Shiftable multiscale transforms

One of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavelet transforms are also unstable with respect to dilations of the input signal and, in two dimensions, rotations of the input signal. The authors formalize these problems by defining a type of translation invariance called shiftability. In the spatial domain, shiftability corresponds to a lack of aliasing; thus, the conditions under which the property holds are specified by the sampling theorem. Shiftability may also be applied in the context of other domains, particularly orientation and scale. Jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored. Two examples of jointly shiftable transforms are designed and implemented: a 1-D transform that is jointly shiftable in position and scale, and a 2-D transform that is jointly shiftable in position and orientation. The usefulness of these image representations for scale-space analysis, stereo disparity measurement, and image enhancement is demonstrated. >

[1]  Dennis Gabor,et al.  Theory of communication , 1946 .

[2]  Elie J. Baghdady,et al.  Lectures on communication system theory , 1961 .

[3]  Ronald N. Bracewell,et al.  The Fourier Transform and Its Applications , 1966 .

[4]  B Julesz,et al.  Experiments in the visual perception of texture. , 1975, Scientific American.

[5]  D. Esteban,et al.  Application of quadrature mirror filters to split band voice coding schemes , 1977 .

[6]  G. Granlund.  In search of a general picture processing operator , 1978 .

[7]  Takeo Kanade,et al.  An Iterative Image Registration Technique with an Application to Stereo Vision , 1981, IJCAI.

[8]  David Marr,et al.  VISION A Computational Investigation into the Human Representation and Processing of Visual Information , 2009 .

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

[10]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[11]  R. Wilson,et al.  Anisotropic Nonstationary Image Estimation and Its Applications: Part I - Restoration of Noisy Images , 1983, IEEE Transactions on Communications.

[12]  Hans Knutsson,et al.  Texture Analysis Using Two-Dimensional Quadrature Filters , 1983 .

[13]  Alex Pentland,et al.  Fractal-Based Description of Natural Scenes , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  M. Vetterli.  Multi-dimensional sub-band coding: Some theory and algorithms , 1984 .

[15]  A. Grossmann,et al.  DECOMPOSITION OF HARDY FUNCTIONS INTO SQUARE INTEGRABLE WAVELETS OF CONSTANT SHAPE , 1984 .

[16]  Edward H. Adelson,et al.  PYRAMID METHODS IN IMAGE PROCESSING. , 1984 .

[17]  Andrew P. Witkin,et al.  Scale-space filtering: A new approach to multi-scale description , 1984, ICASSP.

[18]  J. Daugman.  Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters. , 1985, Journal of the Optical Society of America. A, Optics and image science.

[19]  P. Vaidyanathan.  On power-complementary FIR filters , 1985 .

[20]  Hamid Gharavi,et al.  Sub-Band Coding Of Digital Images Using Two-Dimensional Quadrature Mirror Filtering , 1986, Other Conferences.

[21]  John W. Woods,et al.  Subband coding of images , 1986, IEEE Trans. Acoust. Speech Signal Process..

[22]  Kou-Hu Tzou,et al.  An efficient pyramid image coding system , 1987, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[23]  Andrew B. Watson,et al.  The cortex transform: rapid computation of simulated neural images , 1987 .

[24]  Edward H. Adelson,et al.  Orthogonal Pyramid Transforms For Image Coding. , 1987, Other Conferences.

[25]  Martin Vetterli,et al.  A theory of multirate filter banks , 1987, IEEE Trans. Acoust. Speech Signal Process..

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

[27]  John G. Daugman,et al.  Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression , 1988, IEEE Trans. Acoust. Speech Signal Process..

[28]  Eero P. Simoncelli.  Orthogonal sub-band image transforms , 1988 .

[29]  Stéphane Mallat,et al.  Multifrequency channel decompositions of images and wavelet models , 1989, IEEE Trans. Acoust. Speech Signal Process..

[30]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[31]  Gilbert Strang,et al.  Wavelets and Dilation Equations: A Brief Introduction , 1989, SIAM Rev..

[32]  Jae S. Lim,et al.  Two-Dimensional Signal and Image Processing , 1989 .

[33]  Ingrid Daubechies,et al.  The wavelet transform, time-frequency localization and signal analysis , 1990, IEEE Trans. Inf. Theory.

[34]  Ramesh A. Gopinath,et al.  Efficient computation of the wavelet transforms , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[35]  Jitendra Malik,et al.  Detecting and localizing edges composed of steps, peaks and roofs , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[36]  Jean-Bernard Martens.  The Hermite transform-applications , 1990, IEEE Trans. Acoust. Speech Signal Process..

[37]  John W. Woods,et al.  Subband Image Coding , 1990 .

[38]  D. G. Vass,et al.  OSA Technical Digest Series , 1990 .

[39]  Jean-Bernard Martens,et al.  The Hermite transform-theory , 1990, IEEE Trans. Acoust. Speech Signal Process..

[40]  Eero P. Simoncelli,et al.  Non-separable extensions of quadrature mirror filters to multiple dimensions , 1990, Proc. IEEE.

[41]  Edward H. Adelson,et al.  The Design and Use of Steerable Filters , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[42]  Stéphane Mallat,et al.  Zero-crossings of a wavelet transform , 1991, IEEE Trans. Inf. Theory.