrFT) theory, which helps to reveal the laws of optical information processing and opportunities to create fundamentally new methods and systems for optical information processing.

In 2000 scientific research on theory FrFT basing on distribution signals method began for the first time in Ukraine (M.V. Shovgenyuk, Yu.M. Kozlovski). It was proved theoretically that input signal distribution revolves in information diagram of conjugated coordinates – position, spatial frequency. Kernel of FrFT with optical constants was obtained, which allowed to investigate formation patterns of FrFT conjugated images in real optical systems.

Based on image recognition FrFT theory an optical system for generalized correlator of reference and considered image mutual FrFT was developed for the first time. The system allows writing a high-contrast interference pattern of optically superimposed images into arbitrary plane of FrFT domain. Developed correlation scheme for image recognition scheme can enhance the reliability of images identification significantly. Way of recognition and identification device is protected by the patent and PCT application.

The theory of self-images of periodic phase elements (Talbot effect) in the FrFT domain for interferometric measurements was developed. Invariant conditions for self-images forming were determined. Analytical solutions were obtained for different invariant conditions, and it was shown that the self-images forming is a result of interference of a finite number of phase element unit cells.

The model allows accurate calculating of self-images intensity levels and measuring phase difference of periodic optical elements experimentally. Investigations on applied problems of interferometry are carried out jointly with the Institute of photonics and micromechanics of Warsaw Polytechnic. Basing on the Talbot effect conditions of self-images forming is studied theoretically for phase grating with 100% contrast in Fresnel diffraction domain and FrFT, which maybe will be used in microlithography, X-ray tomography and atomic interferometry.

The possibility of using Talbot effect for optical sensing light absorbing medium with micro-particles is theoretically justified. Taking into account the refractive index of the medium leads to a longitudinal displacement of equidistance planes of phase gratings self-images, and the presence of absorbing microparticles (<1%) in the medium stimulates the appearance of self-images in fractional Talbot planes.

New methods of digital image processing based on the discrete Hadamard transform were developed. They are used in modern technologies of securities protection (M.V. Shovgenyuk, M.P. Kozlovsky, T.Ye. Krohmalskyy, T.V. Fityo, L.A. Didukh). On the basis of orthogonal Hadamard matrices images encryption methods and algorithms were developed; fundamentally new type of graphic element for securities protection was proposed. The element consists of encoded image and its key, which are produced by computer program “GraphiCode 4”.

Graphic interface of “GraphiCode 4”.

The advantages of the proposed method of image encoding with the help of aperiodic ordered structures are: absolute invisibility encoded visual image, large amount of different keys (about 2x10⁸ variants) for image decoding, possibility of high resolution image decoding with minimal noise, and identification reliability and high level of protection. Securities protection technology developed by the Institute is protected by patents of Ukraine and the USA, PCT application.

A study of industrial commissioning of specialized software and securities protection technology at the facilities of state printing house "Ukraine" and National Bank of Ukraine was performed in the frame of innovative project of NAS of Ukraine in 2007. The technology of securities optical protection was presented at exhibitions in Ukraine, USA and Germany.

New methods of color images digital processing for publishing are developing (M.V. Shovgenyuk, N.S. Pysanchyn, T.V. Fityo, N.V. Zanko). Based on the discrete Hartley transform a new color space ICaS is proposed, which is used to develop color-separation methods, taking into account the real parameters and characteristics of the printing process that can simulate the real conditions of synthesis of color inks on prints. Within the innovation project of NAS of Ukraine in 2008 specialized computer program “ICaS Color Print-1” was developed, which is based on the new color-separation technology, and software package for determining of the optimal process for color reproduction in the printing systems.