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)). To localize a corner in this window you need to multiply the inverse of the correlation matrix C by a 2x1vector Q. Compute the vector Q and add its entries to form your answer

Answer 1

To compute the vector Q, we need to calculate the correlation matrix C and its inverse. The vector Q is then obtained by multiplying the inverse of C by a 2x1 vector Q. The answer is found by adding up the entries of Q.

Step-by-step explanation:

To compute the vector Q, we need to first calculate the correlation matrix C. The correlation matrix is a 2x2 matrix where each entry represents the correlation between two gradient vectors. In this case, the entries are:

C(1, 1) = (0, 1) • (0, 1) = 1

C(1, 2) = C(2, 1) = (0, 1) • (1, 0) = 0

C(2, 2) = (1, 0) • (1, 0) = 1

To compute the inverse of C, we need to find the determinant and cofactor matrix of C. The determinant of C is |C| = (1)(1) - (0)(0) = 1. The cofactor matrix of C is:

|C₁₁|C₁₂|

|C₂₁|C₂₂|

To find the inverse of C, we need to divide the cofactor matrix by the determinant of C. The inverse of C is:

|C₁₁|C₁₂|

|C₂₁|C₂₂|

Now, we can calculate the vector Q by multiplying the inverse of C by the 2x1 vector Q. The vector Q is:

Q = inverse(C) • Q = |C₁₁ C₁₂| • |Q₁| = |C₂₁ C₂₂| |Q₂|

Finally, we add up the entries of Q to find our answer:

Q₁ + Q₂ = entry 1 + entry 2

Answer 2

The task to calculate vector Q for corner localization is missing essential details about the correlation matrix C, making it impossible to provide the correct computation and sum of its entries.

Step-by-step explanation:

Calculating a vector Q for corner localization in a window using a correlation matrix C (not explicitly provided in the question) and its inverse. To compute vector Q, one typically needs to consider the gradients in the window and potentially other factors if the correlation matrix C was provided.

However, with the current information provided, there seems to be an error or lack of necessary details to compute vector Q correctly. Furthermore, the correlation matrix is not fully specified, which is required to calculate the inverse and subsequently vector Q. Therefore, we cannot accurately compute the vector Q and sum its entries without the full definition of the correlation matrix C.