Two-dimensional directional wavelets and the scale-angle representation

被引:113
作者
Antoine, JP
Murenzi, R
机构
[1] Inst. de Physique Théorique, Univ. Catholique de Louvain, B-1348 Louvain-la-Neuve, 2, Chemin du Cyclotron
[2] CTSPS, Clark Atlanta University, Atlanta
关键词
image analysis; directional features detection; continuous wavelet transform; scale-angle representation; directional wavelets; reproducing kernel; wavelet calibration; angular resolving power; scale resolving power;
D O I
10.1016/0165-1684(96)00065-5
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
The two-dimensional continuous wavelet transform (CWT) is characterized by a rotation parameter, in addition to the usual translations and dilations. This enables it to detect edges and directions in images, provided a directional wavelet is used. First we briefly review the general properties of the 2-D CWT and describe several classes of wavelets, including the directional ones. Then we turn to the problem of wavelet calibration. We show, in particular, how the reproducing kernel may be used for defining and evaluating the scale and angle-resolving power of a wavelet. Finally, we illustrate the usefulness of the scale-angle representation of the CWT on the problem of disentangling a train of damped plane waves.
引用
收藏
页码:259 / 281
页数:23
相关论文
共 45 条
[21]   WAVELET TRANSFORMS AND THEIR APPLICATIONS TO TURBULENCE [J].
FARGE, M .
ANNUAL REVIEW OF FLUID MECHANICS, 1992, 24 :395-457
[22]   THE DESIGN AND USE OF STEERABLE FILTERS [J].
FREEMAN, WT ;
ADELSON, EH .
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 1991, 13 (09) :891-906
[23]  
GROSSMANN A, 1986, ANN I H POINCARE-PHY, V45, P293
[24]   TRANSFORMS ASSOCIATED TO SQUARE INTEGRABLE GROUP-REPRESENTATIONS .1. GENERAL RESULTS [J].
GROSSMANN, A ;
MORLET, J ;
PAUL, T .
JOURNAL OF MATHEMATICAL PHYSICS, 1985, 26 (10) :2473-2479
[25]   DECOMPOSITION OF HARDY FUNCTIONS INTO SQUARE INTEGRABLE WAVELETS OF CONSTANT SHAPE [J].
GROSSMANN, A ;
MORLET, J .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1984, 15 (04) :723-736
[26]  
Grossmann A., 1990, WAVELETS, P2, DOI DOI 10.1007/978-3-642-75988-8_1
[27]  
Grossmann A., 1986, STOCHASTIC PROCESSES, P149
[28]  
Holschneider M., 1995, WAVELETS ANAL TOOL
[29]   RECEPTIVE FIELDS, BINOCULAR INTERACTION AND FUNCTIONAL ARCHITECTURE IN CATS VISUAL CORTEX [J].
HUBEL, DH ;
WIESEL, TN .
JOURNAL OF PHYSIOLOGY-LONDON, 1962, 160 (01) :106-&
[30]  
Kirillov AA., 1976, ELEMENTS THEORY REPR, DOI [10.1007/978-3-642-66243-0, DOI 10.1007/978-3-642-66243-0]