An Exploratory Study on Powell Optimization Method for Block Matching Evaluation on Ultrasound Images

This paper presents the application of an elastography model based on block matching using ultrasound mathematical phantoms. Elastography can be defined as the visualization of differences in the biomechanical properties of healthy and diseased tissues. The differences are seen and measured from comparisons of the tissue examined in two states: equilibrium and after an applied perturbation. Therefore, an algorithm was developed for application in two ultrasound images, one with deformation and a non-deformed one. The proposed algorithm uses the Powell optimization method to evaluate the displacements between the two images. It also uses cubic-spline interpolation to evaluate sub-pixel displacements. As this research has an exploratory bias, only a part of the image was selected for a first analysis of the results. The results proved promising, showing opportunities for future optimizations and applications of the proposed model presenting root-mean-squared errors and absolute errors of order \(10^{-3}\) and relative errors of 4%, but still need improvements on the computational time.