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Question2: Pinhole Camera model [20marks] The pinhole camera model is the most popular projection model in analytical photogrammetry. The model projects 3Dimensional points onto a camera screen by the relationship: \[ x_{c}=\frac{X_{w}}{Z_{w}} ; y_{c}=\frac{Y_{w}}{Z_{w}} \] Withxc,ycthe camera coordinates andXw,Yw,Zwthe 3Dimensional point's coordinates. 2.1. Write the pinhole coordinates transformation in a matrix form that accommodates3Dhomogeneous coordinate's representation of points.[4marks] 2.2. Calculate the projected coordinates of a point located on the camera screen through the pinhole transformation matrix you formulated above (NB the camera coordinate system has its origin located on the screen plane). [4marks] 2.3. Calculate the projected coordinate of a point located at the focal point though the same pinhole transformation matrix. [4marks] 2.4. Calculate the image of a point located at infinity with3Dcoordinates(0;0;Z;0)[4marks] 2.5. From the results above can you say that the pinhole is an accurate representation of how points in the 3D space are projected onto the camera screen? Why? [4marks]

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