
doi: 10.5772/13040
An image is a two dimensional projection of a three dimensional scene. Hence a degeneration is introduced since no information is retained on the distance of a given point in the space. In order to extract information on the three dimensional contents of a scene from a single image it is necessary to exploit some a priori knowledge either on the features of the scene, i.e. presence/absence of architectural lines, objects sizes, or on the general behaviour of shades, textures, etc. Everything becomes much simpler if more than a single image is available. Whenever more viewpoints and images are available, several geometric relations can be derived among the three dimensional real points and their projections onto the various two dimensional images. These relations can be mathematically described under the assumption of pinhole cameras and furnish constraints among the various image points. If only two images are considered, this research topic is usually referred to as epipolar geometry. Naturally there is no mathematical difference whether the considered images are taken at the same time by two different cameras (the stereoscopic vision problem) or at different times by a single moving camera (optical flow or structure from motion problem). In Robotics both these cases are of great significance. Stereoscopy yields the knowledge of objects and obstacles positions providing a useful key to obtain the safe navigation of a robot in any environment (Zanela & Taraglio, 2002). On the other hand the estimation of the ego-motion, i.e. the measure of camera motion, can be exploited to the end of computing robot odometry and thus spatial position, see e.g. (Caballero et al., 2009). In addition the visual sensing of the environment is becoming ubiquitous out of the ever decreasing costs of both cameras and processors and the cooperative coordination of more cameras can be exploited in many applicative fields such as surveillance or multimedia applications (Arghaian & Cavallaro, 2009). Epipolar geometry is then the geometry of two cameras, i.e. two images, and it is usually represented by a 3 x 3 fundamental matrix, from which it is possible to retrieve all the relevant geometrical information, namely the rigid roto-translation between camera positions. The estimation of the fundamental matrix is based on a set of corresponding features present in both the images of the same scene. Naturally the error in the process is directly linked to the accuracy in the computation of these correspondences. In the following a novel genetic approach to epipolar geometry estimation is presented. This algorithm searches an optimal or sub-optimal solution for the rigid roto-translation between two camera positions in a evolutionary framework. The fitness of the tentative solutions is measured against the full set of correspondences through a function that is able to correctly cope with outliers, i.e. the incorrectly matched points usually due to errors in feature detection and/or in matching. Finally the evolution of the 1
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