Flow fields are usually visualized relative to a global observer, i.e., a single frame of reference. However, often no global frame can depict all flow features equally well. Likewise, objective criteria for detecting features such as vortices often use either a global reference frame, or compute a separate frame for each point in space and time. We propose the first general framework that enables choosing a smooth trade-off between these two extremes. Using global optimization to minimize specific differential geometric properties, we compute a time-dependent observer velocity field that describes the motion of a continuous field of observers adapted to the input flow. This requires developing the novel notion of an observed time derivative. While individual observers are restricted to rigid motions, overall we compute an approximate Killing field, corresponding to almost-rigid motion. This enables continuous transitions between different observers. Instead of focusing only on flow features, we furthermore develop a novel general notion of visualizing how all observers jointly perceive the input field. This in fact requires introducing the concept of an observation time, with respect to which a visualization is computed. We develop the corresponding notions of observed stream, path, streak, and time lines. For efficiency, these characteristic curves can be computed using standard approaches, by first transforming the input field accordingly. Finally, we prove that the input flow perceived by the observer field is objective. This makes derived flow features, such as vortices, objective as well.

Fig. 1. Observer motion relative to the time evolution of features: Hurricane Isabel in a time-dependent global wind data set. (Bottom left) The actual path of Isabel (from NHC/Wikipedia). (Top left) Our observer field u automatically follows the motion of Isabel without explicit tracking of its path. The shown path is simply a path line of u. (Right) Feature-relative visualization, focused on Isabel in the center, enabling analysis of its time evolution "in place." The hurricane appears steady, with the Earth moving inversely underneath.

Abstract-Dynamic contrast-enhanced image data (perfusion data) are used to characterize regional tissue perfusion. Perfusion data consist of a sequence of images, acquired after a contrast agent bolus is applied. Perfusion data are used for diagnostic purposes in oncology, ischemic stroke assessment, or myocardial ischemia. The diagnostic evaluation of perfusion data is challenging, since the data are complex and exhibit various artifacts, e.g., motion artifacts. We provide an overview on existing methods to analyze and visualize CT and MR perfusion data. The integrated visualization of several 2D parameter maps, the 3D visualization of parameter volumes, and exploration techniques are discussed. An essential aspect in the diagnosis of perfusion data is the correlation between perfusion data and derived time-intensity curves as well as with other image data, in particular with high-resolution morphologic image data. We discuss visualization support with respect to the three major application areas: ischemic stroke diagnosis, breast tumor diagnosis, and the diagnosis of coronary heart disease.

This paper describes a method to visualize the thickness of curved thin objects. Given the MRI volume data of articular cartilage, medical doctors investigate pathological changes of the thickness. Since the tissue is very thin, it is impossible to reliably map the thickness information by direct volume rendering. Our idea is based on unfolding of such structures preserving their thickness. This allows to perform anisotropic geometrical operations (e.g., scaling the thickness). However, flattening of a curved structure implies a distortion of its surface. The distortion problem is alleviated through a focusand-context minimization approach. Distortion is smallest close to a focal point which can be interactively selected by the user.

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