**Author details**

Andrzej Zak Polish Naval Academy, Gdynia, Poland

\*Address all correspondence to: a.zak@amw.gdynia.pl

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Chapter 2

Abstract

1. Introduction

5

Estimation

Formation of Inter-Frame

Alexander Tashlinskii and Pavel Smirnov

a moving object in a video sequence are given.

trajectory of the object is extracted from the image.

Deformation Field of Images

Using Reverse Stochastic Gradient

The effectiveness of the use of stochastic gradient estimation to detect motion in a sequence of images is investigated. Pixel-by-pixel reverse estimation of the deformation field is used. The representation of the shift vector is considered both by the projections on the basic axes and by the polar parameters. Two approaches to estimate the parameters of the deformation field are proposed and analyzed. In the first approach, the stochastic gradient procedure sequentially processes all rows of an image to find estimates of shifts for all points of the reference image. The joint processing of the results allows compensating the inertia of the stochastic estimation. In the second approach, to improve the accuracy of estimation, the correlation of image rows is taken into account. As a criterion for the formation of the resulting estimate, the minimum of gradient estimation and correlation maximum were investigated. The computational complexity of the proposed algorithms is investigated. The algorithms are compared with the MVFAST algorithm. Examples of experimental results on the formation of the deformation field, the selection of a moving object area, and the finding of the movement and trajectory parameters of

Keywords: image processing, video sequence, motion, shift vector, detection, stochastic estimation, stochastic gradient, trajectory, reverse estimation, correlation

One of the challenges in video processing is moving object detection and tracking. Some tasks require only detection of the motion, while others require extraction of the moving object or the motion area boundary. The biggest challenge is to estimate trajectory parameters of a moving object in a video sequence. A solution quality to the problem largely depends on the accuracy of moving object area detection, since all the information needed to determine motion parameters and

There are various approaches to identify the area of moving object based on the inter-frame difference [1, 2], background subtraction [2, 3], the use of statistics [2, 4], block estimation [5], and optical flow analysis [6]. The processing can be presented as estimation of inter-frame geometric deformations of two images, one
