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.
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