Morphological Multiscale Gradient Watershed Image Analysis 1..1 Morphological Scale-space

We introduce a scale-space causality theorem for regions of a image deened by watersheds of a gradient function modiied to retain only the local minima or maxima of its parent function. We then illustrate an application of the new theorem to the scale dependent extraction of texture elements from the nucleii of cervical cells. As background, in the next two subsections we introduce morphological scale-space, and the watershed transform, then in section 2 we outline the new theory of the morphological multiscale gradient watershed which is the central topic of this paper. Finally we demonstrate a potential application to the scale dependent extraction of texture features from the nucleii of cervical cells. The scale-space concept was introduced to image analysis by Witkin 1]. Scale-space theory provides a way to associate signal descriptions through multiple scales, this approach emphasises the relationship between signal descriptions across scale and the existence of a mathematical monotonic property since the number of signal features must be a monotone decreasing function of scale. We have previously developed a new scale-space theory, based around a scale-dependent non-linear image smoother, called the multiscale-morphological-dilation-erosion 2, 3]. The method is deened for both positive and negative scales: for positive scales we perform a dilation, for negative scales an erosion, indeed it is the magnitude of the scale parameter, jj, which corresponds to the intuitive notion of scale.