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Resampling 
For the creation of the final image, one having axes parallel to 
the external reference system, the technique of inverse mapping 
is used . which consists of filling an appropriately dimensioned 
empty image with values obtained by interpolation of the 
original image. 
X? X'p 
Ongsnai smage matrix Recced image matnx 
fig. 5a: the inverse method of rectification 
The algorithms used for the resampling work according to three 
methods: nearest neighbor assignment bilinear interpolation or 
bicubic splines. 
m ~ | -ui*«-sisî*-suî** is<si<z 
0 2Sfc? 
*» * ‘Ha** is 
* (Ax - 1) 
A 'M~ 
_%•. resampling methods: bicubic spline interpolation 
The formula used by the zero order interpolation (nearest 
neighbor) is: 
^i r \ 
a ?4«-T 
Ax «os & ay <o,5 
Ax'¿OS & Ay <0.5 
Ax «OS & Ay a 0,5 
ax ao.s & ayac.5 
fig. 5b: resampling methods: zero order interpolation 
The formula used by the bilinear interpolation is: 
Input image matra A 
Output image matra A* 
^'k,i ** A,j 
* & x ( A i+ t.j * A i.j} 
* ¿Y{ A i.i+i * A fc _|> 
+ Ax * Ay(A{ j - - A* A i+1J *t) 
fig. 5c: resampling methods: bilinear interpolation 
Applications 
The software has been largely used for the rectification of the 
images for which two images of the survey work for the Arena 
of Verona have been reported. 
The formula used by me bilinear interpolation is: 
fig. 6b 
Figures 6: the residuals of some control points in the Arena survey