Wavelet Based Texture Resampling

The integral equation arising from space variant 2-D texture res-ampling is reformulated through wavelet analysis. We transform the standard convolution integral in texture space into an inner product over sparse representations for both the texture and the warped lter function. This yields an algorithm that operates in constant time in the area of the domain of convolution, and that is sensitive to the frequency content of both the lter and the texture. The reformulation admits further acceleration for space-invariant resampling. 1 Issues The problem of eeciently processing two-dimensional textures that undergo space variant warps is both important and technically challenging. In most rendering situations, textures are diierentially mapped onto surfaces through parameterisa-tion and they are viewed through a perspective projection. Both mappings in principle require texture resampling operations at a cost that can vary signiic-antly from pixel to pixel. The constant-time space variant resampling problem is to compute ltered pixel values in image space at a cost that is independent of the area of the texture involved in the computation. The importance of eecient resampling algorithms is increasing with the advent of image-based rendering 11]. Most practical approaches use fast but lower quality space invariant algorithms such as those based on MIP mapping 15]. An important design criterion of a general space variant resampler is that it should readily specialise to and accelerate space invariant resampling. Even if the problem of constant-time resampling is solved theoretically, there remains the nagging problem of making the constant as small as possible. Indeed, few \constant-time" resampling techniques are practical , with perhaps the only exception being clamped elliptical weighted average (EWA) ltering on a pyramid 9]. Lansdale demonstrated that with suitable clamping (which itself restricts the degree of space variance), remarkably better