Question

Let W be a 3 x 3 window centered about the pixel (1,1) (coordinates start with 0). Let the gradient vectors in this window (top to bottom, left to right) be {(0, 1), (0, 1), (0, 1), (1, 0), (1, 0), (1, 0), (0, 0), (0, 0), (0, 0)}. Compute the correlation matrix C in this window. Compute the sum of of entries in this matrix to form your answer

Answer 1

The correlation matrix C for the given window of gradient vectors is a 2x2 matrix with entries [3, 0; 0, 3], and the sum of the entries in this matrix is 6.

Step-by-step explanation:

The question asks us to compute the correlation matrix C for a 3 x 3 window of gradient vectors and to find the sum of the entries in this matrix. The given gradient vectors are:

• (0, 1)
• (0, 1)
• (0, 1)
• (1, 0)
• (1, 0)
• (1, 0)
• (0, 0)
• (0, 0)
• (0, 0)

To find the correlation matrix, we calculate the sums of the squares and cross products of the x and y components of the gradient vectors:

• Sum of the x-components squared: 3
• Sum of the y-components squared: 3
• Sum of the cross products of x and y: 0

Using this, we can form the correlation matrix C as:

C = [

[ 3, 0],

[ 0, 3]
]

We then add up the entries in the matrix to find the sum:

Sum of entries in C = 3 + 0 + 0 + 3 = 6.