Discrete 2-dimensional fractional brownian motion as a model for medical images
Date of Original Version
In previous work, the concept of estimation theory has been applied to provide a basis for determining the fractal dimension of a given data set when fractional Brownian motion (FBM) is assumed to be a suitable model. However, the generated FBM functions used to test the approach were only one dimensional, even though the estimation was applied to images. In the current work, the generation process is extended to two dimensions so that FBM images are generated directly. A series of 32 × 32 FBM images were formed for fractal dimensions of 2.2 to 2.8. The texture in these images is seen to be representative of textures observed in xray images of bone. Furthermore by combining the FBM realization with a deterministic function such as a sinusoid, it is found that complex appearing images can be broken down into two basic components: Fractal, and determinisitic. Thus this methodology may prove useful in the analysis and presentation of medical images. © 1987 SPIE.
Proceedings of SPIE - The International Society for Optical Engineering
Ohley, William J., and Torbjorn Lundahl. "Discrete 2-dimensional fractional brownian motion as a model for medical images." Proceedings of SPIE - The International Society for Optical Engineering 845, (1987): 227-232. doi:10.1117/12.976509.