The growing interest in recent years towards the multimedia and the large amount of information exchanged across the network involves the various fields of research towards the study of methods for automatic identification. One of the main objectives is to associate the information content of images, using techniques for identifying composing objects. Among image descriptors, contours reveal are very important because most of the information can be extracted from them and the contour analysis offers a lower computational complexity also. The contour analysis can be restricted to the study of some salient points with high curvature from which it is possible to reconstruct the original contour. The thesis is focused on the polygonal approximation of closed digital curves. After an overview of the most common shape descriptors, distinguished between simple descriptors and external methods, that focus on the analysis of boundary points of objects, and internal methods, which use the pixels inside the object also, a description of the major methods regarding the extraction of dominant points studied so far and the metrics typically used to evaluate the goodness of the polygonal approximation found is given. Three novel approaches to the problem are then discussed in detail: a fast iterative method (DPIL), more suitable for realtime processing, and two metaheuristics methods (GAPA, ACOPA) based on genetic algorithms and Ant Colony Optimization (ACO), more com- plex from the point of view of the calculation, but more precise. Such techniques are then compared with the other main methods cited in literature, in order to assess the performance in terms of computational complexity and polygonal approximation error, and measured between them, in order to evaluate the robustness with respect to affine transformations and conditions of noise. Two new techniques of shape matching, i.e. identification of objects belonging to the same class in a database of images, are then described. The first one is based on the shape alignment and the second is based on a correspondence by ACO, which puts in evidence the excellent results, both in terms of computational time and recognition accuracy, obtained through the use of dominant points. In the first matching algorithm the results are compared with a selection of dominant points generated by a human operator while in the second the dominant points are used instead of a constant sampling of the outline typically used for this kind of approach.