CENTROID SCALE-SPACE MAPS

An image representation based on mapping image centroids as a function of spatial and scale variables is introduced. This new representation has the advantage that the contours within this scale-space coordinate system consist primarily of curves (i.e., one-dimensional forms) even when the input function is an image with two (or more) spatial coordinates. This is contrasted with the more well-known scale-space approaches based on tracking edge locations through scale when the scale-space contours become curved surfaces for two-dimensional input images. The one-dimensional form of the centroid scale-space contours simplifies the process of extracting useful information from the scale-space maps. Centroid scale-space maps for one- and two-dimensional input functions are examined, and a preliminary set of properties relating the inputs to the maps is presented. We demonstrate the applications of finding the locations and size distributions of objects in an image and of determining the medial-axis transform of an image.