Fast normalized cross correlation for motion tracking using basis functions

Digital image-based elasto-tomography (DIET) is an emerging method for non-invasive breast cancer screening. Effective clinical application of the DIET system requires highly accurate motion tracking of the surface of an actuated breast with minimal computation. Normalized cross correlation (NCC) is the most robust correlation measure for determining similarity between points in two or more images providing an accurate foundation for motion tracking. However, even using fast Fourier transform (FFT) methods, it is too computationally intense for rapidly managing several large images. A significantly faster method of calculating the NCC is presented that uses rectangular approximations in place of randomly placed landmark points or the natural marks on the breast. These approximations serve as an optimal set of basis functions that are automatically detected, dramatically reducing computational requirements. To prove the concept, the method is shown to be 37-150 times faster than the FFT-based NCC with the same accuracy for simulated data, a visco-elastic breast phantom experiment and human skin. Clinically, this approach enables thousands of randomly placed points to be rapidly and accurately tracked providing high resolution for the DIET system.