Connectivity Graphs for Space-variant Active Vision

Abstract

Space-variant sensors have nonuniform sampling across the image plane. Partially motivated by the observation that human vision is strongly space-variant, yielding an image compression for the human system that is estimated to be as much as four orders of magnitude, a number of research groups have been experimenting with space-variant sensors. Such systems cover wide solid angles yet maintain high acuity in their central regions. Implementation of space-variant systems pose at least two outstanding problems. First, such a system must be active, in order to utilize its high acuity region; second, there are fascinating image processing problems introduced by the non-uniform pixel size, shape and connectivity. Familiar image processing operations such as connected components, convolution, template matching, and even image translation, take on new and different forms when defined on space-variant arrays. The present paper provides a general method for space-variant image processing, based on a connectivity graph which represents the neighbor-relations in an arbitrarily structured sensor. We illustrate this approach with the following applications: Connected components is reduced to ils graph theoretic counterpart. We illustrate this on a logmap sensor, which possesses a difficult topology due to the branch cut associated with the complex logarithm function We show how to write local image operators in the connec-tivity graph that are independent of the sensor geometry. We relate the connectivity graph to pyramids over irregular tessalations, and implement a local binarization operator in a 2-level pyramid Finally, we expand the connectivity graph into a structure we call a translation graph, representing the effects of translation in space-variant image sensors. Using the translation graph, we define an efficient algorithm for translation in the logmap image and solve the template matching problem for space-variant images