Discrete space representation of images arise as a consequence of the transducers between the physical and informational domains. While discrete representations (arrays of pixels) are simple, they are also verbose and structureless. We present a method of converting between a discrete space representation to a particular continuous space representation, viz. the  binary space partitioning tree . The conversion is accomplished using standard discrete space operators developed for edge detection, followed by a Hough transform to generate candidate hyperplanes that are used to construct the partitioning tree. The result is a segmented and compressed image represented in continuous space suitable for elementary computer vision operations and improved image transmission/storage. The method is more noise tolerant than methods whose target is a topological representation, and more adaptive than axis-aligned spatial partitioning schemes. Affine transformations needed for interactive manipulation are fast and edges do not blur with enlargement of the image. Efficient algorithms are known for spatial operations, such as masking/clipping and compositing. We give several examples of 256x256 medical images for which we have estimated the compression to range between 1 and 0.5 bits/pixel.
['Kalpathi R. Subramanian', 'Bruce F. Naylor']
Representing medical images with partitioning trees