The fields of image analysis, computer vision, and artificial intelligence all make use of descriptions of shape in grey-level images. Most existing algorithms for the automatic recognition and classification of particular shapes have been devel­ oped for specific purposes, with the result that these methods are often restricted in their application. The use of advanced and theoretically well-founded math­ ematical methods should lead to the construction of robust shape descriptors having more general application. Shape description can be regarded as a meeting point of vision research, mathematics, computing science, and the application fields of image analy­ sis, computer vision, and artificial intelligence. The NATO Advanced Research Workshop "Shape in Picture" was organised with a twofold objective: first, it should provide all participants with an overview of relevant developments in these different disciplines; second, it should stimulate researchers to exchange original results and ideas across the boundaries of these disciplines. This book comprises a widely drawn selection of papers presented at the workshop, and many contributions have been revised to reflect further progress in the field. The focus of this collection is on mathematical approaches to the construction of shape descriptions from grey-level images. The book is divided into five parts, each devoted to a different discipline. Each part contains papers that have tutorial sections; these are intended to assist the reader in becoming acquainted with the variety of approaches to the problem.