The application of fractal geometric analysis to microscopic images

Fractal geometry is a relatively new tool for the quantitative microscopist that is a more valid way of measuring dimensions of complex irregular objects than the integer-dimensional geometries (such as Euclidean geometry). This review discusses the theory of fractal geometry using the classic examples of the Von Koch curve, the Cantor set and the Sierpinski gasket. The problems of describing the dimensions of these objects are discussed and the concept of fractal dimensionality is introduced. Methods for measuring fractal dimensions are discussed, including their implementation on microcomputer-based image analysis systems . The advantages and problems of fractal geometric analysis are discussed and current applications in the field of microscopy are reviewed.