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MidTermExam

# MidTermExam - Auto-calibration Consider the same cameras as...

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EECS 442 Computer Vision -- Mid Term Exam Due: on Friday October 30 th at midnight Return your midterm exam in the box by Prof Savarese’s office door Problem 1: Assume that we have two cameras with camera matrices P 1 and P 2 , where: P 1 = K 1 [R 1 T 1 ] P 2 = K 2 [R 2 T 2 ] K 1 = K 2 = K R 1 = I = Identity matrix R 2 = R T 1 = T 2 = [0 0 0] T Suppose that the cameras generate images I 1 and I 2 , respectively, as below: p’ 4 p 4 p 2 p’ 2 p’ 1 p 1 p 3 p’ 3 I 1 I 2 Where p’ 1 , p’ 2 , p’ 3, p’ 4 and p 1 , p 2 , p 3, p 4 are corresponding points across the two images Prove that the homographic transformation H defined by p’ 1 , p’ 2 , p’ 3, p’ 4 and p 1 , p 2 , p 3, p 4 can be expressed as: H = K R K -1 Do N>3 corresponding points necessarily need to belong to the same planar surface in 3D in order for the above result to be true? Justify your answer

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Problem 2 (
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Unformatted text preview: Auto-calibration): Consider the same cameras as in problem 1. Write a computer program that estimates the internal matrix K and external parameter R from a set of at least 3 corresponding points selected across the 2 images. You can use your own code in HW3 for selecting the corresponding points manually and compute the relevant homographic transformation H. You must return: • An outline of the algorithm that you are using to compute R and K • The source codes • The numerical values of K and R • Comments about your results The original images can be downloaded from: http://www.eecs.umich.edu/~silvio/teaching/Homeworks/midterm/garden1.png http://www.eecs.umich.edu/~silvio/teaching/Homeworks/midterm/garden2.png...
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MidTermExam - Auto-calibration Consider the same cameras as...

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