Logo: to the web site of Uppsala University

The subject of digital image analysis deals with extracting relevant information from image data, stored in digital form in a computer. A fundamental problem in image analysis is image segmentation, i.e., the identification and separation of relevant objects and structures in an image. Accurate segmentation of objects of interest is often required before further processing and analysis can be performed.

Despite years of active research, fully automatic segmentation of arbitrary images remains an unsolved problem. Interactive, or semi-automatic, segmentation methods use human expert knowledge as additional input, thereby making the segmentation problem more tractable. The goal of interactive segmentation methods is to minimize the required user interaction time, while maintaining tight user control to guarantee the correctness of the results. Methods for interactive segmentation typically operate under one of two paradigms for user guidance: (1) Specification of pieces of the boundary of the desired object(s). (2) Specification of correct segmentation labels for a small subset of the image elements. These types of user input are referred to as boundary constraints and regional constraints, respectively.

This thesis concerns the development of methods for interactive segmentation, using a graph-theoretic approach. We view an image as an edge weighted graph, whose vertex set is the set of image elements, and whose edges are given by an adjacency relation among the image elements. Due to its discrete nature and mathematical simplicity, this graph based image representation lends itself well to the development of efficient, and provably correct, methods.

The contributions in this thesis may be summarized as follows:

• Existing graph-based methods for interactive segmentation are modified to improve their performance on images with noisy or missing data, while maintaining a low computational cost.
• Fuzzy techniques are utilized to obtain segmentations from which feature measurements can be made with increased precision.
• A new paradigm for user guidance, that unifies and generalizes regional and boundary constraints, is proposed.

The practical utility of the proposed methods is illustrated with examples from the medical field.