We perceive objects in the world as having structures at both coarse and fine scales. A tree, for instance, may appear as having a roughly round or cylindrical shape when seen from a distance, even though it is built up from a large number of branches. At a closer look, individual leaves become visible, and we can observe that they in turn have texture at an even finer scale. The fact that objects in the world appear in diffrent ways, depending upon the scale of observation, has important implications when analyzing measured data, such as images, with automatic methods. This work describes a formal framework, called "scale-space representation", for handling the notion of scale in image data. It gives an introduction to the general foundations of the theory and shows how it applies to essential problems in computer vision such as computation of image features and cues to surface shape. The subjects range from mathematical underpinning to practical computational techniques. The power of the methodology is illustrated by a set of examples.