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85
Marching cubes: A high resolution 3D surface construction algorithm
 COMPUTER GRAPHICS
, 1987
"... We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divideandconquer approach to generate interslice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical d ..."
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Cited by 2070 (4 self)
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We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divideandconquer approach to generate interslice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scanline order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the interslice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and singlephoton emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.
The quadtree and related hierarchical data structures
 ACM Computing Surveys
, 1984
"... A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics ..."
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Cited by 421 (11 self)
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A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics. There is a greater emphasis on region data (i.e., twodimensional shapes) and to a lesser extent on point, curvilinear, and threedimensional data. A number of operations in which such data structures find use are examined in greater detail.
Efficient ray tracing of volume data
 ACM Transactions on Graphics
, 1990
"... Volume rendering is a technique for visualizing sampled scalar or vector fields of three spatial dimensions without fitting geometric primitives to the data. A subset of these techniques generates images by computing 2D projections of a colored semitransparent volume, where the color and opacity at ..."
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Cited by 325 (4 self)
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Volume rendering is a technique for visualizing sampled scalar or vector fields of three spatial dimensions without fitting geometric primitives to the data. A subset of these techniques generates images by computing 2D projections of a colored semitransparent volume, where the color and opacity at each point are derived from the data using local operators. Since all voxels participate in the generation of each image, rendering time grows linearly with the size of the dataset. This paper presents a fronttoback imageorder volumerendering algorithm and discusses two techniques for improving its performance. The first technique employs a pyramid of binary volumes to encode spatial coherence present in the data, and the second technique uses an opacity threshold to adaptively terminate ray tracing. Although the actual time saved depends on the data, speedups of an order of magnitude have been observed for datasets of useful size and complexity. Examples from two applications are given: medical imaging and molecular graphics.
Spatial Data Structures
, 1995
"... An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarch ..."
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Cited by 287 (13 self)
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An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarchical data structures are based on the principle of recursive decomposition. They are attractive because they are compact and depending on the nature of the data they save space as well as time and also facilitate operations such as search. Examples are given of the use of these data structures in the representation of different data types such as regions, points, rectangles, lines, and volumes.
Octrees for faster isosurface generation
 IEEE TRANSACTIONS ON MEDICAL IMAGING
, 2000
"... The large size of many volume data sets often prevents visualization algorithms from providing interactive rendering. The use of hierarchical data structures can ameliorate this problem by storing summary information to prevent useless exploration of regions of little or no current interest within ..."
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Cited by 274 (3 self)
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The large size of many volume data sets often prevents visualization algorithms from providing interactive rendering. The use of hierarchical data structures can ameliorate this problem by storing summary information to prevent useless exploration of regions of little or no current interest within the volume. This paper discusses research into the use of the octree hierarchical data structure when the regions of current interest can vary during the application, and are not known a priori. Octrees are well suited to the sixsided cell structure of many volumes. A new spaceefficient design is introduced for octree representations of volumes whose resolutions are not conveniently a power of two; octrees following this design are called branchonneed octrees (BONOs). Also, a caching method is described that essentially passes information between octree neighbors whose visitation times may be quite different, then discards it when its useful life is over. Using the application of octrees to isosurface generation as a focus, space and time comparisons for octreebased versus more traditional "marching" methods are presented.
Accelerating Volume Animation by SpaceLeaping
, 1993
"... f i In this paper we present a method for speeding the process of volume rendering a sequence o mages. Speedup is based on exploiting coherency between consecutive images to shorten the n path rays take through the volume. This is achieved by providing each ray with information eeded to leap over th ..."
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Cited by 66 (9 self)
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f i In this paper we present a method for speeding the process of volume rendering a sequence o mages. Speedup is based on exploiting coherency between consecutive images to shorten the n path rays take through the volume. This is achieved by providing each ray with information eeded to leap over the empty space and commence volume traversal at the vicinity of mean  b ingful data. The algorithm starts by projecting the volume into a Cbuffer (Coordinates uffer) which stores, at each pixel location, the objectspace coordinates of the first nonempty s t voxel visible from that pixel. For each change in the viewing parameters, the Cbuffer i ransformed accordingly. In the case of rotation the transformed Cbuffer goes through a pro  b cess of eliminating coordinates that possibly became hidden. The remaining values in the C uffer serve as an estimate of the point where the new rays should start their volume traverc sal. This spaceleaping method can be combined with existing accele...
TemplateBased Volume Viewing
, 1992
"... We present an efficient threephase algorithm for volume viewing that is based on exploit  t ing coherency between rays in parallel projection. The algorithm starts by building a ray emplate and determining a special plane for projection  the baseplane. Parallel rays are cast t into the volume ..."
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Cited by 61 (17 self)
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We present an efficient threephase algorithm for volume viewing that is based on exploit  t ing coherency between rays in parallel projection. The algorithm starts by building a ray emplate and determining a special plane for projection  the baseplane. Parallel rays are cast t into the volume from within the projected region of the volume on the baseplane, by repeating he sequence of steps specified in the raytemplate. We carefully choose the type of line to be s employed and the way the template is being placed on the baseplane in order to assure uniform ampling of the volume by the discrete rays. We conclude by describing an optimized software K implementation of our algorithm and reporting its performance. eywords: volume rendering, ray casting, template, parallel projection 1. Introduction Volume visualization is the process of converting complex volume data to a format that is p amenable to human understanding while maintaining the integrity and accuracy of the data. Th...
3D distance fields: A survey of techniques and applications
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2006
"... A distance field is a representation where, at each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface, and when the ..."
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Cited by 54 (2 self)
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A distance field is a representation where, at each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface, and when the distance field is signed, we may also determine if the point is internal or external to objects within the domain. The distance field has been found to be a useful construction within the areas of computer vision, physics, and computer graphics. This paper serves as an exposition of methods for the production of distance fields, and a review of alternative representations and applications of distance fields. In the course of this paper, we present various methods from all three of the above areas, and we answer pertinent questions such as How accurate are these methods compared to each other? How simple are they to implement?, and What is the complexity and runtime of such methods?
OctoMap: A probabilistic, flexible, and compact 3D map representation for robotic systems
 In Proc. of the ICRA 2010 workshop
, 2010
"... Abstract—In this paper, we present an approach for modeling 3D environments based on octrees using a probabilistic occupancy estimation. Our technique is able to represent full 3D models including free and unknown areas. It is available as an opensource library to facilitate the development of 3D m ..."
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Cited by 46 (9 self)
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Abstract—In this paper, we present an approach for modeling 3D environments based on octrees using a probabilistic occupancy estimation. Our technique is able to represent full 3D models including free and unknown areas. It is available as an opensource library to facilitate the development of 3D mapping systems. We also provide a detailed review of existing approaches to 3D modeling. Our approach was thoroughly evaluated using different realworld and simulated datasets. The results demonstrate that our approach is able to model the data probabilistically while, at the same time, keeping the memory requirement at a minimum. I.
Opacityweighted color interpolation for volume sampling
 In “Proc. IEEE Proc. Volume Visualization
, 1998
"... volume rendering, compositing, ray tracing Volume rendering creates images from sampled volumetric data. The compute intensive nature of volume rendering has driven research in algorithm optimization. An important speed optimization is the use of preclassification and preshading. We demonstrate an a ..."
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Cited by 41 (3 self)
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volume rendering, compositing, ray tracing Volume rendering creates images from sampled volumetric data. The compute intensive nature of volume rendering has driven research in algorithm optimization. An important speed optimization is the use of preclassification and preshading. We demonstrate an artifact that results when interpolating from preclassified or preshaded colors and opacity values separately. This method is flawed, leading to visible artifacts. We present an improved technique, opacityweighted color interpolation, evaluate the RMS error improvement, hardware and algorithm efficiency, and demonstrated improvements. We show analytically that opacityweighted color interpolation exactly reproduces material based interpolation results for certain volume classifiers, with the efficiencies of preclassification. Our proposed technique may also have broad impact on opacitytexturemapped polygon rendering.