Image Registration based on a new Wavelet – based Similarity Metric

We present a registration algorithm based on a new image similarity metric, the wavelet normalized root mean square error (WNRMSE). Such a metric is based on a wavelet decomposition, and it is obtained by suitably combining contributions of different dyadic frequency bands after divisive re-normalization. The metric is included as a brick in an algorithm with a flexible modular structure, well suited to generalization and expansion, which allows to combine and interchange different "image models”, transformation classes, both rigid and not, and cost functionals. By construction, the new metric, which has a strong relation with the well-known structural similarity index (SSIM), its multiscale versions multiscale SSIM (MSSSIM) and complex wavelet SSIM (CWSSIM), dampens the weight of high frequencies when the image is noisy and enhances it, when sharp changes are present in clean images, thus making the resulting algorithm particularly robust with respect to noise. This robustness has already been demonstrated in the framework of image classification, where on a reference database in the literature (the TID2013 database), the new metric outperforms well known indexes that can be found in the literature such as the Feature Pyramid Hashing index (FPH), the MSSSIM and CWSSIM indexes and Peak Signal to Noise Ratio (PSNR). We test the algorithm on both some toy problem of photographic type and on some images coming from medical applications, and compare its performance with other widely used metrics.