Fast computation of fractal dimension for 2D, 3D and 4D data

The box-counting (BC) algorithm is one of the most popular methods for calculating fractal dimension (FD) binary data. FD analysis has many important applications in biomedical field, such as cancer detection from 2D computed axial tomography images, Alzheimer’s disease diagnosis magnetic resonance 3D volumetric data, and consciousness states characterization based on 4D data extracted electroencephalography (EEG) signals, among others. Currently, these kinds use whose size amount can be very large, with high computation times needed to calculate BC whole datasets. In this study we present a efficient parallel implementation its execution Graphics Processing Units (GPU). Our process 2D, tested it two platforms different hardware configurations. results showed speedups up 92.38× (2D), 57.27× (3D) 75.73× (4D) respect corresponding CPU single-thread implementations same algorithm. Against an OpenMP multi-thread implementation, our GPU achieved 16.12× 6.86× 7.49× (4D). We have also compared previous 3D, achieving speedup 4.79×. Finally, practical application comparing EEGs schizophrenia patient healthy subject was performed. time processing 40 matrices reduced three hours (sequential CPU) less than minutes • computes Speedups were regarding more four faster applied accelerating EEG