26 Acta Electrotechnica et Informatica Vol. 8, No. 3, 2008, 26–30 ISSN 1335-8243 © 2008 FEI TUKE THE FAST SEARCH MOTION ESTIMATION ALGORITHMS AND THEIR ERRORS Ján GAMEC, Mária GAMCOVÁ Department of Electronics and Multimedia Communications University of Technology Košice Park Komenského 13, Košice, Slovak Republic e-mail: jan.gamec@tuke.sk ABSTRACT This paper presents the analysis of errors produced by block matching motion estimation methods with lower computational cost (fast search algorithms). We try to find an answer on the question what measure can be used to determine correctness of searched motion vectors and which motion vectors are founded as fault (corrupted by noise). We consider the vector fields obtained by using of full search algorithm (FSA) as lossless data. We take the vectors of movement obtained by using 2D logarithmic (2D log) search procedure as data corrupted by noise. The results of analysis can help optimize post processing of motion vectors in endeavoring to reduce computational cost or regularize vector fields. Keywords: motion estimation, block matching, motion vector 1. INTRODUCTION The purpose of the motion estimation (ME) and compensation is reduction of redundancy caused by interframe correlation of movement objects [1-6]. However, the estimation and coding of movement vectors should be appropriated to computational costs and bit rates at the perspective high compression systems. That’s way is very important relationship between accuracy of movement estimation and simplicity of the description vector fields. Better motion estimation means higher space decorrelation of prediction errors in time area. The most popular approach is to reduce the number of search locations by using the assumption of unimodal error surface in which the matching error decreases monotonically when the searching location approaches to the global optimum. However, this assumption is not usually satisfied, thus resulting in local optimal solution. Instead of limiting the number of search locations, another interesting tech-nique aims at reducing computation of block matching with pixel subsampling, successive elimination algorithm (SEA). The above two techniques achieves computation reduction with or without loss of search performance. This paper is concentrated on analyze one of often mentioned method of ME with reduced searching steps - 2Dlog method. The 2Dlog method is analyzed from point of view of estimation and localization of potentially possible errors of motion vectors in the searching procedure. 2. THE REASONS OF ERRORS The essential condition of the correct displacement vector finding (for ME methods with reduced searching steps) is flatness of matching criteria. It means that function of matching criteria monotonically increases as we move away from direction of minimum matching criteria in each of the four quadrants [7]. The example of founded motion vectors (MV’s) from the image sequence “Railway station” is in fig. 1. The black arrows are MV’s founded by 2Dlog method for subblock size BS = 16x16 pel and proposed maximum displacement d m = 13 pel in all directions. The white arrows are MV’s founded by full search (FS) method with the same searching parameters and can be seen for the subblocks in which vectors are different from 2Dlog MV’s. A darker rectangle in fig. 1 highlights one of subblocks with mismatch vector (2Dlog-black, FS-white). Fig. 1 The frame from the image sequence “Railway station” with motion vectors founded by FS method (white) and 2Dlog method (black) All computed values by FS method of matching criteria (MAD - Mean Absolute Difference) of highlighted subblock in fig. 1 are plotted in fig. 2. The number of these values is (2d m + 1)x(2d m + 1), i.e. 27x27 values. It can bee seen that values of matching criteria do not increase monotony. The position of global matching criterion (MAD) minimum corresponds with actual MV. The values of criterion MAD are represented as gray levels in fig. 2b. The white point in very dark area indicates the position of minimum. The white arrow is searched MV by FS method. The positions of searching