A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Set operations on polyhedra using binary space partitioning trees
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
A survey of the Hough transform
Computer Vision, Graphics, and Image Processing
Merging BSP trees yields polyhedral set operations
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Use of the Hough transformation to detect lines and curves in pictures
Communications of the ACM
Computer Vision
On visible surface generation by a priori tree structures
SIGGRAPH '80 Proceedings of the 7th annual conference on Computer graphics and interactive techniques
Finding Edges and Lines in Images
Finding Edges and Lines in Images
Applying space subdivision techniques to volume rendering
VIS '90 Proceedings of the 1st conference on Visualization '90
Converting Discrete Images to Partitioning Trees
IEEE Transactions on Visualization and Computer Graphics
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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.