The novel scale-spectrum space for representing gray-level shape

This paper presents the construction of a novel representation of shape called the scale-spectrum space, which makes both spatial frequency channels of speciic importance (concerning spectrum information being isolated) as well as signiicant scale levels from the viewpoint of these spectrum bands explicit. The scale concept in the vision literature stands for the characteristic length over which gray-level variations in the image take place and/or the operator size used for processing the given image. In scale-space representation where gray-level shape generally comprises multiple structures at diierent levels of scale, it is often not possible to obtain an image where all the structures are described at their best scale levels, if one structure is well-enhanced, the other ones appear blurred. At best, some forms of compromise among the structures at diierent scale levels can be sought. To overcome this problem we present an eecient multi-channel scheme which may be employed to automatically describe each gray-level structure at its most suitable level of smoothing. This representation allows for a data-driven detection of those spectrum bands, and the evolution of scale levels from the viewpoint of such domains, and it is not an eeect of some externally chosen criteria or tuning parameters. As a result, it is derived a multichannel organization selectively sensitive to spatial frequency and size which is biologically inspired in the behavior of visual cortex neurones as well as retinal cells. In absence of further information, the scale-spectrum space can serve as a guide to subsequent processing requiring knowledge about the scales at which grey-level structure with particular frequency components (high, medium or low frequency content) occurs.