SPACE-VARIANT IMAGE-PROCESSING

This paper describes a graph-based approach to image processing, inten ded for use with images obtained from sensors having space variant sam pling grids. The connectivity graph (CG) is presented as a fundamental framework for posing image operations in any kind of space variant se nsor. Partially motivated by the observation that human vision is stro ngly space variant, a number of research groups have been experimentin g with spade variant sensors. Such systems cover wide solid angles yet maintain high acuity in their central regions. Implementation of spac e variant systems pose at least two outstanding problems. First, such a system must be active, in order to utilize its high acuity region; s econd, there are significant image processing problems introduced by t he nonuniform pixel size, shape and connectivity. Familiar image proce ssing operations such as connected components, convolution, template m atching, and even image translation, take on new and different forms w hen defined on space variant images. The present paper provides a gene ral method for space variant image processing, based on a connectivity graph which represents the neighbor-relations in an arbitrarily struc tured sensor. We illustrate this approach with the following applicati ons: (1) Connected components is reduced to its graph theoretic counte rpart. We illustrate this on a logmap sensor, which possesses a diffic ult topology due to the branch cut associated with the complex logarit hm function. (2) We show how to write local image operators in the con nectivity graph that are independent of the sensor geometry. (3) We re late the connectivity graph to pyramids over irregular tessalations, a nd implement a local binarization operator in a 2-level pyramid. (4) F inally, we expand the connectivity graph into a structure we call a tr ansformation graph, which represents the effects of geometric transfor mations in space variant image sensors. Using the transformation graph , we define an efficient algorithm for matching in the logmap images a nd solve the template matching problem for space variant images. Becau se of the very small number of pixels typical of logarithmic structure d space variant arrays, the connectivity graph approach to image proce ssing is suitable for real-time implementation, and provides a generic solution to a wide range of image processing applications with space variant sensors.