As discussed in Chapter 10, the pel recursive technique is one of the three major approaches to two-dimensional displacement estimation in image planes for the signal processing community. Conceptually speaking, it is one type of region-matching technique. In contrast to block matching (which was discussed in the previous chapter), it recursively estimates displacement vectors for each pixel in an image frame. The displacement vector of a pixel is estimated by recursively minimizing a nonlinear function of the dissimilarity between two certain regions located in two consecutive frames. Note that region means a group of pixels, but it could be as. | 12 Pel Recursive Technique As discussed in Chapter 10 the pel recursive technique is one of the three major approaches to two-dimensional displacement estimation in image planes for the signal processing community. Conceptually speaking it is one type of region-matching technique. In contrast to block matching which was discussed in the previous chapter it recursively estimates displacement vectors for each pixel in an image frame. The displacement vector of a pixel is estimated by recursively minimizing a nonlinear function of the dissimilarity between two certain regions located in two consecutive frames. Note that region means a group of pixels but it could be as small as a single pixel. Also note that the terms pel and pixel have the same meaning. Both terms are used frequently in the field of signal and image processing. This chapter is organized as follows. A general description of the recursive technique is provided in Section . Some fundamental techniques in optimization are covered in Section . Section describes the Netravali and Robbins algorithm the pioneering work in this category. Several other typical pel recursive algorithms are introduced in Section . In Section a performance comparison between these algorithms is made. PROBLEM FORMULATION In 1979 Netravali and Robbins published the first pel recursive algorithm to estimate displacement vectors for motion-compensated interframe image coding. Netravali and Robbins 1979 defined a quantity called the displaced frame difference DFD as follows. DFD x y dx dy f xy -fn-1 x - dx y- dy where the subscript n and n - 1 indicate two moments associated with two successive frames based on which motion vectors are to be estimated x y are coordinates in image planes dx dy are the two components of the displacement vector d along the horizontal and vertical directions in the image planes respectively. DFD x y dx dy can also be expressed as DFD x y d. Whenever it does not cause .
