A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image rendering by adaptive refinement
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Set operations on polyhedra using binary space partitioning trees
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Display of Surfaces from Volume Data
IEEE Computer Graphics and Applications
A survey of the Hough transform
Computer Vision, Graphics, and Image Processing
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Gaze-directed volume rendering
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
Binary space partitioning trees as an alternative representation of polytopes
Computer-Aided Design
Merging BSP trees yields polyhedral set operations
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Three-pass affine transforms for volume rendering
VVS '90 Proceedings of the 1990 workshop on Volume visualization
Hierarchical splatting: a progressive refinement algorithm for volume rendering
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Fast algorithms for volume ray tracing
VVS '92 Proceedings of the 1992 workshop on Volume visualization
Interactive solid geometry via partitioning trees
Proceedings of the conference on Graphics interface '92
Multi-dimensional trees for controlled volume rendering and compression
VVS '94 Proceedings of the 1994 symposium on Volume visualization
Use of the Hough transformation to detect lines and curves in pictures
Communications of the ACM
Transparency and Antialiasing Algorithms Implemented with the Virtual Pixel Maps Technique
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
Preprocessing and Volume Rendering of 3D Ultrasonic Data
IEEE Computer Graphics and Applications
Computer
Generation and display of geometric fractals in 3-D
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
On visible surface generation by a priori tree structures
SIGGRAPH '80 Proceedings of the 7th annual conference on Computer graphics and interactive techniques
The A -buffer, an antialiased hidden surface method
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Finding Edges and Lines in Images
Finding Edges and Lines in Images
A priori based techniques for determining visibility priority for 3-d scenes
A priori based techniques for determining visibility priority for 3-d scenes
Applying space subdivision techniques to volume rendering
VIS '90 Proceedings of the 1st conference on Visualization '90
Representing medical images with partitioning trees
VIS '92 Proceedings of the 3rd conference on Visualization '92
Connected component labeling based on the EVM model
SCCG '02 Proceedings of the 18th spring conference on Computer graphics
Binary-Space-Partitioned Images for Resolving Image-Based Visibility
IEEE Transactions on Visualization and Computer Graphics
ACM Transactions on Graphics (TOG)
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The discrete space representation of most scientific datasets (pixels, voxels, etc.), generated through instruments or by sampling continuously defined fields, while being simple, is also verbose and structureless. We propose the use of a particular spatial structure, the binary space partitioning tree, or, simply, partitioning tree, as a new representation to perform efficient geometric computation in discretely defined domains. The ease of performing affine transformations, set operations between objects, and correct implementation of transparency (exploiting the visibility ordering inherent to the representation) makes the partitioning tree a good candidate for probing and analyzing medical reconstructions, in such applications as surgery planning and prostheses design. The multiresolution characteristics of the representation can be exploited to perform such operations at interactive rates by smooth variation of the amount of geometry. Application to ultrasound data segmentation and visualization is proposed.$$\sum\limits^{d \log h}_{i=1} \tilde O\!\!\left({{n}\over{k^3_i}}\right) = \sum\limits^{d \log h}_{i=1}\tilde O\!\!\left({{n}\over{{\left(k/2^i\right)}^3\right)}}=\tilde\!\!{O} (n).$$The paper describes methods for constructing partitioning trees from a discrete image/volume data set. Discrete space operators developed for edge detection are used to locate discontinuities in the image from which lines/planes containing the discontinuities are fitted by using either the Hough transform or a hyperplane sort. A multiresolution representation can be generated by ordering the choice of hyperplanes by the magnitude of the discontinuities. Various approximations can be obtained by pruning the tree according to an error metric. The segmentation of the image into edgeless regions can yield significant data compression. A hierarchical encoding schema for both lossless and lossy encodings is described.