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## Discrepancy as a Quality Measure for Sample Distributions (1991)

Venue: | In Eurographics '91 |

Citations: | 77 - 7 self |

### Citations

912 | T.: The rendering equation
- KAJIYA
- 1986
(Show Context)
Citation Context ...rendering problem can also be viewed as a sampling problem in several one and twodimensional spaces [2]. This sampling can be static [2], where all the sample points are known in advance, or adaptive =-=[9, 4, 6, 10, 11]-=-, where new sample points are chosen in `interesting' areas. If static sampling is used, or adaptive sampling as done by Lee et al. [9], then we need a module to produce `good' sets of N samples on a ... |

467 | Distributed ray tracing
- Cook, Porter, et al.
- 1984
(Show Context)
Citation Context ... and then somehow reconstruct a continuous image function from the colors at those points [10]. The rendering problem can also be viewed as a sampling problem in several one and twodimensional spaces =-=[2]-=-. This sampling can be static [2], where all the sample points are known in advance, or adaptive [9, 4, 6, 10, 11], where new sample points are chosen in `interesting' areas. If static sampling is use... |

360 |
Approximate Calculation of Multiple Integrals
- Stroud
- 1971
(Show Context)
Citation Context ...n in the form of twodimensional frequency distributions which are hard to interpret. Our question, `what are good sample point sets?', has been examined in depth in the field of numerical integration =-=[15, 14]-=-. The approach used in integration theory is to test whether a set of points is equidistributed by calculating the discrepancy of the set. This approach has the advantage of assigning a single quality... |

335 |
Stochastic sampling in computer graphics.
- Cook
- 1986
(Show Context)
Citation Context ...onte Carlo integration [2], but this discussion did not provide a good quality measure for a set of sample points. Signal processing theory has also been used to examine different sampling strategies =-=[1, 4]-=-, but this approach only provides quantitative information in the form of twodimensional frequency distributions which are hard to interpret. Our question, `what are good sample point sets?', has been... |

194 |
Monte Carlo Methods
- Kalos, Whitlock
- 2008
(Show Context)
Citation Context ...nsional subspace (time), and then associating the strata of each dimension at random. He called this technique uncorrelated jittering. This basic strategy has also been discussed in the book by Kalos =-=[7]-=-. This idea can be applied in two dimensions by randomly associating rows and columns of a N by N grid, so that each row and column will have one sample[13]. A particularly descriptive name for this s... |

186 | Generating antialiased images at low sampling densities,”
- Mitchell
- 1987
(Show Context)
Citation Context ...uction One way we can calculate a computer image is to first find the color at many points on the image plane, and then somehow reconstruct a continuous image function from the colors at those points =-=[10]-=-. The rendering problem can also be viewed as a sampling problem in several one and twodimensional spaces [2]. This sampling can be static [2], where all the sample points are known in advance, or ada... |

174 |
The Art of Computer Programming, volume 3
- Knuth
- 1973
(Show Context)
Citation Context ...y been invented and reinvented several times. For eaxmple, the idea, as well as the generalized discrepancy presented in Section 4, can be easily extracted from the Kolmogrov-Smirnov statistical test =-=[8]-=-. In this paper, discrepancy is used for evaluation in to computer graphics sampling problems. It is tested on several test images and sampling strategies. These tests are preliminary, and are not int... |

100 |
Statistically optimized sampling for distributed ray tracing.
- LEE, REDNER, et al.
- 1985
(Show Context)
Citation Context ...rendering problem can also be viewed as a sampling problem in several one and twodimensional spaces [2]. This sampling can be static [2], where all the sample points are known in advance, or adaptive =-=[9, 4, 6, 10, 11]-=-, where new sample points are chosen in `interesting' areas. If static sampling is used, or adaptive sampling as done by Lee et al. [9], then we need a module to produce `good' sets of N samples on a ... |

100 |
Antialiased Ray Tracing by Adaptive Progressive Refinement
- PAINTER, SLOAN
- 1989
(Show Context)
Citation Context ...rendering problem can also be viewed as a sampling problem in several one and twodimensional spaces [2]. This sampling can be static [2], where all the sample points are known in advance, or adaptive =-=[9, 4, 6, 10, 11]-=-, where new sample points are chosen in `interesting' areas. If static sampling is used, or adaptive sampling as done by Lee et al. [9], then we need a module to produce `good' sets of N samples on a ... |

79 | Physically Based Lighting Calculations for Computer Graphics.
- Shirley
- 1991
(Show Context)
Citation Context ...has also been discussed in the book by Kalos [7]. This idea can be applied in two dimensions by randomly associating rows and columns of a N by N grid, so that each row and column will have one sample=-=[13]-=-. A particularly descriptive name for this strategy is N-rooks sampling, because an acceptable set of sample cells will be the squares of an N by N chessboard with N rooks that cannot capture each oth... |

56 |
The aliasing problem in computer-generated shaded images
- CROW
- 1977
(Show Context)
Citation Context ...-rooks sampling does so well with horizontal and vertical lines; both the x and y components are fully jittered. 4 Non-uniform Sample Distributions If a non-uniform `filter' is used to sample a pixel =-=[3]-=-, we would like to take weighted averages of sample point colors, or to distribute the samples nonuniformly. The second strategy, often called importance sampling [1], is preferred if no samples are s... |

20 |
Dippe and Erling Henry Wold, “Antialiasing through stochastic sampling,”
- Mark
- 1985
(Show Context)
Citation Context |

8 |
A Retrospective and Prospective of the Monte Carlo Method
- Halton
- 1970
(Show Context)
Citation Context ...points (x i ; y i ) from the unit square is to pick every x i and y i independently by setting them to canonical random pairs ( i ;s0 i ). A canonical random number is uniformly distributed on [0; 1] =-=[5]-=-. This strategy, called random sampling, or sometimes poisson sampling, can be summarized as: for i = 0 to N \Gamma 1 x i = randfrom(0; 1) y i = randfrom(0; 1) where randfrom(a; b) returns a random nu... |

8 |
The Mathematical Basis of Monte Carlo and Quasi-Monte Carlo Methods
- Zeremba
- 1968
(Show Context)
Citation Context ...n in the form of twodimensional frequency distributions which are hard to interpret. Our question, `what are good sample point sets?', has been examined in depth in the field of numerical integration =-=[15, 14]-=-. The approach used in integration theory is to test whether a set of points is equidistributed by calculating the discrepancy of the set. This approach has the advantage of assigning a single quality... |

3 |
The Monte Carlo Method
- Screider
- 1966
(Show Context)
Citation Context ...d to functions defined on nonCartesian manifolds. This requires dealing with the joint distribution function and non-constant metrics, but otherwise the same techniques apply. Details can be found in =-=[12, 13]-=-. An immediate question is whether the concept of discrepancy can be extended to such non-uniform distributions. If we were generating N random points in some region R according to some probability de... |