This thesis describes and proposes solutions to some of the currently most important problems in pattern recognition and image analysis of two-dimensional gel electrophoresis (2DGE) images. 2DGE is the leading technique to separate individual proteins in biological samples with many biological and pharmaceutical applications, e.g., drug development. The technique results in an image, where the proteins appear as dark spots on a bright background. However, the analysis of these images is very time consuming and requires a large amount of manual work so there is a great need for fast, objective, and robust methods based on image analysis techniques in order to significantly accelerate this key technology. The methods described and developed fall into three categories: image segmentation, point pattern matching, and a unified approach simultaneously segmentation the image and matching the spots. The main challenges in the segmentation of 2DGE images are to separate overlapping protein spots correctly and to find the abundance of weak protein spots. Issues in the segmentation are demonstrated using morphology based methods, scale space blob detection and parametric spot modelling. A mixture model for parametric modelling of several spots that may also be overlapping is proposed. To enable comparison of protein patterns between different samples, it is necessary to match the patterns so that homologous spots are identified. Protein spot patterns, represented by the spot centre coordinates can be regarded as two-dimensional points sets and methods for point pattern matching can be applied. This thesis presents a range of state-of-the-art methods for this purpose and also suggests a regionalised scheme. The general point pattern matching methods focussed on are the Robust Point Matching methods and among the methods developed in the literature specifically for matching protein spot patterns, the focus is on a method based on neighbourhood relations. These methods are applied to a range of 2DGE protein spot data in a comparative study. The point pattern matching requires segmentation of the gel images and since the correct image segmentation can be difficult, a new alternative approach, exploiting prior knowledge from a reference gel about the protein locations to segment an incoming gel image, is proposed.