Sparse PDF maps for non-linear multi-resolution image operations

Abstract

Figure 1: sPDF-maps are a compact multi-resolution image pyramid data structure that sparsely encodes pre-computed pixel neighborhood probability density functions (pdfs) for all pixels in the pyramid. They enable the accurate, anti-aliased evaluation of non-linear image operators directly at any output resolution. A variety of operators can be computed at run time from the same pre-computed data structure in a way that scales to gigapixel images, such as local Laplacian filters for (b,d) detail enhancement or (c,e) smoothing, (f) median filters, (g) dominant mode filters, (h) maximum mode filters, (i) bilateral filters. The original image (a) has resolution 16, 898 × 14, 824 (250 Mpixels). AbstractWe introduce a new type of multi-resolution image pyramid for high-resolution images called sparse pdf maps (sPDF-maps). Each pyramid level consists of a sparse encoding of continuous probability density functions (pdfs) of pixel neighborhoods in the original image. The encoded pdfs enable the accurate computation of non-linear image operations directly in any pyramid level with proper pre-filtering for anti-aliasing, without accessing higher or lower resolutions. The sparsity of sPDF-maps makes them feasible for gigapixel images, while enabling direct evaluation of a variety of non-linear operators from the same representation. We illustrate this versatility for antialiased color mapping, O(n) local Laplacian filters, smoothed local histogram filters (e.g., median or mode filters), and bilateral filters.

Screen-Space Normal Distribution Function Caching for Consistent Multi-Resolution Rendering of Large Particle Data

“…Representing image and volume data via probability density functions (PDFs) allows for consistent multi-resolution rendering and processing of both image [14] and volume data [27,40]. These PDFs can be approximated sparsely and, e.g., be stored in sparse PDF maps [14] and sparse PDF volumes [27], respectively. These representations are very similar to standard mipmaps [36], but enable the accurate and efficient evaluation of color mapping and non-linear filtering.…”

“…These representations are very similar to standard mipmaps [36], but enable the accurate and efficient evaluation of color mapping and non-linear filtering. Accurate approximation of PDFs is possible using isotropic Gaussians [14,27]. Our approach uses This makes it impossible to discern small features (orange circles) in large particle data, such as the Copper/Silver mixture shown here, during interactive exploration.…”

Sparse PDF Volumes for Consistent Multi-Resolution Volume Rendering

“…Hadwiger et al [17] sparsely encoded pixel neighborhood distributions in their sparse pdf maps data structure to accurately apply nonlinear image operations to multi-resolution gigapixel images. Instead of approximating distributions individually, they fitted 3D Gaussians in the combined space × range domain of the image in order to exploit coherence in this 3D domain.…”

Filtering Non-Linear TransferFunctions on Surfaces

“…We refer the reader to the independent and concurrent work of Hadwiger et al [15] on using distribution representations for image processing. We instead focus on high-performance texture and geometry filtering using specialized Gaussian representations in the context of a real-time rendering system.…”

“…We approximate the PDF p h of h (within filter region w P ) with the 1D Gaussian N (h, σ 2 h ), and we use this distribution in Equation (15).…”