Figure 4

Computer-aided estimate of the surface fractal dimension (D _s ) of a vascular network in 2-D biopsy sections. A. Hepatocellular carcinoma section stained with antibodies raised against CD31 (Dako, Milan, Italy) that specifically react with vessels. B. Image segmentation: immunopositive vessels are specifically selected on the basis of the similarity of the color of adjacent pixels. C. Determination of D _s using the box-counting algorithm. Briefly, the method counts the number of boxes of length ε required to cover the object being measured, indicated as N(ε). D. Prototypical curve obtainable using the box-counting method that highlights the so-called fractal windows ranged by box size ε ₁ and ε ₂, and represents the appropriate region in which to estimate the dimension. Box sizes of more than ε ₂ approach the size of the image until one box covers it completely, at which point N(ε) = 1 and the slope = 0. Box sizes smaller than ε ₁ approach a single pixel or the resolution of the image: in this region, box counting simply gives the area of the image.