This paper addresses fast parallel methods for the computation of the Radon (or Hough) transform. The Radon transform of an image is a set of projections of the image taken at different angles. Its computation is important in image processing and computer vision for problems such as pattern recognition and reconstruction of medical images. A unique new method for combining partial results is presented, from which an algorithm is constructed that computes a provably good approximation to the discrete Radon transform. The approximate discrete Radon transform (ADRT) algorithm computes 4, N - 4 projections through an $N \times N$ image in time $O(N^2\mathrm{lg}N)$ (the majority of previous algorithms are O(N 3, )). The method is quite simple and easy to parallelize. A parallel version of the ADRT requires only $O(\mathrm{lg}N)$ parallel steps on O(N 2 ) processors, ignoring communication time. An additional property of the algorithm is that it can be applied directly to compute the backprojection step of the inverse RT.

Volume navigation is the interactive exploration of volume data sets by "flying" the viewpoint through the data, producing a volume rendered view at each frame. We present an inexpensive perspective volume navigation method designed to be run on a PC platform with accelerated 3D graphics hardware. The heart of the method is a two-phase perspective ray casting algorithm that takes advantage of the coherence inherent in adjacent frames during navigation. The algorithm generates a sequence of approximate volume-rendered views in a fraction of the time that would be required to compute them individually. The algorithm handles arbitrarily large volumes by dynamically swapping data within the current view frustum into main memory as the viewpoint moves through the volume. We also describe an interactive volume navigation application based on this algorithm. The application renders gray-scale, RGB, and labeled RGB volumes by volumetric compositing, allows trilinear interpolation of sample points, and implements progressive refinement during pauses in user input.

Volume navigation is the interactive exploration of volume data sets by "flying" the view point through the data, producing a volume rendered view at each frame. The authors present an inexpensive perspective volume navigation method designed to run on a PC platform with accelerated 3D graphics hardware. They compute perspective projections at each frame, allow trilinear interpolation of sample points, and render both gray scale and RGB volumes by volumetric compositing. The implementation handles arbitrarily large volumes, by dynamically swapping data within the local depth-limited frustum into main memory as the viewpoint moves through the volume. They describe a new ray casting algorithm that takes advantage of the coherence inherent in adjacent frames to generate a sequence of approximate animated frames much faster than they could be computed individually. They also take advantage of the 3D graphics acceleration hardware to offload much of the alpha blending and resampling from the CPU.

This paper presents algorithms for routing channels with L ≥2 layers. For the unit vertical overlap model, we describe a two-layer channel routing algorithm that uses at most d + O(√d) tracks to route two-terminal net problems and 2d + O(√d) tracks to route multiterminal nets. We also show that d + Ω(log d) tracks are required to route two-terminal net problems in the worst case even if arbitrary vertical overlap is allowed. We generalize the algorithm to unrestricted multilayer routing and use only d/(L -1) + O(√d/L + 1)> tracks for two-terminal net problems (within O(√d/L + 1) tracks of optimal) and d/(L-2) +O(√d/L + 1) tracks for multiterminal net problems (within a factor of(L-1)/(L-2) times optimal). We demonstrate the generality of our routing strategy by showing that it can be used to duplicate some of the best previous upper bounds for other models (two-layer Manhattan routing and two and three-layer knock-knee routing of two-terminal, two-sided nets), and gives a new upper bound for rotuing with 45-degree diagonal wires.

In this paper, we parallelize a new efficient approximate projection algorithm for volume rendering. The algorithm is unique in that it computes N different views simultaneously, much faster than these projections could be computed independently. It is thus ideal for computing animated sequences of views. We implement and evaluate the algorithm on a MasPar MP-1. We render a 128x128x128 data set at up to 21 frames per second average on a 1K PE MasPar MP-1 using gray scale volumetric compositing (simpler transformations are computed even faster).

A new component labeling algorithm for SIMD meshes is presented whose time complexity is O(frac{{n^2 }} {{p^2 }} + n) for an n x n image on a p x p mesh. The algorithm is efficient in terms of total work for p leqslant n^{frac{1} {2}} . It was evaluated on a MasPar MP-1 with 1K processors and 64KB of memory per processor. For most of the 1K x 1K size test inputs, our algorithm is faster than a neighbor updating algorithm that is extremely simple but asymptotically slower on images of large diameter.

Article Fast parallel discrete approximation algorithms for the radon transform Share on Authors: Martin L. Brady View Profile , Whanki Yong View Profile Authors Info & Claims SPAA '92: Proceedings of the fourth annual ACM symposium on Parallel algorithms and architecturesJune 1992 Pages 91–99https://doi.org/10.1145/140901.140911Online:01 June 1992Publication History 15citation641DownloadsMetricsTotal Citations15Total Downloads641Last 12 Months21Last 6 weeks10 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

The 60 degrees grid consists of vertical columns and diagonal tracks running at slopes of +or-30 degrees . This model offers a potentially large reduction in channel width, without resorting to wire overlap. For a channel routing problem with density d, the availability of the diagonal tracks leads to a lower bound of d/ square root 3. The authors present two near-optimal channel routing algorithms. The first uses 5 layers and always routes in width at most d/ square root 3+ square root 3. The second algorithm uses at most 4 layers and routes in width omega , where d/ square root 3+O(1)>

An algorithm is presented which, given a two-dimensional wire layout in knock-knee mode, produces a legal wiring (layer-assignment) using only adjacent-layer vias and at most four layers. The previous four-layer wiring algorithm requires technologically impractical vias between non-adjacent layers. This algorithm has important implications for practical automatic wire routing, since many knock-knee layout algorithms rely on the four-layer wiring technique to complete their routing.>

Article Disjoint paths through a 3-dimensional grid Share on Authors: M. Brady Lockheed R&D Div., O-9740 / B-202, 3251 Hanover St., Palo Alto, CA Lockheed R&D Div., O-9740 / B-202, 3251 Hanover St., Palo Alto, CAView Profile , D. Brown Coordinated Science Laboratory, University of Illinois, 1101 W. Springfield Ave., Urbana, IL Coordinated Science Laboratory, University of Illinois, 1101 W. Springfield Ave., Urbana, ILView Profile , P. McGuinness Beckman Institute, University of Illinois, 405 N. Matthews Ave., Urbana, IL Beckman Institute, University of Illinois, 405 N. Matthews Ave., Urbana, ILView Profile Authors Info & Claims SPAA '90: Proceedings of the second annual ACM symposium on Parallel algorithms and architecturesMay 1990 Pages 224–233https://doi.org/10.1145/97444.97689Online:01 May 1990Publication History 1citation274DownloadsMetricsTotal Citations1Total Downloads274Last 12 Months6Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

The problem of stretching a knock-knee layout in the knock-knee mode to ensure its wirability is considered. An optimal algorithm for the problem in two layers is presented. A 4/3 approximation algorithm for the corresponding problem in three layers, shown to be NP-complete, is devised.>