MATLAB Implementation of the Standard Three-Step Search Algorithm

The Standard Three-Step Search (TSS) is an efficient block matching algorithm for motion estimation, widely used in video compression and motion compensation applications. This algorithm reduces computational complexity by progressively narrowing the search range while maintaining high matching accuracy. In the implementation process, the current frame is first divided into fixed-size macroblocks (e.g., 16x16 pixels). For each macroblock, the search follows a specific pattern in the reference frame: First Stage: The initial search step size is 4 pixels, calculating matching errors at 9 positions in the reference frame (the current macroblock position plus 8 surrounding positions). Second Stage: Using the best match point from the first stage as the center, the step size is halved to 2 pixels, and another 9-point search is performed. Third Stage: Continuing with the best point from the second stage as the center, a final refinement search is conducted using a 1-pixel step size. Boundary handling must be carefully implemented during coding - when search points extend beyond image boundaries, appropriate padding or constraint mechanisms should be applied. Matching criteria typically use SAD (Sum of Absolute Differences) or MSE (Mean Square Error) as similarity measures. The algorithm's main advantage lies in reducing the complexity from O(n²) for full search to O(logn), while maintaining matching quality through multi-level refinement. Experimental results show that for video sequences with smooth motion, TSS achieves performance close to full search with significantly reduced computation time. MATLAB's matrix operations can efficiently implement the block matching process. Using pre-allocated arrays and vectorized operations can further improve runtime efficiency. In practical applications, the initial step size or number of search points can be adjusted according to specific requirements to balance accuracy and speed. Key implementation considerations include: - Preallocating memory for cost matrices to avoid dynamic resizing - Using vectorized calculations for SAD/MSE computations across multiple blocks - Implementing efficient boundary checks using MATLAB's indexing capabilities - Structuring the search pattern using modular functions for each step size