In this work it is shown that vascular structures of the human retina represent geometrical multifractals, characterized by a hierarchy of exponents rather then a single fractal dimension. A number of retinal images from the STARE database (www.parl.clemson.edu/stare) are analyzed, corresponding to both normal and pathological states of the retina. In all studied cases a clearly multifractal behavior is observed, where capacity dimension is always found to be smaller then the information dimension, which is in turn always smaller then the correlation dimension, all the three being significantly lower then the DLA (Diffusion Limited Aggregation) fractal dimension. We also observe a tendency of images corresponding to the pathological states of the retina to have lower generalized dimensions and a shifted spectrum range, in comparison with the normal cases.PACS numbers: 61.43.Hv, 87.57.Nk Over the past decade, there have been several attempts [1,2,3,4,5,6] in the direction of employing the fractal dimension as a measure for quantifying the "state" of human retinal vessel structures (considered as geometrical objects), with the expectation that such analysis may contribute to automatic detection of pathological cases, and therefore to computerization of the diagnostic process. While this is certainly a valid question with possibly high impact on real world diagnostic issues, there are some issues that should be addressed before such investigations may prove useful for the standard clinical practice. First, the fact that retinal vessels represent "finite size" realizations of a fractal growth process, imposes questions about how exactly should one go about measuring the fractal dimension of a particular instance (e.g. an electronic image of a retinal vessel structure, taken from a given angle, with a given resolution and lightning conditions). A related question is to what extent these calculations may correspond to the limiting fractal (which would have been attained if the growth process could have been extended to infinity), or equivalently, to what degree they may be compared with calculations on other such finite instances. Although various issues related to these questions have already been addressed (for a current review see e.g. [6]), it seems that many of them remain open for further investigation. Second, some of these works [3,4] address the point that the retinal vessels may have different properties in different regions, and do indeed find different characteristics depending on the locale of measurement, although the procedures adopted in these works are only remotely related to established concepts of multifractality, and the corresponding commonly accepted procedures for its measurement (see e.g. [7,8,9,10,11,12] and references therein).In this work we concentrate on the latter of the above issues, that is, we show that the human retinal vessel * Electronic address: borko@ufpe.br structures are geometrical multifractals, characterized by a hierarchy of exponents rather then a single fractal dimens...
