Performance Evaluation of Different Cost Functions in Motion Vector Estimation

1. Introduction

Video refers to series of images or image frames, which suggests that a bigger storage or higher bandwidth is required to store or transfer the video through the network. The existence of high temporal redundancy in video can be removed using different international video compression standards. The most important part of every coding standard is motion compensation. Therefore in MPEG standard (Lameillieure & Schäfer, 1994) the frames are divided into three categories. First type is intra-coded frame (Gall, 1991) or I-Frame. I-Frame is a completely original frame which does not depend on the information of other frames, and the frame is sent once at the beginning and periodically after certain intervals to avoid the propagation of transmission error. Generally the interval is 12. For our study, the interval was pre-defined as 6 in the algorithm. The other two types of frames where MPEG achieves (Schwarz et al., 2006) higher compression are predicted frames or P-Frame and bi-directional frame or B-frame. The frames are closely related. Hence, one frame can be predicted by translational model of the previous (Barjatya, 2004) frame. This prediction is done by using motion vector estimation and motion compensation. P-Frames are divided into m × n macro blocks and every macro block is predicted using previous I-Frame. The movement of the macro block in horizontal and vertical direction is referred as motion vectors. B-Frames never transmit error because they are not used for motion prediction. Previous I-Frame or P-Frame and the next P-Frame helps to measure the motion vector for B-Frames (See Figure 1).

Figure 1.

Frame structure

Evaluation of motion vectors demand match between the block of current frame (P-Frame or B-Frame) and the block of reference frame (I-Frame or P-Frame).The matching operation of one block with another is completely dependent on the output of cost function (Acharjee & Chaudhuri, 2012). The cost functions (Wang et al., 2014) evaluate similarity between two blocks (Nguyen et al., 2010). During this evaluation, the best match between two blocks (Anantha et al., 2013) refers to the block with the best output. In another scenario, if the cost function (Hussein et al., 2011) evaluates dissimilarity, then the block (Takahashi et al., 2012) with least output of cost function (Davies et al., 2007) is the best match. The cost function (Acharjee et al., 2012) with higher value and increasing dependency between two blocks finds the similarity among those blocks. Similarly, the cost function finds the dissimilarity between two blocks, only if the cost function has produced lower value and the dependency between those two blocks has increased. The popular cost functions like MAD, MSE etc. are the cost function which finds the dissimilarity. Minimum ratio, Spearman’s rho, Kendall’s tau etc finds the similarity between two blocks. Reducing computational complexity and time consumption has always been a challenging task. But most of the computation task was performed to calculate the cost of the blocks. Hence, our main focus was to reduce computation and time consumption using different cost functions. The proposed system tried to evaluate the performance of some new and some commonly used cost functions.