Pyramidal parametrics

By Lance Williams. 1983

The mapping of images onto surfaces may substantially increase the realism and information content of computer-generated imagery. The projection of a flat source image onto a curved surface may involve sampling difficulties, however, which are compounded as the view of the surface changes. As the projected scale of the surface increases, interpolation between the original samples of the source image is necessary; as the scale is reduced, approximation of multiple samples in the source is required. Thus a constantly changing sampling window of view-dependent shape must traverse the source image. To reduce the computation implied by these requirements, a set of prefiltered source images may be created. This approach can be applied to particular advantage in animation, where a large number of frames using the same source image must be generated. This paper advances a “pyramidal parametric” prefiltering and sampling geometry which minimizes aliasing effects and assures continuity within and between target images. Although the mapping of texture onto surfaces is an excellent example of the process and provided the original motivation for its development, pyramidal parametric data structures admit of wider application. The aliasing of not only surface texture, but also highlights and even the surface representations themselves, may be minimized by pyramidal parametric means.

Subfields: Numerical Methods & Scientific Computing

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In Numerical Methods & Scientific Computing

1. Hugues Hoppe
2. Bo Dai
3. Janne Hellsten
4. Thomas Lokovic
5. Christian Theobalt
6. Marc Pollefeys
7. Timo Aila
8. Miika Aittala

Citations in the corpus

• Analyzing and Improving the Image Quality of StyleGAN (2019, methodology): “The MSG-GAN generator is modified to output a mipmap [37] instead of an image, and a similar representation is computed for each real imFFHQ D original D input skips D residual FID PPL FID PPL FID PPL G original 4.”
• Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes (2021, unknown): “While signal processing techniques can filter textures [46], geometry filtering is representation-specific and challenging.”
• Multi-resolution real-time stereo on commodity graphics hardware (2003, methodology): “By utilizing the mipmap functionality [13] on the graphics hardware, we can compute this dissimilarity measure very efficiently.”
• Systems and Experiment Paper: Construction of Panoramic Image Mosaics with Global and Local Alignment (2000, unknown): “This operation is ,andtosupportfilteringoperationssuchasbilinear texturemappingandMIPmapping(Williams,1983).”
• Deep shadow maps (2000, background): “Since deep shadow maps are filtered like textures, it is straight-forward to apply mip-mapping [12].”
• Neural Point-Based Graphics (2019, background): “Such progressive (coarse-to-fine) mechanism is reminiscent to texture mipmapping [36] as well as many other coarse-to-fine/varying level of details rendering algorithms in computer graphics.”
• Crowdsourcing in Computer Vision (2016, unknown): “One can think of the various levels of tessellation as a MIP map [137] of tessellated geometry; the ray differential is used to select the appropriate tessellation.”
• NeRF: Representing scenes as neural radiance fields for view synthesis (unknown): “…highest honor, primarily for pioneering the image-based approach to graphics or “brute force in image space” including shadow mapping [ 75 ] and mip-mapping [ 76 ]. or view synthesis offered an alternative of using by definition photorealistic input images and combining them to create new images.”
• Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields (2023, background): “Mip mapping [33] (mip-NeRF’s namesake) precomputes a datastructure that enables fast antialiasing, but it is unclear how this approach can be applied to the hashed datastructures underlying iNGP.”
• Mip-Splatting: Alias-Free 3D Gaussian Splatting (2023, background): “There are two principal strategies to combat aliasing: super-sampling , which increases the number of samples [7], and prefiltering , which applies low-pass filtering to the signal to meet the Nyquist limit [8, 15, 31, 47, 50, 59].”
• Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields (2021, background): “In the context of rendering, prefiltering can be thought of as tracing a cone instead of a ray through each pixel [1, 16]: wherever the cone intersects scene content, a precomputed multiscale representation of the scene content (such as a sparse voxel octree [15, 21] or a mipmap [47]) is queried at ”
• Geometry clipmaps: terrain rendering using nested regular grids (2004, methodology): “To prevent spatial aliasing, an image is prefiltered into a mipmap pyramid of power-of-two grids [Williams 1983].”
• BungeeNeRF: Progressive Neural Radiance Field for Extreme Multi-scale Scene Rendering (2021, background): “Compared to traditional mipmapping [40] which requires a pyramid of pre-defined models at each scale, this strategy unifies different levels of detail into a single model and can be controlled with L.”