Segmentation is an important part of any image analysis and computer vision tasks from ranging medical imaging to robot navigation. Ideally it should be efficient to compute and correspond well with the physical objects depicted in the image. In the last decade hierarchical segmentation schemes using either superficial (homogeneity) or deep (multi-scale) image structure information have emerged for obtaining precise and (semi) automatic segmentations. The goal of this research project is to create a hierarchical segmentation scheme that integrates color gradient-watersheds and non-linear scale space. Along with the introduction of a hyper-stack, which defines a linking model connecting points in adjacent scale levels, the proposed integration scheme embodies image features such as color homogeneity, color contrast and scale. In this project color is seen as an attribute inherent to the human vision system. The perceived color difference should therefore be proportional to the measure color difference. This introduces in project a study of color gradients methods, color contrast and color homogeneity in relation to color-space. The idea is to measure these features in a color space, which allows the feature to act similar to what a human would expect. The partitioning of the image is obtained with a color-gradient-watershed. The watershed results in a full partitioning of the image domain in closed contours and homogenous regions. It provides a one to one relationship between the local minima in the gradient and a region of the partitioning, which allows a region to be represented by its corresponding local minima. An inherent drawback is oversegmentation or over-partitioning of the image domain. Its reduction can be achieved with different strategies. This project applies a hierarchical method to achieve the removal of the redundant contours. The hierarchy among gradient-watersheds is achieved using information of the deep image structure. The deep image structure or the scale-space image can be obtained in several ways. The most common one to be used is the linear scale-space, even though it suffers from some serious drawbacks such as de-localization, the similar treatment of noise and image features and its non-causality in multiple dimensions. The majority of scale-space methods is based on the diffusion equation and can therefore be expressed as a PDE. This ensures a firm mathematical background for the scale-space theory. Other methods than the linear diffusion can thus be used to obtain the scale-space representation of the image. The non-linear methods do suffer from the de-localization and can subsequently avoid the correspondence problem. However, their drawback is computation time. Recently that drawback is been diminished by the enormous increase in computing power and the proposal of new more efficient numerical implementation. The idea is to obtain the deep image structure using a non-linear diffusion method. For this purpose an investigation of the non-linear methods and their usefulness for watersheds segmentation is conducted, we also compare their performance with the linear method with respect to gradient-watersheds and feature measurement in the scales. An important part of any multi-resolution scheme is the determination of the measurement scales. It is evident that adding scale information ad random will complicate the segmentation process rather than simplifying it. Most existing multi resolution scheme have experimentally determined the relevant measurement scales. Lindeberg et al have proposed the use of gamma-normalized derivatives with the scale invariance property for the linear scale-space. The majority of other linear scale selection methods are a derived from his method. The proposed method might be extended to the non-linear case provided one can circumvent the scale-invariance requirement. During this project we will explore the possibility for creating a scale-selection method based on a study of the evolution of the top-points of the squared gradient magnitude.

Runtime: 2000 - 2003