Imaging transforms for visualizing surfaces and volumes

Three-dimensional (3D) visualization in biomedical and other imaging areas is a rapidly emerging discipline. The major developments in this field are described in a unified and concise way. To this end, we introduce an operator notation to describe the basic imaging transforms commonly used in 3D visualization and to identify a comprehensive set of basic transforms. We also introduce several new basic transforms for filtering and interpolating scenes and structures and for rendering surfaces and volumes. We demonstrate not only how the existing visualization methodologies can be described concisely, but we also show how a great variety of new methodologies can be generated using both the existing imaging transforms and the new transforms introduced in this paper. A comprehensive evaluation method to compare objectively rendering methods used in visualization based on task-specific mathematical phantoms is described. We examine in detail separate transform sequences that are best suited for rendering robust and frail structures (ie, structures with well- and poorly defined boundaries).