1 Abstract— A video sequence consists of series of frames. The Block Matching is a temporal compression technique used in the video encoding. The main purpose of this method is to determine the displacements of each block of pixels between two successive frames. Motion estimation (ME) is to be done in the encoder side to find the best MV so that it can be applied on stored frames by motion compensated block to generate the predicted video in video compression. Widely motion estimation is used to reduce temporal redundancy in many standards. This technique, performed in the step of motion estimation, consumes the majority of the total time and mathematical complexity of video coding. This paper presents logarithmic search algorithm for block based motion estimation. The performance of the algorithm is evaluated using standard video sequences and the results are compared to a traditional full search algorithm (FSA) and three step search (3SS) algorithm. The estimation considers the accuracy of the matching procedure with respect to the time requires. Moreover, the PSNR of the Logarithmic Search (LS) method is as good as that of the full search method and 3SS. With this, LS can be used as an alternative to FSA and 3SS. Index Terms—Logarithmic search, block matching algorithm, video compression, motion estimation I. INTRODUCTION Block matching techniques consist of three main components: Block determination, Search methods and Matching criteria. For each reference block in the current frame, BMA searches for the best matched block within a search window of size (2W+N) x (2W+N) in the previous frame, where W stands for the maximum allowed displacement and N x N is number pixels in macro-block. Then the relative position between the reference and its best matched block is represented as the motion vector of the reference block. The basic procedure involves coding the initial frame and then tracking the trajectories traversed by the various objects. Through this ample magnitude of compression is achieved with this [4]. A video sequence typically contains temporal redundancy; that is, two successive pictures are often very similar except for changes encouraged by object movement, illumination, camera movement, and so on. Motion estimation and compensation are used to reduce this type of redundancy in moving pictures. The block-matching algorithm (BMA) for motion estimation has proved to be very efficient in terms of quality and bit rate; therefore, it has been implemented by many standard video encoders. The basic principle of block matching motion estimation and compensation is introduced. Also fast motion search algorithms are simulated. The smoothness of algorithm makes full search interactive algorithm. It requires extremely large computation time which makes it unsuitable for practical and real-time implementation. Based on analysis of variants of BMA, Logarithmic method is simulated and presented in this paper. This paper is divided into four sections. Section I contains introduction. Section II includes basic concepts related to block matching algorithm and variants of BMA. Section III comprises algorithmic implementation method for Logarithmic block matching algorithms. Section IV embraces result analysis and comparative study. II. BLOCK MATCHING ALGORITHM AND ITS VARIANTS The two-dimensional logarithmic search was the first block-matching algorithm to exploit the quadrant monotonic model to match blocks. The iŶitial step size s is 4 w       (where   is the upper integer truncation function) where w is the searĐh raŶge iŶ either direĐtioŶ. The ďl ock at the center of the search area and the four candidate blocks at a distaŶĐe s froŵ the ĐeŶter on the x and y axes are compared to the target block to determine the best match. Fig 1. Block Matching Method Full Search Method (a) Full search algorithm examines all positions in search window. It is optimal for correctly defined Logarithmic Search for Motion Estimation Saloni R. Mistry, Heni S. Modi, Rahul N. Gonawala B.E. Student, B.E. Student, Assistant Professor mistrysaloni15@gmail.com, henyymodi@gmail.com, rgonawala@gmail.com