D. Salesin, D. Lischinski, and T. DeRose, "Reconstructing illumination functions with selected discontinuities," Proc. of the Third Eurographics Workshop on Rendering, pp. 99--112 #1992#.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....e#ective surface meshes. Irradiance gradient has been used to get higher order approximation of irradiance function. For example, Ward et al. 84] and Vedel [80, 81] estimated irradiance gradients by Monte Carlo path tracing and used them to improve the interpolation accuracy. Salesin et al. [68] and Bastos et al. 12] employed gradients to construct higher order interpolants for irradiance functions. Drettakis et al. 28] estimated gradients as well as isolux contours from a collection of discrete samples and used them to guide subsequent sampling, placing more samples where the ....

David Salesin, Dani Lischninski, and Tony DeRose. Reconstructing illumination functions with selected discontinuities. In Proceedings of the Third Eurographics Workshop on Rendering, Bristol, United Kingdom, pages 99--112, May 1992.

....points on the corners of the patch. Other control points on the boundary and interior determine the tangent to the surface at the patch corners and the shape of the surface on the interior. Surfaces with the desired continuity can also be constructed using more general B splines. Salesin et.al. [11]have applied the Clough Tocher element to rendering for radiosity. This element is constructed from three cubic triangular Bezier patches and provides a C 1 interpolant at boundaries. 7.2 Two Pass Methods Two pass methods evaluate the rendering equation directly at image resolution, using the ....

Salesin, D., Lischinski, D., and DeRose, T. Reconstructing illumination functions with selected discontinuities. In Third Eurographics Workshoop on Rendering (Bristol, UK, May 1992), pp 99-112.

....e#ective surface meshes. Irradiance gradient has been used to get higher order approximation of irradiance function. For example, Ward et al. 84] and Vedel [80, 81] estimated irradiance gradients by Monte Carlo path tracing and used them to improve the interpolation accuracy. Salesin et al. [68] and Bastos et al. 12] employed gradients to construct higher order interpolants for irradiance functions. Drettakis et al. 28] estimated gradients as well as isolux contours from a collection of discrete samples and used them to guide subsequent sampling, placing more samples where the ....

David Salesin, Dani Lischninski, and Tony DeRose. Reconstructing illumination functions with selected discontinuities. In Proceedings of the Third Eurographics Workshop on Rendering, Bristol, United Kingdom, pages 99--112, May 1992.

....computations. It remains to be seen how well this approach will extend to global illumination. While most radiosity methods use Gouraud interpolation, recently there has been work with other forms of interpolation. Heckbert [23] 25] explored finite element methods. Salesin, Lischinski, and DeRose [37] produced a scheme for representing the intensity function with superlinear basis functions. These methods produce excellent images and require less mesh refinement, but rendering times are too slow for interactive viewing. 3 THE PROBLEM Discontinuities in the illumination function for a surface ....

David Salesin, Dani Lischinski, and Tony DeRose. Reconstructing illumination functions with selected discontinuities. In Third Eurographics Workshop on Rendering, pages 99--112, Bristol, UK, May 1992.

.... see this is a good approximation inside the region being represented, but it is not at the edges [3] 4] 17] Our visual system is sensitive to derivative discontinuities [13] and the C 0 bilinear interpolation between any neighboring regions leads to noticeable visual Mach band artifacts [1] [15]. According to Bastos [1] a bicubic interpolation scheme can ensure up to C 1 continuity (first derivative) of the reconstructed function. This type of interpolation can prevent Mach band artifacts often resulting in lower order interpolation. 1.1.2 Radiosity As Texture RAT The fairly ....

SALESIN, David; LISCHINSKI, Dani and DeROSE, Tony. Reconstructing Illumination Functions with Selected Discontinuities. In 3 rd Eurographics Workshop on Rendering (Proceedings), Bristol, 1992.

....visible through a portal sequence (i.e. in each other s antipenumbrae) can interact directly by exchanging luminous energy. Knowing a light source s antipenumbra would also be useful in the polygonal subdivision that shadowing and global illumination algorithms employ to model shadow boundaries [3, 4, 12, 13, 21]. Finally, the algorithm is of theoretical interest for two reasons. First, for the class of input described here, the algorithm computes strong (antiumbral) and weak (antipenumbral) polygon visibility [17] with respect to a polygon (area light source) in 3D. Second, again for this input ....

David Salesin, Dani Lischinski, and Tony DeRose. Reconstructing illumination functions with selected discontinuities. In Proc. 3 rd Eurographics Workshop on Rendering, 1992.

....function before display, or to check the consistency of our discretisation hypothesis. Reconstructing the illumination function If we know the radiosity values and the gradient at our sample points, we can then reconstruct the radiosity function as, e.g. a bicubic spline. Salesin et al. [10] and Bastos et al. 3] proposed such methods for reconstruction of radiosity using estimates of gradient. Ward and Heckbert [12] computed irradiance gradients to interpolate irradiance on receiving surfaces. Refinement criterion Many radiosity algorithms assume a constant radiosity over patches. ....

Salesin, D., Lischinski, D., DeRose, T.: Reconstructing Illumination Functions with Selected Discontinuities. Third Eurographics Workshop on Rendering (May 1992) 99--112

.... complex scenes (m on the order of hundreds of thousands or millions of polygons) The radiosity method has been generalized to non diffuse scenes using spherical harmonics as an approximation to directional distributions [Sillion et al. 91] Higher degree elements [Heckbert Winget91,Max Allison92,Salesin et al. 92,Troutman Max93] Galerkin methods [Heckbert Winget91,Zatz93] and improved integration techniques [Schroder93,Pietrek93] have been used to improve the accuracy of an approximation. The following two chapters discuss radiosity in two and three dimensional scenes, respectively, with qualitative ....

David Salesin, Dani Lischinski, and Tony DeRose. Reconstructing illumination functions with selected discontinuities. In Alan Chalmers and Derek Paddon, editors, Third Eurographics Workshop on Rendering, pages 99--112, Bristol, UK, May 1992. Finite Element Methods for Radiosity 5-7

.... have also generated a great deal of research[23] Once the solution (b) is computed one can simply output flat shaded surface elements to the screen, but one may also use more sophisticated methods such displaying Gouraud shaded polygons, or employing some more complicated method of reconstruction[63]. Some research has focussed on methods for solving the linear system (Equation (71) Obviously one could use a direct matrix inversion technique such as Gaussian elimination, but this takes O(n 3 ) time. In [21] it was noted this matrix is diagonally dominant, and hence can be solved by ....

David Salesin, Dani Lischinski, and Tony DeRose. Reconstructing illumination functions with selected discontinuities. Third Eurographics Workshop on Rendering, pages 99--112, 1992. BIBLIOGRAPHY 182

....geometrical considerations [1] power transfer [5] or view dependent criteria [13] These approaches are to a large extent more concerned with the light transfer calculations, and less with the display of radiance. Other approaches use piecewise polynomial representations on triangular grids [9][12], but their main goal is to deal with the problems introduced by shadow boundaries. Similar considerations due to shadows are presented in [6] 7] Higher order interpolants are considered, but the emphasis is on the accuracy of light transfer calculations in the context of a finite element ....

....goal is to deal with the problems introduced by shadow boundaries. Similar considerations due to shadows are presented in [6] 7] Higher order interpolants are considered, but the emphasis is on the accuracy of light transfer calculations in the context of a finite element approach. Salesin et al. [12], perform cubic reconstruction given a mesh of samples. The use of cubic reconstruction seems more suited to the situations that include shadow boundaries, since we believe that for the unoccluded case presented here, linear and quadratic interpolants are sufficient. However, this choice depends ....

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Salesin, David, Dani Lichinski, and Tony DeRose, "Reconstructing Illumination Functions with Selected Discontinuities," 3rd Eurographics Workshop on Rendering, Bristol, UK May 1992.

....is continuous in value (C 0 ) This technique allows an interactive walkthrough of the environment. As illumination varies smoothly across surfaces (except at shadow boundaries) higher order reconstruction methods can be used, as an alternative. Lischinski [LTG92] used quadratic and Salesin [SLR92] cubic Bezier triangles. Both approaches exploit the precalculated discontinuities to correctly approximate the illumination function. The reconstruction algorithm of Salesin [SLR92] provides a C 1 smooth interpolation of the surface illumination. 4 Implementation and Results Our simple test ....

....higher order reconstruction methods can be used, as an alternative. Lischinski [LTG92] used quadratic and Salesin [SLR92] cubic Bezier triangles. Both approaches exploit the precalculated discontinuities to correctly approximate the illumination function. The reconstruction algorithm of Salesin [SLR92] provides a C 1 smooth interpolation of the surface illumination. 4 Implementation and Results Our simple test scene consisted of a cube floating above a plane lighted by two lightsources was modeled (analguous to [LTG92] Figure 4 shows the mesh in the upper part and a Gouraud shaded version ....

Salesin, D., Lischinski, D., DeRose, T.: Reconstructing Illumination Functions with Selected Discontinuities. Third Eurographics Workshop on Rendering (May 1992) 99--112

....considered radiosity functions that are piecewise linear. Zatz [25] has used Legendre polynomials to arrive at solutions that are piecewise polynomial of higher order. Other researchers have explored the use of higher order bases in the mesh construction and reconstruction phases of the algorithm [18] as well as discontinuity meshing [15, 13] The use of higher order bases, which we will refer to as galerkin radiosity (GR) has been shown to lower the number of basis functions needed to obtain a particular level of accuracy, albeit at a higher cost per basis. A second avenue of research has ....

Salesin, D., Lischinski, D., and DeRose, T. Reconstructing Illumination Functions with Selected Discontinuities. Third Eurographics Workshop on Rendering (1992), 99--112.

....consistent representation across solution and display stages, as well as potentially faster convergence in certain solution techniques. Lischinski, Tampieri and Greenberg used quadratic triangular interpolants in [39] described in more detail by Tampieri [60] Salesin, Lischinski and DeRose [49] used cubic reconstruction over triangular elements to represent radiance. To this end a Clough Tocher cubic polynomial was built over triangles, and shadow discontinuities were subsequently represented by relaxing constraints over shadow boundaries. Non polynomial approximate reconstruction has ....

....a small number of multiplications to evaluate a function at any point. Following these principles, we limit ourselves to linear and quadratic interpolants. Higher order interpolants can introduce ringing artifacts, and therefore should be used with caution. As discussed in Section 2. 3, cubic [49] and quadratic [38] interpolants have been used in previous work. To see why caution must be used in these cases, let us consider a specific example of uniform linear and quadratic interpolation. The function originally depicted in Figure 3 2(a) is used, over a receiver that is twice as long to ....

Salesin, David, Dani Lischinski, and Tony DeRose, "Reconstructing Illumination Functions with Selected Discontinuities," 3rd Eurographics Workshop on Rendering, Bristol, UK May 1992.

....in partially occluded faces for which the values do not di#er significantly, are good candidates for lower order interpolation, specifically linear or quadratic. The experiments presented below will indicate that this is su#cient in general, obviating the need for cubic interpolants as proposed in [26], for a large class of scenes. In the following section we will present an algorithm for edge elimination, and an algorithm for degree selection. The fact that irradiance in the penumbra is largely monotonic motivates the need to simplify the mesh: if the function is well behaved a coarser ....

David Salesin, Dani Lischinski, and Tony DeRose. Reconstructing illumination functions with selected discontinuities. Third Eurographics Workshop on Rendering, pages 99--112, May 1992.

....implementation correctly resolves D discontinuities. The actual radiance function is C continuous across D boundaries. Currently, we do not impose C continuity across these boundaries. It is possible to do so using the piecewise cubic interpolation scheme described by Salesin et al. [23]. 5.4 Computing the Source Contribution to a Point The radiance contributed by a source s j to a point x was given by Equation (4) We distinguish between the case where s j is completely visible and the case where s j is partially occluded from x. The Unoccluded Case If the unshot radiance ....

D. Salesin, D. Lischinski, and T. DeRose. "Reconstructing Illumination Functions with Selected Discontinuities," in Proceedings of the Third Eurographics Workshop on Rendering (Bristol, UK, May 18--20,

....constructs radiance interpolants in ray space where the ray trees have the same topology. Discontinuity Meshing: Discontinuity meshing is the idea of explicitly representing function discontinuities in a mesh used to construct an approximation to the function. Heckbert [6] and Lischinski et al. [7, 8, 11] have used discontinuity meshing to drastically improve the accuracy of radiosity simulations. Salisbury et al. 12] used a discontinuity mesh containing sharp edges in an image in order to maintain the sharpness of these edges when the image is magnified. 2 Algorithm The goal of our previewer ....

David Salesin, Dani Lischinski, and Tony DeRose. Reconstructing illumination functions with selected discontinuities. In Proceedings of the Third Eurographics Workshop on Rendering (Bristol, UK, May 18--20, 1992), pages 99--112, May 1992.

....used in the original model must be generated. Since this explosion in the number of primitives can drastically reduce the frame rate of the walkthrough, the designer must strike a balance between fidelity and speed. Some authors have advocated higher order color interpolation to reduce artifacts [1,2,8,10]. Using second or, preferably, third order interpolation, one can guarantee C 1 continuity [2,8] thus reducing the chances of Mach banding. Since fewer primitives are required to represent the model accurately, this technique can also lead to increased frame rates. As a simple example of the ....

Salesin, D., D. Lischinski, and T. DeRose, Reconstructing Illumination Functions with Selected Discontinuities, Eurographics Workshop on Rendering, 1992, 99-112.

....be used for this purpose in any of these systems. The idea of making explicit use of discontinuities in functions, surfaces, and images is not new. Discontinuities have been used to construct good meshes for radiosity [13, 15] and to fit piecewisecubic interpolants for radiance functions [22]. Franke and Nielson described several methods for surface reconstruction from scattered data with known discontinuities [10] Zhong and Mallat [30] pioneered work in image compression by storing edges detected at multiple scales. Yomdin and Elichai [29] also describe an image compression ....

David Salesin, Daniel Lischinski, and Tony DeRose. Reconstructing illumination functions with selected discontinuities. In Third Eurographics Workshop on Rendering, pp. 99--112, Bristol, UK, May 1992.

....conceivably be used for this purpose in any of these systems. The idea of making explicit use of discontinuities in functions and in images is not new: discontinuities have been used to construct good meshes for radiosity [12, 14] and to fit piecewise cubic interpolants for radiance functions [22]. Yomdin and Elichai [29] also describe an image compression algorithm that locates and utilizes various types of edges in images to obtain a lossy compression scheme that avoids reconstruction artifacts in the vicinity of edges. 1.2 Overview In the next section we describe in more detail our ....

David Salesin, Daniel Lischinski, and Tony DeRose. Reconstructing illumination functions with selected discontinuities. In Third Eurographics Workshop on Rendering, pages 99--112, Bristol, UK, May 1992.

....bivariate polynomial. This scheme yields a C 0 piecewise quadratic interpolant to the radiance on each polygon. This interpolant was found to provide approximations that look smoother and are less prone to Mach bands than the traditional piecewise linear interpolation [18] Salesin et al. [21] describe a piecewise cubic interpolant that can be used instead, if C 1 interpolation is desired. To obtain a radiance value at a point x we use the information available to us from the hierarchical solution. Below we describe four different methods that we have experimented with. Pseudocode ....

Salesin, David, Dani Lischinski, and Tony DeRose. "Reconstructing Illumination Functions with Selected Discontinuities," in Proceedings of the Third Eurographics Workshopon Rendering, May 1992, pp. 99-- 112.

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D. Salesin, D. Lischinski, and T. DeRose, "Reconstructing illumination functions with selected discontinuities," Proc. of the Third Eurographics Workshop on Rendering, pp. 99--112 #1992#.

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Salesin D., Lischinski D., DeRose T. : Reconstructing Illumination Functions with Selected Discontinuities, 3rd Eurographics Workshop on Rendering, Bristol, UK May 1992.

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D. Salesin / D. Lischinski / T. DeRose, Reconstructing illumination functions with selected discontinuites, Proc. Third Eurographics Workshop on Rendering '92, pp. 99--112

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