TY - JOUR
T1 - Non-Separable Extensions of Quadrature Mirror Filters to Multiple Dimensions
AU - Simoncelli, Eero P.
AU - Adelson, Edward H.
N1 - Funding Information:
Manuscript received January 14,1989; revised June 25,1989. This work was supported in part by IBM Corporation, the National Science Foundation, under grant NSF IRI 871-939-4, and the Defense Research Projects Agency, under grant DARPAIRADC F30602-89-C-0022. The views expressed are those of the authors, and do not necessarily represent the views of MIT or the sponsors.
PY - 1990/4
Y1 - 1990/4
N2 - Quadrature Mirror Filter (QMF) banks have been used in a variety of one-dimensional signal processing applications, and have been applied separably in two dimensions. As with most one-dimensional filters, separable extension to multiple dimensions produces a transform in which the orientation selectivity of some of the high-pass filters is poor. We describe generalized non-separable extensions of QMF banks to two and three dimensions, in which the orientation specificity of the high-pass filters is greatly improved. In particular, we discuss extensions to two dimensions with hexagonal symmetry, and three dimensional spatio-temporal extensions with rhombic-dodecahedral symmetry. Although these filters are conceived and designed on non-standard sampling lattices, they may be applied to rectangularly sampled images. As in one dimension, these transformations may be hierarchically cascaded to form a multi-scale “pyramid” representation. We design a set of example filters and apply them to the problems of image compression, progressive transmission, orientation analysis, and motion analysis.
AB - Quadrature Mirror Filter (QMF) banks have been used in a variety of one-dimensional signal processing applications, and have been applied separably in two dimensions. As with most one-dimensional filters, separable extension to multiple dimensions produces a transform in which the orientation selectivity of some of the high-pass filters is poor. We describe generalized non-separable extensions of QMF banks to two and three dimensions, in which the orientation specificity of the high-pass filters is greatly improved. In particular, we discuss extensions to two dimensions with hexagonal symmetry, and three dimensional spatio-temporal extensions with rhombic-dodecahedral symmetry. Although these filters are conceived and designed on non-standard sampling lattices, they may be applied to rectangularly sampled images. As in one dimension, these transformations may be hierarchically cascaded to form a multi-scale “pyramid” representation. We design a set of example filters and apply them to the problems of image compression, progressive transmission, orientation analysis, and motion analysis.
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U2 - 10.1109/5.54805
DO - 10.1109/5.54805
M3 - Article
AN - SCOPUS:0025414259
SN - 0018-9219
VL - 78
SP - 652
EP - 664
JO - Proceedings of the IEEE
JF - Proceedings of the IEEE
IS - 4
ER -