Face: Fractal analysis in cell engineering

Abstract

Most fractal compression schemes encode an image as a collection of transforms that analyse image detail at every scale, typically allowing a receiver to regenerate or synthesize the output using "instructions" from the transmitter. Conceived in the mid 1980s, such an analyse/synthesis approach to image transformation exploits the self-affine approximations as the basis functions for capturing image detail which is subsequently used in the reconstruction algorithm. The latter often entails the application of an iterative procedure which specifies a set of (growth) rules, not unlike the so called L-system (of Lindenmayer) constructed to describe the intricate developmental patterns of biological plants at multiple scales of resolution. Based on the computational science of fractals and image transforms, this paper furthers our earlier development of an investigative visualisation platform which sought to characterise the diversity of patterns observed in the columnar branching of cartilage cells during growth/repair, by providing objective quality measures of the structural organisation and biochemical composition of the repaired tissue. Our analysis was compared with previous studies on histological assessments of cartilages via polarised light microscopy, revealing promising results. © 2013 Springer Science+Business Media.