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.