Fast Multiresolution Image Operations in the Wavelet Domain

A wide class of operations on images can be performed directly in the wavelet domain by operating on coefficients of the wavelet transforms of the images and other matrices defined by these operations. Operating in the wavelet domain enables one to perform these operations progressively in a coarse-to-fine fashion, operate on different resolutions, manipulate features at different scales, trade off accuracy for speed, and localize the operation in both the spatial and the frequency domains. Performing such operations in the wavelet domain and then reconstructing the result is also often more efficient than performing the same operation in the standard direct fashion. In this paper, we demonstrate the applicability and advantages of this framework to three common types of image operations: image blending, 3D warping of images and sequences, and convolution of images and image sequences.

[1]  Henry Fuchs,et al.  The Delta Tree: An Object-Centered Approach to Image-Based Rendering , 1996 .

[2]  Ahmad Zandi,et al.  CREW Lossless/Lossy Medical Image Compression , 1995 .

[3]  Richard Kronland-Martinet,et al.  A real-time algorithm for signal analysis with the help of the wavelet transform , 1989 .

[4]  Richard Szeliski,et al.  Layered depth images , 1998, SIGGRAPH.

[5]  I. Daubechies,et al.  Factoring wavelet transforms into lifting steps , 1998 .

[6]  I. Daubechies,et al.  Wavelet Transforms That Map Integers to Integers , 1998 .

[7]  P. Dutilleux.  An Implementation of the “algorithme à trous” to Compute the Wavelet Transform , 1989 .

[8]  Paul E. Debevec,et al.  Acquiring the reflectance field of a human face , 2000, SIGGRAPH.

[9]  Shenchang Eric Chen,et al.  QuickTime VR: an image-based approach to virtual environment navigation , 1995, SIGGRAPH.

[10]  Lawrence A. Rowe,et al.  Algorithms for manipulating compressed images , 1993, IEEE Computer Graphics and Applications.

[11]  G. Beylkin,et al.  On the representation of operators in bases of compactly supported wavelets , 1992 .

[12]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[13]  Julie Dorsey,et al.  Effic ient Re-rendering of Naturally Illuminated Environments , 1994 .

[14]  H. Nussbaumer.  Fast Fourier transform and convolution algorithms , 1981 .

[15]  Jr. Leonard McMillan,et al.  An Image-Based Approach to Three-Dimensional Computer Graphics , 1997 .

[16]  Lance Williams,et al.  View Interpolation for Image Synthesis , 1993, SIGGRAPH.

[17]  Israel Cohen,et al.  Orthonormal shift-invariant wavelet packet decomposition and representation , 1997, Signal Process..

[18]  David Salesin,et al.  Wavelets for computer graphics: theory and applications , 1996 .

[19]  Pat Hanrahan,et al.  An efficient representation for irradiance environment maps , 2001, SIGGRAPH.

[20]  Lawrence A. Rowe,et al.  Compressed Domain Processing of JPEG-encoded imaages , 1996, Real Time Imaging.

[21]  I. Daubechies,et al.  Biorthogonal bases of compactly supported wavelets , 1992 .

[22]  Julien Reichel.  Complexity related aspects of image compression , 2002 .

[23]  Wim Sweldens,et al.  The lifting scheme: a construction of second generation wavelets , 1998 .

[24]  Ronen Basri,et al.  Lambertian reflectance and linear subspaces , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[25]  C. Sidney Burrus,et al.  Convolution using the undecimated discrete wavelet transform , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[26]  Leonard McMillan,et al.  Post-rendering 3D warping , 1997, SI3D.

[27]  Dani Lischinski,et al.  Wavelet Warping , 2000, Rendering Techniques.

[28]  Martin Vetterli,et al.  Fast Fourier transforms: a tutorial review and a state of the art , 1990 .

[29]  Mark J. Shensa,et al.  The discrete wavelet transform: wedding the a trous and Mallat algorithms , 1992, IEEE Trans. Signal Process..

[30]  Leonard McMillan,et al.  Plenoptic Modeling: An Image-Based Rendering System , 2023 .

[31]  William A. Pearlman,et al.  An image multiresolution representation for lossless and lossy compression , 1996, IEEE Trans. Image Process..

[32]  Ramana Rao.  Nonstandard Wavelet Decomposition of the Convolution and the Derivative Operators , 1997 .

[33]  Ronald A. DeVore,et al.  Image compression through wavelet transform coding , 1992, IEEE Trans. Inf. Theory.

[34]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[35]  Edward H. Adelson,et al.  The Laplacian Pyramid as a Compact Image Code , 1983, IEEE Trans. Commun..

[36]  R. Coifman,et al.  Fast wavelet transforms and numerical algorithms I , 1991 .