Core Atoms and the Spectra of Scale

Our purpose is to characterize figures in medical images as a first step toward finding and measuring anatomical structures. For clinical use, we require complete automation and reasonably short computation times. We do not require that a sharp boundary be determined, only that the structure be identified and measurements taken of its size and shape. Our method involves the detection and linking of locations within an image that possess high "medialness," i.e., locations that are equidistant from two opposing boundaries. The method produces populations of core atoms, each core atom consisting of a center point (where medialness is high) and the two associated boundary points. We can cluster core atoms by the proximity of their centers and by the similarity of their size (scale). We generate statistical signatures of clusters to identify the underlying figure. In particular, we compute three spectra vs. scale for a cluster, including (1) magnitude: the number of core atoms, (2) eccentricity: their aggregate directional asymmetry, and (3) orientation: their aggregate direction. We illustrate the production of these spectra for various graphical test images, demonstrating translational, rotational, and scale invariance of the spectra, as well as specificity between targets. We observe the effects of image noise on the spectra and show how clustering reduces these effects. Early results suggest that the scale spectra of core atoms provide an efficient and robust method for identifying figures, suitable for practical application in medical image analysis.