A wide variety of measures is currently in use in the morphometry of vascular systems. We introduce two additional classes of measures based on erosions and dilations of the image. Each measure has a clear biological interpretation in terms of the measured structures and their function. The measures are illustrated on images of the arterial tree of the quail chorioallantoic membrane (CAM). The new measures are correlated with widely-used measures, such as fractal dimension, but allow a clearer biological interpretation. To distinguish one CAM arterial tree from another, we propose reporting just three independent, uncorrelated numbers: (i) the fraction of tissue which is vascular (VF₀, a pure ratio), (ii) a measure of the typical distance of the vascularized tissue to its vessels (CL, a length), and (iii) the flow capacity of the tissue (P, an area). An unusually large CL would indicate the presence of large avascular areas, a characteristic feature of tumor tissue. CL is inversely highly correlated with fractal dimension of the skeletonized image, but has a more direct biological interpretation.