Filtering and processing of panoramic images obtained using a camera and a wide-angle-imaging reflective surface

There is an increasing interest in wide-angle imaging of the environment using curved reflective surfaces. With this comes the need for appropriate filtering and processing of the acquired images. Here we present a technique for homogeneous, fast filtering of panoramic images captured using a camera and a wide-angle-imaging reflective surface. Imaging of the panoramic environment onto a two-dimensional (2-D) plane necessarily introduces spatial distortions such as stretching and bending that vary with the viewing direction. Therefore, if the panoramic image is to be filtered homogeneously in all viewing directions, it is necessary to match the filtering to the distortions. We show how this can be accomplished. The image acquired by the camera is first digitally unwarped and represented in Cartesian coordinates representing azimuth and elevation. The mappings of patches of uniform size and shape on the viewsphere are then established. Next, for each filter patch the local mappings of great circles along two principal axes (along the local longitudinal and elevational directions) on the image plane are determined. The mappings of these great circles are used to perform the 2-D convolution required by the filtering operation. Convolution along the directions of local, mutually orthogonal great circles permits the filtering to be carried out in a quasi-separable fashion, resulting in increased computational speed and efficiency. Examples of homogeneous filtering using this procedure are presented.

Honeybee navigation: odometry with monocular input.

Recent studies have revealed that navigating honeybees, Apis mellifera, estimate the distance to a food source by integrating over time the image motion that they experience en route. Here we examine the ability of honeybees to gauge distance travelled when visual input is available primarily to one eye. Bees were trained to fly into a tunnel, lined with textured patterns, to collect a reward at a feeder placed at a certain distance. Their ability to estimate distance flown was then assessed by testing them in a fresh tunnel without the feeder. The results show that (1) bees can estimate distance flown under monocular conditions, performing nearly as accurately as when information is available to both eyes; (2) bees can learn to fly two different distances, where each distance is measured in terms of the image motion experienced by a different eye; and (3) bees that have acquired information on the distance to a food source using one eye can measure out the same distance when they are required to use the other (naive) eye. The need to measure distance using signals from a single eye becomes important when a bee flies to a food source along the face of a cliff or the edge of a forest. Furthermore, under such conditions, it is important to be able to deal with odometric signals that are transposed interocularly when the bee returns home from the food source. This is because, although distances are learnt primarily on the way to a food source, foraging bees monitor distance flown on the homebound as well as the outbound routes. Copyright 1998 The Association for the Study of Animal Behaviour.

Uniform discrimination of pattern orientation by honeybees.

To explore how honeybees, Apis cerana, discriminate the orientation of patterns, we trained workers to discriminate between a black stripe of a certain orientation on a white disc and a pure white disc. We tested trained bees for their ability to discriminate between the trained orientation and deviations from it. This was done either in a dual choice situation where the bees had to choose between the trained orientation and one deviation from it at a time, or in a multiple choice situation where bees had to choose simultaneously between the trained orientation and 11 successive deviations from it. In the dual choice situation, bees did not discriminate behaviourally between the trained orientation and deviations up to 25 degrees, whereas in a multiple choice situation, they discriminated between the trained orientation and a deviation of 15 degrees or more. Thus, orientation can be analysed more precisely in multiple choice experiments. The response of the bees was independent of the orientation of the trained orientation; the 12 different trained orientations all yielded identical results. This finding, considered together with a model that we present for orientation discrimination, suggests that at least three orientation-sensitive channels (a neuron or a set of neurons that respond maximally to a particular orientation) participate in the analysis of pattern orientation. (c) 1998 The Association for the Study of Animal Behaviour.