Methods for measuring small displacements of television images

Abstract

Various techniques are described to measure, small displacements of television images. If two successive video frames are considered, their differences are approximately a linear combination of the components of the displacement of the object. If all the points of the frame undergo the same movement, then the velocity estimation problem is solved using linear estimation. However, if some points belong to the moving object and the others to the background, the problem can be stated in the same way only if an algorithm is available to segment the image into fixed and moving areas. Afterwards, linear estimation can be applied to the moving area only. In this paper a segmentation algorithm is proposed which uses dynamic programming (Viterbi algorithm with three states). A more complex situation arises when the points belonging to the moving area are subjected to different movements. The problem can be solved once more using dynamic programming if the displacement components are quantized into <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(2M + 1) (2M + 1)</tex> values, and the number of states of the Viterbi algorithm is augmented to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(2M + 1)^{2}</tex> . To reduce the technical difficulties of this approach, a simpler method that makes possible the estimation of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> most probable displacements is proposed. Then the image is segmented into n moving areas with different displacements and a background area using a Viterbi algorithm with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n + 1</tex> states. Experimental results show that the precision obtainable is about 0.1 pel when the displacements are up to 2-3 pels, the object had approximate dimensions of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">90 \times 90</tex> pels, and the signal-to-noise ratio was higher than 33 dB.