Optimization algorithm of the velocity field determining in image processing

Pavel Bazhanov,Elena Kotina,Dmitri Ovsyannikov,Victor Ploskikh

doi:10.35470/2226-4116-2018-7-4-174-181

Pavel Bazhanov, Elena Kotina + Show 2 more

Open Access

https://doi.org/10.35470/2226-4116-2018-7-4-174-181

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Journal: Cybernetics and Physics	Publication Date: Dec 23, 2018
Citations: 3	License type: cc-by

Affiliation: St Petersburg University

Abstract

The paper proposes a new algorithm for constructing the velocity field, which is based on the study of the integral functional on the ensemble of trajectories. The resulting analytical representation of the variation of the integral functional gives us the gradient of the investigated functional. It allows to find the desired parameters using gradient methods, which determine the velocity field. This approach allows both optical flow and non-optical flow construction. The proposed algorithm can be used in the analysis of various images, in particular in radionuclide image processing.

Highlights

There is a large number of image processing algorithms corresponding to different purposes: image restoring, improving image quality, object recognition and motion analysis, contour detection etc
This paper proposes a new algorithm for the velocity field construction, which is based on the variation of the integral functional in the problems of trajectory ensembles control presented in works [Ovsyannikov, 1990; Ovsyannikov, 2012]
Let us consider the iterative algorithm for determining the velocity field

Summary

Introduction

There is a large number of image processing algorithms corresponding to different purposes: image restoring, improving image quality, object recognition and motion analysis, contour detection etc. The brightness but its gradient, Laplacian or Hessian are considered [Papenberg et al, 2006] In this formulation, functionals of quality (energy function) are constructed, which include in addition spatial smoothness assumptions for the required velocity field [Horn and Schunck, 1981; Black and Anandan, 1996]. Let us introduce the distribution density ρ = ρ(t, x), which plays the role of the mass or charge density in various problems of mechanics and electrodynamics In our case, it is quantitative characteristics of the image (brightness) depending on the spatial coordinates and time, or the intensity of radiopharmaceutical distribution in the processing of radionuclide studies [Kotina and Ovsyannikov, 2018; Kotina and Pasechnaya, 2014]. Let us write out the gradient of the functional (14) for this case:

Calculate the gradient of the integral functional

Conclusion