Edge Detection Using a Complex Wavelet
Abstract
A complex wavelet of the form Psi(x, y) = C(x jy)exp(-p(x-sq+y-sq))) is used in the continuous wavelet transform to obtain edges from a digital image in two orthogonal directions. In the above equation Psi(x, y) is a two dimensional complex wavelet, C and p are constants, j is the square root of -1 and x and y are position variables. The square root of the sum of the squares of the real and imaginary parts of the wavelet transform are used to find the edges in an arbitrary direction. Theoretical models are derived for the cases of a step edge and a ramp edge. The computer implementation of the wavelet edge detector involves the creation of two masks; one for the real part and one for the imaginary part. An expression is derived for the size of the edge masks using the inflection points of a curve derived from the wavelet. Finally the edge detector is applied to two synthetic aperture radar images and the resulting images are shown. Continuous wavelet transform, Digital image.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1993
- Accession Number
- ADA273699
Entities
People
- Eugene A. Margerum
- Richard A. Hevenor
Organizations
- Army Geospatial Center