The design and illustration of most internet sites today reveal the divide between raster images and vector graphics. Raster formats such as JPEG (Joint Photographic Experts Group) provide photographic quality, but at the cost of large file sizes. Vector graphics formats such as Macromedia Flash [38], on the other hand, remain compact yet they are fully scalable and often offer real-time user interactivity; unfortunately the limitations of existing solutions make them only adequate for low-detail, cartoon-like pictures. This thesis attempts to narrow the gap between these two concepts by introducing a novel type of image representation that aims to offer the flexibility of vector graphics whilst retaining the high level of detail associated with raster images. Chapter 1 of this thesis introduces the notion of image representation by drawing a parallel between human and computer vision, then identifies different types of representations and their properties. Chapter 2 discusses the qualities and drawbacks of existing approaches related to image representation and selects several criteria that will be the focus of the approach developed here. Isochromatic contours are shown to have the properties required to serve as a basis for an efficient vector image representation. Chapter 3 examines in detail the concept of isochromatic contours, describes a standard contourisation approach and exposes its limitations. It is shown that the use of a global contour sampling step imposes a trade-off between over- and underrepresentation, implying that representations based on standard contourisation methods cannot be both compact and accurate. It is concluded that, in order to be efficient, contourisation methods must adapt to the local surface topology. Chapter 4 looks at the concepts of topology and Morse theory, and investigates the relation between Morse Points and contours. A novel analysis method termed the Reel) Transform is then introduced that defines the minimal set of contours required to characterise a smooth surface. The use of the Reeb Transform to improve upon standard contourisation techniques is then described, with the limitation that it can only be applied to fully continuous surfaces. Chapter 5 opens by stating that an image can be regarded as a discontinuous juxtaposition of continuous regions. Following this idea, a novel approach termed multiresolution image labeling is introduced that aims to partition an image into its continuous components, to each of which the Reeb Transform can be applied. Chapter 6 assesses whether the work described in this thesis meets the criteria defined in Chapter 2. A set of experiments are presented that measure the performance of each of the algorithms introduced in chapter 4 and 5 with respect to these criteria. The experimental data is then analysed and interpreted. Finally, the possibility of integrating the algorithms introduced earlier into a single representational process is discussed. Chapter 7 concludes this thesis by summarising its achievements and discussing outstanding issues. The last part of this thesis presents several novel techniques, including continuity-driven Least Squares fitting that are being developed to address the limitations of the current approach.