An ef®cient voxel-based visualization system from an implicit skeletal surface characterization By Ste Âphanie Pre Âvost and Laurent Lucas* .......................................................................................... This paper presents a new algorithm of volume rendering based on a dual representation of data. The algorithm improves both the image generation speed and its quality. Two shape descriptors are used to characterize the object: a Euclidean distance transform (EDT) and a digital Euclidean skeleton. The EDT is used at one point in time to accelerate the image generation and compute the skeleton of the shape, whilst the skeleton is used as an initialization of the processing of the implicit surface. The goal is to build an interactive system of visualization for the analysis of volumetric data, either in the setting of a qualitative exploration or as a guide for qualitative measurements. The speed of treatment together with good visualization should give the feasibility to achieve a 3D survey of a natural object in an interactive manner. The method has been successfully applied to both synthetic and real data. Copyright # 2000 John Wiley & Sons, Ltd. Received: 15 March 1999; Revised: 7 September 1999 KEY WORDS: volume rendering; implicit surface; EDT; morphologic skeleton Introduction With the recent development of advanced range- imaging sensors (e.g. X-ray CT scanner, MRI and PET modalities in medicine and confocal microscopy in biology), requirements for three-dimensional data visualization have increased signi®cantly over the past few years to the point of becoming a very important issue in computer graphics. The basic problem in volume visualization can be de®ned as follows: given a volume data set, how can we extract and visualize structures contained in the volume in a way that allows the user to perform accurate analysis? A wide variety of methods have been developed during this period to reconstruct, visualize and manipulate 3D regular scalar ®elds directly. They can be classi®ed in various ways, but usually they are grouped into two concurrent approaches: surface- based methods and volume-based methods. Surface-rendering methods are based on the bound- ary representation of the object by ®tting geometric primitives to raw data. 1±3 The complexity of these methods depends on the surface primitives used, and most of them owe their success to their ability to interact with 3D data sets at or near video rates. However, such representations are incomplete: they lack information about the global properties of objects. Besides, they can generate a large number of primitives. In contrast, volume-rendering methods consist in taking into account the whole data set at once. 4,5 Algorithms in this category use only raw data, so no geometric intermediates such as polygonal meshes are necessary. One of the most popular techniques used to render volumetric data is the direct volume ray-casting algorithm. The principle consists in sending rays from each pixel in the image plane through the volume data and determining whether they intersect with the surface contained within the data. Direct volume ray casting is well known to offer the highest ¯exibility in terms of integrated feature enhancement, but often to the detriment of the time required to generate a high-quality image. Another problem concerns this kind of algorithm: the discrete form of a 3D scene. This is the cause of many problems *Correspondence to: L. Lucas, Laboratoire d'Etudes et de Recherches Informatiques, Universite  de Reims, Champagne- Ardenne, Rue des Craye Áres, BP 1035, F-51687 Reims Cedex 2, France. E-mail: laurent.lucas@univ-reims.fr THE JOURNAL OF VISUALIZATION AND COMPUTER ANIMATION J. Visual. Comput. Animat. 2000; 11: 39±49 ............................................................................................................... ............................................................................................................... Copyright # 2000 John Wiley & Sons, Ltd.