In recent years, kernel principal component analysis (KPCA) has been suggested for various image processing tasks requiring an image model such as, e.g., denoising or compression. The original form of KPCA, however, can be only applied to strongly restricted image classes due to the limited number of training examples that can be processed. We therefore propose a new iterative method for performing KPCA, the kernel Hebbian algorithm, which iteratively estimates the kernel principal components with only linear order memory complexity. In our experiments, we compute models for complex image classes such as faces and natural images which require a large number of training examples. The resulting image models are tested in single-frame super-resolution and denoising applications. The KPCA model is not specifically tailored to these tasks; in fact, the same model can be used in super-resolution with variable input resolution, or denoising with unknown noise characteristics, in spite of this, both super-resolution and denoising performance are comparable to existing methods.

Imitation learning is a promising technique for teaching robots complex movement sequences. One key problem in this area is the transfer of perceived movement characteristics from perception to action. For the solution of this problem, representations are required that are suitable for the analysis and the synthesis of complex action sequences. We describe the method of Hierarchical Spatio-Temporal Morphable Models that allows an automatic segmentation of movements sequences into movement primitives, and a modeling of these primitives by morphing between a set of prototypical trajectories. We use HSTMMs in an imitation learning task for human writing movements. The models are learned from recorded trajectories and transferred to a human-like robot arm. Due to the generalization properties of our representation, the arm is capable of synthesizing new writing movements with a few learning examples.

In this chapter we review two pieces of work aimed at understanding the principal limits of extracting egomotion parameters from optic flow fields (Dahmen et al. 1997) and the functional significance of the receptive field organization of motion sensitive neurones in the fly's visual system (Franz and Krapp 1999). In the first study, we simulated noisy image flow as it is experienced by an observer moving through an environment of randomly distributed objects for different magnitudes and directions of simultaneous rotation R and translation T. Estimates R', of the magnitude and direction of R, and t', of the direction of T, were derived from samples of this perturbed image flow and were compared with the original vectors using an iterative procedure proposed by Koenderink and van Doom (1987). The sampling was restricted to one or two cone-shaped subregions of the visual field, which had variable angular size and viewing directions oriented either parallel or orthogonal with respect to the egomotion vectors R and T. We also investigated the influence of environmental structure, such as various depth distributions of objects and the role of planar or spherical surfaces. From our results we derive two general rules how to optimize egomotion estimates: (i) Errors are minimized by expanding the field of view. (ii) Sampling image motion from opposite directions improves the accuracy, particularly for small fields of view.From the iterative algorithm we derived a fast, non-iterative "matched filter" to extract R' and t', which under many conditions yields results very similar to those obtained by iteration. Its structure shows striking similarities to the receptive field organization of wide-field motion sensitive neurones in the visual system of the fly (Krapp and Hengstenberg 1996), but there are characteristic differences. To explain these differences, we developed a more elaborate version of this approach in which the statistical properties of the fly's environment and behaviour, i.e. the distribution of object distances and flight directions, are taken into account. A matched filter was directly derived from an optimization principle that minimizes the variance of the filter output caused by noise and distance variabilities. The optimized filters were then compared to the detailed organization of the receptive fields of the fly's wide-field neurones. Our analysis suggests that these neurones are not optimal for estimating the magnitude of R and t', but rather for consistently encoding the presence and the sign of rotatory or translatory flow fields along a particular set of axes.

The so-called tangential neurons in the fly brain are sensitive to the typical optic flow patterns generated during self-motion. This suggests a possible involvement in the self-motion estimation process. In this study, the authors examine whether a simplified matched filter model of these neurons can be used to estimate self-motion from the optic flow. They present a theory for the construction of an optimal matched filter incorporating both the noise properties of the motion signal, and prior knowledge about the distance distribution of the environment. Tests on a mobile robot demonstrate that the matched filter approach works for real time camera input and the noisy motion fields computed by Reichardt motion detectors.

Although artificial and biological systems face similar sensorimotor control problems, until today only a few attempts have been made to implement specific biological control structures on robots. Nevertheless, the process of designing the sensorimotor control of a robot can contribute to our understanding of these mechanisms and can provide the basis of a critical evaluation of existing biological models. Flies have developed a specialized visuomotor control for tasks such as course stabilization, fixation and approach towards stationary objects, tracking of moving objects and landing, which are based on the analysis of visual motion information. Theoretical and experimental results suggest that in flies the visuomotor control for course stabilization as well as fixation and approach towards stationary objects may be implemented at least partially by one common sensory circuit. We present agents with a visuomotor controller that regulates the two behaviors of course stabilization and object fixation. To test this controller under real world conditions, we implemented it on a miniature robot. We have been able to show that in addition to course stabilization and object fixation, the robot also approaches stationary objects.

In visual homing tasks, animals as well as robots can compute their movements from the current view and a snapshot taken at a home position. Solving this problem exactly would require knowledge about the distances to visible landmarks, information, which is not directly available to passive vision systems. We propose a homing scheme that dispenses with accurate distance information by using parameterized disparity fields. These are obtained from an approximation that incorporates prior knowledge about perspective distortions of the visual environment. A mathematical analysis proves that the approximation does not prevent the scheme from approaching the goal with arbitrary accuracy. Mobile robot experiments are used to demonstrate the practical feasibility of the approach.