Space-variant images (images whose resolution changes across the image) supply a powerful image representation for active vision systems. In this article a new log-polar mapping is presented. The main originality of this mapping is its great flexibility. Unlike other approaches the range of the logarithmic function used for the mapping can be fully specified (width and position). In this paper we also propose several efficient algorithms performing basic operations on these images. The originality of the proposed encoding is that log-polar pixels are a fractional part of rectangular pixels. Finally, we present some experimental results describing the use of this mapping in a face detection and tracking application.