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Extrinsic matrix

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Transformations: Transformation is simply the change of position and orientation of a frame attached to a body with respect to a frame attached to another body. Transformations in a planar space is known as 2D transformation and transformations in a spatial world is known as 3D transformation. . Translation: Change in position.

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Convert standard camera intrinsic (focal length, principal point) and extrinsic parameters (rotation and translation) into a vtkCamera for rendering. Assume square pixels and 0 skew for now. - make_vtk_camera.cpp.

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-The matrix containing the extrinsic camera parameters: Mex = r11 r21 r31 r12 r22 r32 r13 r23 r33 −RT 1 T −RT 2 T −RT 3 T -Using homogeneous coordinates: xh yh w =Min Mex Xw Yw Zw 1 =M Xw Yw Zw 1 = m11 m21 m31 m12 m22 m32 m13 m23 m33 m14 m24 m34 Xw Yw Zw 1 -Homogenization is needed to obtain the pixel coordinates: xim = xh w = m11Xw +m12Yw.

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I have a camera matrix (I know both intrinsic and extrinsic parameters) known for image of size HxW. (I use this matrix for some calculations I need). I want to use a smaller image, say: $\frac{H}{2}\times \frac{W}{2}$ (half the original). What changes do I need to make to the matrix, in order to keep the same relation ?.

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