Scale-invariant analysis of wear particle surface morphology: II. Fractal dimension

Fractal dimension is the most popular parameter used to scale-invariantly characterize the roughness of wear particle surfaces. However, methods used to calculate the fractal dimension can be ineffective when applied to data-limited, low-resolution wear particle images or when wear particle surfaces do not conform to a fractional Brownian motion model. In this paper, a new fractal method, which is called a fractal dimension by partition iterated function system (FD-PIFS), was developed and used to estimate the fractal dimension from wear particle surfaces. The newly developed method is based on a PIFS constructed for an image of a wear particle surface. The PIFS is a set of contractive affine transformations that describe scale-invariantly and uniquely the surface topography of a wear particle. The effectiveness of the FD-PIFS method was evaluated. The fractal dimension was first calculated for computer generated images of isotropic fractal surfaces and then calculated for scanning electron microscope images of wear particles found in artificial implants and synovial joints. The effects of measurement conditions such as noise, resolution, gain variations and focusing on fractal dimension calculated were also investigated.