The topic of this thesis is an general introduction to quantitative methods for the analysis of digital microscope images. The images presented are primarily been acquired from Scanning Electron Microscopes (SEM) and interfermeter microscopes (IFM). The topic is approached though several examples in a number work cases. These mainly falls in the three categories: (i) Description of coarse scale measures to quantify surface structure or texture (topography); (ii) Characterization of fracture surfaces in steels (fractography); (iii) Grain boundary segmentation in sintered ceramics. The theoretical foundation of the thesis fall in the areas of: 1) Mathematical Morphology; 2) Distance transforms and applications; and 3) Fractal geometry. Image analysis opens in general the possibility of a quantitative and statistical well founded measurement of digital microscope images. Herein lies also the conditions to correlate the micro-structure of materials to macroscopic properties, such as tensile strength, durability, chemical resistance.