Ying Chen
WifG») [£*vio
= (2)
2 1
W,; fy) f* V»; (x, y)
The modulus and amplitude angle of gradient vector are defined according to formula (2) respectively as:
2 2 2
M,, f Gy) - AW f G XY HW] f Gs») ^
2 1
A, f(x,y) 7 argtan(£., f (x, y) / W,, f (x, y))
Choosing two-dimensional Gaussian or B-
spline as smoothing function, from formulas f(x,y)
(1), (2) and (3), we can obtain corresponding IL
wavelets and obtain the modulus M) f(x,y) Wavelet
and amplitude angle AJ f(x,y) of gradient :
iss 2 translation
vector in image f(x,y) respectively. Then,
image gradient and direction map (g map
and d_map) can be generated from M; f(x,y) G map d map
and A, f(x,y). This is the foundation for the
gradient direction profile detection algorithm AL Gin
presented in this paper. First, the modulus Decomposition &
whose absolute value is maximum is detected reconstruction
along gradient direction. Through tracing and
connecting the points where the modulus and
direction are the most approximate, the edge Profile searching
contours are obtained and expressed by chain
code. Figure 1 shows the detection procedure. i L
Most matching algorithms are done in chain code
pyramid images. The pyramid images in this Jil,
paper are generated using decomposition and
reconstruction base on wavelet. The set of Edge trace
decomposition for image f can be given T T
[Ying,1998.12],
i Fearture contour
FH TE
di^zGH/ line moment
a (4) parameters
d°=HG;" JL
dt = GO 1 Matching
Fig.1: Edge Detection Procedure
The set of reconstruction can be written
eB Hr +H ACI” + GG d** (5)
The results of decomposition and reconstruction are expressed as figure 2.
A remarkable property of wavelet Transform is its ability to characterize the local regularity of functions.The regularity
indicates a singularity of image feature and can be often measured with Lipschitz exponents a . Mallat[1992] have
demonstrated that the maximum of modulus for wavelet translation must satisfy,
M, f(x,y) < AQ)
178 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
