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==3D Reconstruction== | ==3D Reconstruction== | ||
===Triangulation=== | |||
If cameras are intrinsically and extrinsically calibrated, then P is the midpoint of the common perpendicular. | |||
===Point reconstruction=== | |||
Given a point X in R3 | |||
* <math>x=MX</math> is the point in image 1 | |||
* <math>x'=M'X</math> is the point in image 2 | |||
<math> | |||
M = \begin{bmatrix} | |||
m_1^T \\ m_2^T \\ m_3^T | |||
\end{bmatrix} | |||
</math> | |||
<math>x \times MX = 0</math> | |||
<math>x \times M'X = 0</math> | |||
implies | |||
<math>AX=0</math> where <math>A = \begin{bmatrix} | |||
x m_3^T - m_1^T\\ | |||
y m_3^T - m_2^T\\ | |||
x' m_3'^T - m_1'^T\\ | |||
y' m_3'^T - m_2'^T\\ | |||
\end{bmatrix}</math> | |||
==Projects== | ==Projects== |