Generalized Scale-Selection

Structure in digitized images resides within two scales, the inner and outer scale. The inner scale is defined by the sampling resolution, and the outer scale is given by the image size. However, some images contain almost no fine scale structure, and these may be down-sampledwithout essential loss of image detail. Likewise some images may be reduced in size by removing borders with no structure. Hence we define essential inner and outer scales. Such considerations are the essence of local size estimation: A textured patch in an image has an essential inner scale related to the structure of the primitive textons, and an essential outer scale given by the size of the patch. In this paper, several functionals are examined that automatically find both the essential inner and outer scales in local neighborhoods of an image. In this preliminary work we present a general formulation for local scale selection, that is shown to be a generalization of Lindeberg’s Blob-detector and its morphological equivalent, and we present promising results using locally orderless images.