Visual Hull

This article gives an overview of the concept of the Visual Hull and what its advantages and disadvantages are. The Visual hull is a concept of a 3D reconstruction by a Shape-From-Silhouette (SFS) technique. This kind of 3D scene reconstruction first has been introduced by Baumgart in his PhD thesis in 1974 [1]. Since then there have been several different variations of the Shape-From-Silhouette method. The basic principle is to create a 3D representation of an object by its silhouettes within several images from different viewpoints. Each of these silhouettes by different camera views form in their projection a cone, called visual cone and an intersection of all these cones form a description of the real object’s shape (see figure 1.a for a 2D example). By using this basic idea there are many advantages in using Shape-From-Silhouette techniques. First of all the calculation of the silhouettes is easily to implement, when we assume an indoor environment with special conditions, like static light and static cameras. Without these assumptions it can become difficult to calculate an accurate silhouette out of the images, because of shadows or moving backgrounds. Further techniques for this problem will not been discussed any further in this article. On the other hand are the implementations of the SFS-algorithm straight forward and especially compared to other techniques for shape estimations, like multi-baseline stereo far less complex. The result of the SFS construction is an upper bound of the real object’s shape in contrast to a lower bound, which is a big advantage for obstacle avoidance in the field of robotic or visibility analysis in navigation. Another application for SFS estimations are for instance the field of motion capturing [5]. On the other hand there are also disadvantages for these techniques. So there are time consuming testing steps, which are a bottleneck for real-time applications or the silhouette calculations, which are relative sensitive for errors, like noise or wrong camera calibrations. These ends up in problems for the intersection of the visual cones and therefore bad results for the resulting 3D shapes. Furthermore is the result of each SFS algorithm just an approximation of the actual object’s shape (like we will prove later), especially if there are only a limited number of cameras and therefore is this approach not practical for applications like detailed shape recognition or realistic rerendering of objects [5]. The main problem of the SFS-based algorithms are that they are not able to perform an accurate reconstruction of concave objects, like figure 2 (as long as we assume that the camera views are not too near to the object). An obvious question, which occurs in this context is which parts of an object can be reconstructed by standard SFS techniques, or what are the limits of these approaches? To denote this difference Laurentini introduced the term of the Visual Hull in 1991 [2]. His formal definition of the Visual Hull is the following: