In this thesis, a combination of skeletonisation and graph matching techniques, coupled with a blend of supervised and unsupervised learning methodology is applied to the task of characterising and classifying natural shapes. A novel navigation-based skeletonisation algorithm is used to gather low level structural and morphological information about the shape. Subsequently, the data are converted into a series of attributed graphs, which characterise the image. Graphs of the same type can then be compared using an approximate graph matcher, which identifies a degree of similarity between them. Each degree of similarity corresponds to a data point in a conceptual space (as defined by Gärdenfors). The proposed method is applied to two distinct problems; the classification of leaf types, and the characterisation of river networks. The classification and characterisation systems are tested on a database of images of leaves and a collection of satellite images respectively. The novel navigation-based skeletonisation algorithm features several advantages; first, it allows the collection of topological and morphological information on the fly. This eliminates the need for any post-processing on the extracted skeletons. In addition, the adaptation of the algorithm to suit different applications is facilitated by the fact that any sort of morphological information can be included without alterations to the function of the algorithm. The conversion of the skeletons to attributed graphs is simplified by the existence of structural and morphological flags in the skeletal points. Last, concepts are created in the resulting conceptual space by means of a best-guess approach as well as a mechanism for accommodating external user input.