Surface models can be used in several domains, from medical imaging to video games. There are many image acquisition techniques that can be used to extract a volumetric representation from continuous objects. However, a surface is a more suitable representation in several contexts such as visualization, data exploration and simulation. In addition, new acquisition technologies can obtain increasingly bigger
images that can reach several millions of pixels each. The conception of new surface extraction techniques is necessary in order to process this huge quantity of data.

In this dissertation, we have been interested in the surface extraction from the volumetric representation of an object. With this objective, we have been concentrated in the spatial subdivision approach. These approaches divide the volume in order to build a piece-wise approximation of the object's surface. The general idea is to build local approximations of the geometry and the topology of the surface and then
combine them to create a unique surface. Methods based on the Marching Cubes algorithm (MC) have problems to accurately capture the geometry and topology of the surface. Even if several algorithms provided improved versions of MC, they only tackle one or two problems but they do not solve all its limitations.
Dual methods (DC) are more adapted to use an adaptive subdivision over the original volume. These algorithms generate surfaces that are dual to those generated by Marching Cubes or they can also produce dual grids.
DC methods can produce adaptive surfaces that represents better the geometry of the object. Moreover,recent research guarantees that the generated surfaces had good topological and geometrical properties.
We have studied the geometrical and topological characteristics of volumetric objects. We have explored the state of the art on space subdivision methods so to identify advantages and drawbacks in their application on volumetric objects. We have decided to use a dual approach in order to obtain a good compromise between surface quality and geometrical approximation. In a second stage, we have proposed and implemented a surface generation pipeline combining a dual method with a n-dimensional connected components search in order to better capture the topology and the geometry of the original object.
In a third stage, we have developed an out-of-core extension of our pipeline to process huge volumetric data.
First, the volume is divided in sub-volumes that can be loaded individually in memory, then we generate surface patches from each sub-volume while keeping all necessary information to further connect them in order to produce a unique surface. Our approach can be executed in parallel to speed up the surface extraction.
Finally, we have tested our solution over several volumes and we have confirmed the validity of our approach.