Figure 2.

An illustration of the Viterbi algorithm. On this illustration, “N” represents different locations where the displacement vectors need to be simultaneously estimated and “S_m”represents m possible selections of the displacement vector for each location. Therefore, in the framework of block-matching, each circle represents one possible choice in the search window for each location. The cost of choosing a target circle (where the arrow is pointing toward) at the next location is determined by Eqn. (2), given the current choice (i.e. the circle which the arrow is originating from). The resultant cost function value is one element of the three dimensional cost matrix C_ijk and this process is repeated until all elements of C_ijk are determined. If all possible combinations are considered, there will be a large solution pool. The Viterbi algorithm can be utilized to find the “best” set of displacement vectors (the solid blue line) in a cost-effective manner. Of note, small numbers for m and N are used to reduce the size of this illustration.