Fast computation of residual complexity image similarity metric using low-complexity transforms

The authors apply two approaches to reduce the computation time of the residual complexity similarity metric employed in image registration applications aimed at hardware-based implementations with low-complexity transforms. First, the similarity metric is computed in image sub-blocks, which are subsequently combined into a global metric value. Second, the discrete cosine transform (DCT) needed in the computation of the similarity measure is replaced with multiplier-free low-complexity approximate transforms. The authors propose a new low-complexity transform requiring only 18 additions in an 8 × 8 block and compare it to: the round DCT, the signed DCT, the Hadamard transform and the Walsh-Hadamard transform. Detailed computational complexity analysis reveals that block-wise processing alone reduces computational cost by a factor of 8-9 for original DCT composed of multiplications and additions, and up to ≃4.90 when the proposed DCT is utilised; being the computation performed with additions only. Results obtained from computer simulated and realistic X-ray images demonstrate block-wise processing and approximate transforms result in successful image registration, making residual complexity similarity measure available to hardware-accelerated fast image registration applications.