Abstract: The best parameters defining the geometry of a visual sensor generally depend on the particular visual task the sensor is intended to be used in. However, translating task requirements directly into low-level geometric parameters may be difficult, since deep knowledge of the sensor design is usually required, but end users of a sensor need not necessarily be its designers. A framework is suggested to facilitate this translation by including an intermediate layer, the design criteria, between task requirements and sensor parameters. The proposed framework is illustrated with a log-polar space-variant vision model. The motivation behind using this particular sensor is the observation that, in the literature, little attention has been paid to the proper choice of the sensor parameters, or the lack of justification of the chosen configuration. Sets of general-purpose design criteria and task specifications are provided and discussed. The process of finding the best geometric parameters for a given set of (many and/or mutually conflicting) design criteria is automated with a multi-objective genetic algorithm. Some examples are given demonstrating the feasibility and potential of the approach.

Abstract: Image projections provide an effective way of describing image contents or estimate particular kinds of motion. However, most (if not all) of previous literature on projections has been done on Cartesian images. In contrast, the work described in this paper is aimed at exploring how projections can be defined on log-polar images and how they perform in estimating motion. In the proposed algorithm, a set of projection signals is computed in two consecutive frames. Then, 1D affine motion between each pair of corresponding projection signals is estimated. Finally, 2D image affine motion is derived from the set of estimated 1D motion parameters, using a 2D-1D motion mapping model (MMM). A reduced, 5-parameter, affine motion model can be estimated with this MMM. The algorithm is implemented in both, log-polar and Cartesian images. Synthetic motion is used for a careful analysis of the strengths and weaknesses of the algorithm. The comparison of the results with log-polar and Cartesian images reveal that the limitations of the approach are due to the MMM, rather than to the inherent difficulties and distortions introduced by the space-variant nature of log-polar images. Another significant finding is that Cartesian images require much more pixels than log-polar images to get comparable estimation performance.

Abstract: To cope with the huge amount of visual data in the environment, foveal sensing is not only an elegant biological solution, but also an appropriate mechanism in computer-based vision of artificial agents such as robots. An extremely important visual behavior in active vision systems is that of actively tracking moving targets, which is a problem closely related with foveal vision. The work described in this article has precisely to do with active tracking with space-variant images. The two main components of the proposed algorithm are the log-polar image format, and a projection-based motion estimator, whose joint use results in an efficient and effective active tracking scheme. For the successful real-time performance of the proposed approach, it is very important to have an appropriate combination of: (i) an efficient motion estimation technique, (ii) an adequate image representation, and (iii) the dynamic nature of purposive vision.

Abstract: Log-polar mapping has been proposed as a very appropriate space-variant imaging model in active vision applications. This biologically inspired model has several advantages, and facilitates some visual tasks. For example, it provides an efficient data reduction, and simplifies rotational and scaling image transformations. However, simple translations become a difficult transform due to the log-polar geometry. There is no doubt about the importance of translation estimation in active visual tracking. Therefore, in this work, the problem of translation estimation in log-polar images is tackled. Two different approaches are presented, and their performances are evaluated and compared. One approach uses a gradient descent for minimizing a dissimilarity measure, while the other converts the 2D problem into two simpler 1D problems, by using projections. As the experimental results reveal, this second approach, besides being more efficient, can deal with larger translations than the gradient-based search can.

Abstract: A motion estimation algorithm for log-polar images, based on the general framework of Hager and Belhumeur (1998), is presented. The advantages and disadvantages brought by the use of this kind of foveal imaging are discussed. Within this context, a simple, but quite effective approach for figure-ground segmentation is also proposed. Performance results concerning motion estimation and target segmentation are reported.

Abstract: Log-polar images have been being used for pattern recognition and active vision tasks for some years. These images are obtained either from true retina-like sensors or from conventional cartesian images by software conversion. From the hardware perspective, the design of such log-polar retinae faces its own technological limitations. In the case of software remappers, however, their very flexibility has led to many researchers to use them with little or no justification of the choice of the particular log-polar layout. In this paper, a set of design criteria are proposed, and an approach to choose the parameters involved in the log-polar transform is described. This kind of design not only could be used in simulation software, but also could act as design guidelines for artificial hardware-built retinae.