X=6 Y=5

The image sensor on a camera is shown below. The pixel size is 10 micrometers. The focal length is 5cm. The sensor is not skewed. (a) Write the intrinsic matrix. (b) Suppose there is a pixel at position (20+X,20+Y). What is the position of that point in metric units. Suppose we have a point in space. The coordinates of the point with respect to the camera coordinate system is (10cm,20cm,200cm). (c) What is the projection of that point on the image plane in metric units? (d) What is the projection of that point on the image sensor in pixel coordinates? Suppose that the camera is moved from its original position to a new position. The new coordinate system is related to the original position by rotation R=1 (identity matrix) and translation T=(1 meter, 1 meter, 0). (e) What is the representation of the point (10cm,20cm,200cm) with respect to the new coordinate system? (f) What is the essential matrix between these two views