The purpose of an image retrieval system is to organize and index images so that if we have a large number of images in the database, given a query image, the relevant images can be retrieved efficiently upon request. Relevant images is a list of images from the database which are most “similar”in some aspects to the query image. So the main issues of an image retrieval system are the proper indexing of images (see Chapter 7) and similarity comparison during the query process. In this chapter we consider the shape aspect of objects. Given a unique shape signature (based on boundary) for each object, the question is how to measure the distance and similarity between boundaries. For solving this problem, we need two things. First, a feature which represents the shape information of the image (see Chapter 3). Second, a similarity measure to compute the similarity between features of two images. The similarity measure is a matching function, and gives the degree of match or similarity for a given pair of images (represented by shape measures).