Quantifying spatial heterogeneity from images

Visualization techniques are extremely useful for characterizing natural materials with complex spatial structure. Although many powerful imaging modalities exist, simple display of the images often does not convey the underlying spatial structure. Instead, quantitative image analysis can extract the most important features of the imaged object in a manner that is easier to comprehend and to compare from sample to sample. This paper describes the formulation of the heterogeneity spectrum to show the extent of spatial heterogeneity as a function of length scale for all length scales to which a particular measurement is sensitive. This technique is especially relevant for describing materials that simultaneously present spatial heterogeneity at multiple length scales. In this paper, the heterogeneity spectrum is applied for the first time to images from optical microscopy. The spectrum is measured for thin section images of complex carbonate rock cores showing heterogeneity at several length scales in the range 10-10 000 μm.