Novins, K. L., Arvo, J.: Controlled precision volume integration. In Proc.  Home/Search Document Details and Download
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Evaluation of Image Quality in Medical Volume Visualization.. - Pommert, Hoehne (2002) (Correct)
....not cover all parts of the VV pipeline. 3.3 Predefined Error Bounds An attractive solution with respect to image fidelity are rendering methods which guarantee the visualization results to be within certain predefined error bounds. One such approach is the controlled precision volume rendering [30, 42]. However, the controlled precision relates only to a mathematical approximation of the volume rendering integral common to these algorithms, and says little more about the quality of visualization. With respect to the interpolation of volume data, a new class of interpolation filters is ....
Novins, K. L., Arvo, J.: Controlled precision volume integration. In Proc.
Reducing Artifacts in Volume Rendering by Higher Order.. - de Boer, Gröpl.. (Correct)
....integration, which offers good results for smooth volume rendering shading functions. While the rectangle rule is the most common rule for integration used by many researchers [6,10] few researchers have solved the integral via Monte Carlo [11] or trapezoid quadrature rules [3] Novins and Arvo [7] give an error estimation for using different quadrature formulae for numerical evaluation of the rendering equation. Author for correspondence. email: boer mp sun1.informatik.unimannheim. de 2 Rendering Equation Volume rendering simulates the propagation of light through a medium. From each ....
....quadrature formulae. The trapezoid rule is capable of integrating linear functions exactly with two sample points per interval, Simpson s rule can integrate cubic functions exactly with 3 sample points per interval. An estimation for the error resulting from numerical integration is given in [7]. density opacity gradient intensity y Figure 1: Gradient, intensity and density change at a wedge. The following estimation gives the minimum order the numeric integration must integrate exactly: for the wedge shown in Figure 1, opacity, gradient and intensity each change at least linearly, ....
Kevin Novins, James Arvo. Controlled Precision Volume Integration.
A High Accuracy Volume Renderer for Unstructured Data - Williams, Max, Stein (1998) (17 citations) (Correct)
....system and of the visibility ordering algorithm. Section 7 discusses hardware assisted polyhedron projection. Section 8 presents timing results and example images. 2 Previous Work A method for approximating the volume rendering integral with bounded error is described by Novins and Arvo in [21]. By bounding the magnitude of the derivatives of the integrand, they are able to obtain remainder terms that provide bounds on the approximation error. They apply this to the trapezoid rule, Simpson s rule, and a power series method. The first two methods are more suited to low to medium accuracy ....
....diagram of the case analysis for finding the ray segments is given in Fig. 7. The points t 1 , t 2 , and t 3 , where f 0 (t) 0 separate the monotone ranges of f(t) can be found as roots of the cubic polynomial f 0 (t) Either Gaussian quadrature or the power series method of Novins and Arvo [21] can be used to do the integration. The interpolation function for the linear brick is given in (2) It is trilinear, therefore contours within the cells are curved and so the methods described above pertain. The function f(t) is cubic because of the xyz term in (2) To find the roots of the cubic ....
K. Novins and J. Arvo, "Controlled Precision Volume Integration," Proc. 1992 Workshop Volume Visualization, Boston, pp. 83--89, Oct. 1992.
Towards Accurate And Efficient Volume Rendering - Novins (1994) Self-citation (Novins) (Correct)
....and figures have been incorporated into this thesis. Specifically, I would like to thank: Francois Sillion and Donald Greenberg, my co authors for An Efficient Method for Volume Rendering Using Perspective Projection [NSG90] Jim Arvo, my co author for Controlled Precision Volume Rendering [NA92] and Jim Arvo and David Salesin, my co authors for Adaptive Error Bracketing for Controlled Precision Volume Rendering [NAS92] v Program of Computer Graphics staff members provided a great deal of support for me and for this research. Hurf Sheldon was particularly helpful in ensuring that I ....
Kevin L. Novins and James R. Arvo. Controlled precision volume integration. In 1992 Boston Workshop on Volume Visualization, pages 83--89. ACM SIGGRAPH, 1992.
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