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A central task of computer vision is to automatically recognize objects in real-world scenes. The parameters defining image and object spaces can vary due to lighting conditions, camera calibration and viewing position. It is therefore desirable to look for geometric properties of the object which remain invariant under such changes in the observation parameters. The study of such geometric invariance is a field of active research. This paper presents the theory and computation of projective invariants formed from points and lines using the geometric algebra framework. This work shows that geometric algebra is a very elegant language for expressing projective invariants using n views. The paper compares projective invariants involving two and three cameras using simulated and real images. Illustrations of the application of such projective invariants in visual guided grasping, camera self-localization and reconstruction of shape and motion complement the experimental part.

The paper focus on the analysis and computing of the projective structure and motion using geometric invariants. This work relates current approaches in the geometric algebra framework; as a result the approach gains geometric transparency and elegance. The paper presents experiments regarding projective reconstruction of shape and motion using both simulated and real images.

In this paper a special higher order neuron, the hypersphere neuron, is introduced. By embedding Euclidean space in a conformal space, hyperspheres can be expressed as vectors. The scalar product of points and spheres in conformal space, gives a measure for how far a point lies inside or outside a hypersphere. It will be shown that a hypersphere neuron may be implemented as a perceptron with two bias inputs. By using hyperspheres instead of hyperplanes as decision surfaces, a reduction in computational complexity can be achieved for certain types of problems. Furthermore, it will be shown that Multi-Layer Percerptrons (MLP) based on such neurons are similar to Radial Basis Function (RBF) networks. It is also found that such MLPs can give better results than RBF networks of the same complexity. The abilities of the proposed MLPs are demonstrated on some classical data for neural computing, as well as on real data from a particular computer vision problem.

In this chapter we present a geometric approach for the computation of shape and motion using projective invariants in the geometric algebra framework [ 6, 7].

The paper focus on the analysis and computing of the projective structure and motion using geometric invariants. This work relates current approaches in the geometric algebra framework, which results in geometric transparency and elegance. The papers presents experiments regarding projective reconstruction of shape and motion using both simulated and real images.