IEEE TRANSACTIONS ON BROADCASTING, VOL. 49, NO. 4, DECEMBER 2003 383 Brief Papers_______________________________________________________________________________ A Motion Vector Recovery Algorithm for Digital Video Using Lagrange Interpolation Jinghong Zheng and Lap-Pui Chau Abstract—In this paper, we propose an efficient motion vector recovery algorithm for the new coding standard H.264, which makes use of the Lagrange interpolation formula. In H.264, a 16 16 inter macroblock can be divided into different block shapes for motion estimation, and each block has its own motion vector. For nature video the movement within a small area is likely to move in the same direction, hence the neighboring motion vectors are correlative. Because the motion vector in H.264 covers smaller area than previous coding standards, the correlation between neighboring motion vectors increases. We can use the Lagrange interpolation formula to constitute a polynomial that describes the motion tendency of motion vectors, which are next to the lost motion vector, and use this polynomial to recover the lost motion vector. The simulation result shows that our algorithm can efficiently improve the visual quality of corrupted video. Index Terms—Digital video, error concealment, Lagrange inter- polation. I. INTRODUCTION H .264 is a new video coding standard, which adopts some new coding schemes. The traditional picture types Intra (I), Inter (P), and Bi-directional (B) are still supported in H.264. One of the major differences between H.264 and previous coding standards is that the motion estimation scheme is changed. In H.264, a 16 16 macroblock can be divided into different block shapes for motion estimation. Fig. 1 shows the seven different block division modes and the order of encoding motion vectors that are adopted in H.264 [1]. Each block has a corresponding motion vector, thus the number of motion vectors in a mac- roblock depends on the block division mode that the macroblock adopts. In this paper, we present an efficient motion vector recovery algorithm for this new coding standard H.264. The main problem in video transmission is that the bitstream of compressed video is often corrupted by channel errors. To solve this problem, many efficient error concealment approaches have been proposed. The most commonly used technique is to replace the damaged motion vector with (0,0), and this approach is usually referred to as temporal replacement [2]. Maximally smooth is a popular spatial error concealment method. It makes use of the smooth connection property of image to recover the lost blocks [3], [4]. Block matching Manuscript received March 24, 2003; revised July 3, 2003. The authors are with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (e-mail: lpchau@ ieee.org; elpchau@ntu.edu.sg). Digital Object Identifier 10.1109/TBC.2003.819050 principle and neighboring matching principle are often used to recover lost motion vectors [5], [6]. Shirani et al. employ a MAP estimator to recover the missing shape information [7], [8]. Park et al. propose a recovery method that makes use of NURBS interpolation [9]. Turaga and Chen introduce model-based schemes for error concealment [10]. Chen et al. proposed an algorithm that uses overlapped motion compen- sation to recover the lost motion vectors [11]. Al-Mualla et al. introduce a powerful method called MFI, which uses motion field interpolation of neighboring motion vectors to recover one vector per pixel of the damaged blocks [12]. Since the H.264 adopts new motion estimation scheme, most motion vector recovery algorithms that are designed for 16 16 macroblock are not suitable for H.264. Wang et al. have present a modified boundary matching algorithm for the new coding standard H.26L (previous version of H.264) [13]. In this paper, we exploit the Lagrange interpolation formula to recover the lost motion vectors. For nature video the move- ment within a small area is likely to move in the same direction, hence the motion vectors of neighboring blocks are correlated. In H.264, since a macroblock contains more motion vectors than previous coding standards, the correlation between neighboring motion vectors increases. Based on this correlation, we can as- sume that the lost motion vector has similar motion tendency with its neighboring motion vectors. Then we can use Lagrange interpolation formula to constitute a polynomial that can de- scribe the movement tendency of these neighboring motion vec- tors, and use this polynomial to recover the lost motion vector. II. ERROR CONCEALMENT ALGORITHM BASED ON LAGRANGE INTERPOLATION In this section, we present a new motion vector recovery method that is based on Lagrange interpolation formula. First we introduce the formulation of Lagrange interpolation. An interpolation can be defined as a function , which contains independent variable and a number of parameters. For given points ( , ), , by suitable choice of parameters, we can constitute the interpolation function that . Lagrange interpolation formula is one of the most widely used interpolation functions, and its computation cost is lower than most interpolation functions. The format of Lagrange interpolation formula is presented in (1). (1) 0018-9316/03$17.00 © 2003 IEEE