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Next: Koenderink and Van Doorn Up: Affine Structure Previous: Image transfer and linear

Change of basis

Given the current spanning set $\{{\bf e_1},{\bf e_2},{\bf e_3}\}$ and $\{{\bf e'_1},{\bf e'_2},{\bf e'_3}\}$ in the two images, we have that

\begin{displaymath}
\left[ \begin{array}{c} {\bf\Delta x_{i}} \\
{\bf\Delta x...
...}{c} \alpha_{i} \\ \beta_{i} \\ \gamma_{i} \end{array} \right]
\end{displaymath}

Suppose that we now wish to express the same set of points using alternative spanning sets $\{{\bf h_1},{\bf h_2},{\bf h_3}\}$ and $\{{\bf h'_1},{\bf h'_2},{\bf h'_3}\}$, the new affine coordinates must obey

\begin{displaymath}
\left[ \begin{array}{c} {\bf\Delta x_{i}} \\
{\bf\Delta x...
...{i} \\ \hat{\beta}_{i} \\ \hat{\gamma}_{i} \end{array} \right]
\end{displaymath}



Subhashis Banerjee 2002-02-18