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Iterative parametric point (IPP) algorithm

Input: A set of profile maps ${\bf j}_k$, $k=1,\ldots ,L$, acquired from different viewpoints. Initial estimates for the unknown parameters.

Output: Refined estimates for ${\bf a}$, or ${\bf c}$, or ${\bf a}$ and ${\bf c}$.

Iterate until convergence,

1.
Transform the maps ${\bf j}_k$, $k=1,\ldots ,L-1$, onto all the other maps ${\bf j}_l$ for which l>k using the current estimates of the unknown parameters.

2.
For each pair of overlapping maps ${\bf j}_k$ and ${\bf j}_l$, k<l, construct an interpolated image ${\bf\tilde j}_l$ on Sk from the pixel values of ${\bf j}_l$ at the intermediate locations ${\bf s}_{kl}$ hit by the transformed map ${\bf j}_{kl}$. For each pixel $({\bf s}_k,j_k({\bf s}_k))$ of ${\bf j}_k$, the corresponding pixel on ${\bf j}_l$ is chosen to be $({\bf s}_{k},\tilde j_l({\bf s}_{k}))$.

3.
Find compatible matches and compute the weighting images ${\bf w}_{kl}$ on Sk. These include

4.
Update simultaneously all the parameters by taking one step according to the Levenberg-Marquardt algorithm towards the minimum of the mean of the squares of weighted distances between the corresponding points given by

 \begin{displaymath}f_1({\bf j}_1,\ldots ,{\bf j}_L,{\bf a},{\bf c})=\sum _{l=2}^L{\sum _{k=1}^{l-1}{{\bf w}_{kl}^2\bullet{\bf d}_{kl}^2/K}},
\end{displaymath} (3)

where the distance image ${\bf d}_{kl}={\bf j}_{kl}-{\bf\tilde j}_l$, $K=\sum _{l=2}^L{\sum _{k=1}^{l-1}{{\bf w}_{kl}^2\bullet{\bf 1}_k}}$, and ${\bf 1}_k$ is a unit image on Sk having ones at all locations.

Remarks:


next up previous contents
Next: Precision of the estimated Up: Matching of multiple maps Previous: Calibration problem
Olli T Jokinen
1999-08-24