Investigating a 2D or 3D picture with computers requires a form of the picture created by the digitization and quantization of sampled values. Picture analysis derives information about the scene by making measurements of its elements from the digitized data and assigning geometric properties to the elements. These geometric properties can then be viewed and manipulated much as you would in Euclidean geometry. This is known as digital geometry, and it forms the basis for much current work in computer graphics, digital image processing, and image analysis. Digital Geometry: Geometric Methods for Digital Picture Analysis introduces the concepts, algorithms, and practices of the field. The book uses a "picture" approach rather than an "image" approach because contemporary pictures may not involve imaging processes at all, but result from drawing, painting, stitching, modeling, or capturing scenes. Digital Geometry begins by introducing the mathematical foundations of digital geometry including grids, metrics, graphs, topology, and geometry. This is followed by discussion of key topics including digital straightness, hulls, length and curvature of arcs and curves, and area and curvature of surfaces. The remaining chapters address operations on pictures, including transformations and morphological operations. Digital Geometry emphasizes the implementation of algorithms and the practical implications of the theory.