(x) 
th 
— 
X 
na 
i 
a, cos 2wkx/M + .b. sin 2wkx/M + r 
£ 
sin 2wkx/M + I(x) 
k 
uy cos 2mkx/M + 
It is natural to choose k in such a way that the sine and cosine 
functions are orthogonal. The coefficients a,, b,:; U, ànd v, are then 
obtained from the Fourier series of f and g. The matching parameter is 
obtained from these coefficients as 
M 
atk} = i L + a [arctg (b, /4,) - arctg (v, /u,)] (25) 
Li. 0. le Arie Az 
an expression, which is easily shown to be equivalent to (18). As a 
consequence, digital image matching using phase shift methods are 
biased by wrap-around errors as already shown. 
k (24) 
«A 
> 
u 
  
  
  
  
ati (en 
i WM ud Lit e T i n n ih n 
: iid Vm : Alt i jun um ir | 
CN MNA 
ree ibm TR 
  
  
  
un p xu 1 i (ur 
|l jj i i | ai i ii iil did b iiid A Ab 
refte mom"; 
Figure 2: Row vectors showing possible parallaxes. 
Top of aJ, bl, «bh, id) Components Jof rowvectors for each k. 
Bottom of al, 50k, xk, idi: $um of. all row. vectors. 
a) Cyclically displaced sine curve and real image. N=M=64. 
b) Noncyclically displaced sine curve. N=M-64. 
c) Noncyclically displaced real image. N=M=64. 
d) Noncyclically displaced real image window. N:128, M-:65*4. 
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