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Question 2 example 2

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Problem 2: Comprehension and Derivation (25 points)

Part A: Short Answer (15 points total, 5 points each)
Answer the following short questions, which are similar in style to your weekly quizzes [1].

  1. (5 pts) Recall the four classes of images discussed in class. Which class of images maps a discrete domain to a discrete range ($\mathbb{Z}^2 \rightarrow \mathbb{Z}^D$) and is mathematically associated with the Potts model [2]?
  2. (5 pts) State the primary difference between a motion field and optical flow [3].
  3. (5 pts) Explain the scale ambiguity problem that occurs in single-view perspective projection [4]. What prior information is required to overcome this ambiguity [4]?

Part B: Mathematical Proof / Derivation (10 points)
Provide a mathematical derivation for the following classic linear algebra problem [1].

  1. (10 pts) Imagine you are stitching two images together and have identified $N$ distinct pairs of matching 2D points [5]. Let $[u_i, v_i]^T$ be a point in the first image, which you have matched to $[x_i, y_i]^T$ in the second image [6]. Derive the linear least squares objective function to estimate the 6 parameters of the 2D affine transformation matrix that would align these pairs of points, and provide the closed-form solution for the parameters [6, 7].
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