International Conference «Mathematical and Information Technologies, MIT-2016»

28 August – 5 September 2016

Vrnjacka Banja, Serbia – Budva, Montenegro

Rubtsov K.A.   Lazarev S.   Maslakov Y.N.  

Technique of Formation of Panoramic Image for Stand-Alone Portable Digital Device UHDTV

Reporter: Rubtsov K.A.

Modern systems of panoramic photography and video are being treated, as a rule, on the basis of an array of light-sensitive sensors, with different ways of positioning in space. The authors conducted a study task was to create a high-quality portable system panoramic photo and video shooting using a 12 light-sensitive sensors and the formation of the video standard Ultra HD 4K. According to the simulation results, it was found that the optimal arrangement of  12 the light-sensitive sensors in conjunction with lenses is their location in the center of the dodecahedron faces. In this case, part of the image formed on each photosensitive lens sensor is unique (not repeating other sensors) as part of the panorama of a regular pentagon. This design allows you to create a panorama of 360-degrees.
The problem of projecting high quality panoramic images from 12 cameras of the sphere, in real time, requires large computing resources, which makes difficulties the practical implementation in a compact device. This problem is solved by the authors by means of construction and optimization, by reducing the computational procedures, methods of forming the panoramic image on the basis of a mathematical model of a dodecahedron and obtaining transform coefficients from the information of each light-sensitive sensor. In the investigations it was found that the optimal ratio of the sides of light-sensitive sensor is 4:3. The use of different lenses in the system has shown the need to eliminate the distortion [1], and to compensate for possible deviations from the ideal placement of camera models in the mathematical model are calibration parameters for each light-sensitive sensor. Calibration parameters take into account the linear displacement cameras from the center of the dodecahedron and turns. Calibration of the system and eliminating distortion of 12 cameras (at this stage of software development) is performed automatically using a specially calibration table. As a result of the calibration coefficients of the matrix are formed to perform fast image sampling correction and formation of spherical panoramas.
Mathematical model of a dodecahedron made it possible to generate all the transform coefficients without using trigonometric functions. Thus, the set of operations in the formation of the spherical image is limited to addition, subtraction, multiplication, division and square root. For calibration image it was used a mathematical model based on new mathematical operations Zeration and Deltation [2]. These operations have a rank lower than "addition" and "subtraction", and allow us to describe in a unified mathematical formalism as logical operations and systems of equations, and a number of special functions [3]. The resulting mathematical model of a spherical panoramic images with 12 cameras is optimized for implementation on the PLD.
Research on this subject conducted as part of the a state contract No. 14.581.21.0003 Russian Ministry of Education and Science, project ID: RFMEFI58114X0003.

[1] I. S. Konstantinov, B. J. Shuljak, S. A. Lazarev, and A. N. Zalivin, "Singular Point Comparisons During Panoramic Image Formation," Int. J. of Soft. Comp. 10 (6), 454-457 (2015).
[2] K. A. Rubtsov, I. S. Konstantinov, and  S. A. Lazarev, "Application of New Mathematical Operations Zeration and Deltation in Algorithms of Images Processing System Panoramic," ICMSA2015, 77 (2015).
[3] K. A. Rubtsov, G. F. Romerio, Hyperoperations, for science and technology: New algorithmic tools for computer science, (Lambert Academic Publishing, 2011).

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