Spatial derivative-based ray tracing for volume rendering

A machine-implemented display method that, with respect to a volume dataset being rendered, enables a user to navigate to any position in space and look in any direction. Preferably, the volume dataset is derived from a computer tomography (CT) or magnetic resonance imaging (MRI) scan. With the described approach, the user can see details within the dataset that are not available using conventional visualization approaches. The freedom-of-motion capability allows the user to go to places (positions) within the volume rendering that are not otherwise possible using conventional “orbit” and “zoom” display techniques. Thus, for example, using the described approach, the display image enables a user to travel inside physical structures (e.g., a patient's heart, brain, arteries, and the like).