Question

5 Template Matching (20 points) 26 3 184 75 80 128 72 0 84 89 65 0 200 224 18 170 26 54 47 75 127 52 94 26 68 43 199 81 87 86 0 97 3 9 208 218 23 12 188 176 180 1 2 6 3 0 80 54 39 31 22 40 9 2 5 21 9 12 98 176 211 105 9 3 10 20 18 1 5 2 30 3 Figure 1: Left: gray scale values of a 7 × 9 image. Right: gray scale values of a 3 × 3 template. As shown in Figure 1, we have an image and a template. To determine which one of the three positions in the image indicated by the shaded pixels best matches the template, we can use either Sum of squared difference (SSD) or Normalized cross correlation (NCC). Do zero padding at the border if necessary. 1. Compute the sum of squared difference (SSD) at the three positions indicated by the shaded pixels. Explain which position is the best match. (10 points) 2. Compute the normalized cross correlation (NCC) at the three positions indicated by the shaded pixels. Explain which position is the best match. (10 points)

          5 Template Matching (20 points)
26 3 184 75 80 128 72 0 84
89 65 0 200 224 18 170 26 54
47 75 127 52 94 26 68 43 199
81 87 86 0 97 3 9 208 218
23 12 188 176 180 1 2 6 3
0 80 54 39 31 22 40 9 2
5 21 9 12 98 176 211 105 9
3 10 20
18 1 5
2 30 3
Figure 1: Left: gray scale values of a 7 × 9 image. Right: gray scale values of a 3 × 3 template.
As shown in Figure 1, we have an image and a template. To determine which one of the three positions in the image indicated by the shaded pixels best matches the template, we can use either Sum of squared difference (SSD) or Normalized cross correlation (NCC). Do zero padding at the border if necessary.
1. Compute the sum of squared difference (SSD) at the three positions indicated by the shaded pixels. Explain which position is the best match. (10 points)
2. Compute the normalized cross correlation (NCC) at the three positions indicated by the shaded pixels. Explain which position is the best match. (10 points)

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5 template matching 20 points 26 3 184 75 80 128 72 0 84 89 65 0 200 224 18 170 26 54 47 75 127 52 94 26 68 43 199 81 87 86 0 97 3 9 208 218 23 12 188 176 180 1 2 6 3 0 80 54 39 31 22 40 9 2 64644

Added by Luisa M.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Sri K

09/29/2023

Step 1

The three positions in the image are indicated by the shaded pixels. Let's denote these positions as $P_1$, $P_2$, and $P_3$. $P_1$: Top-middle $P_2$: Middle-middle $P_3$: Bottom-middle The template $T$ is: ``` 3 10 20 18 1 5 2 30 3 ``` $P_1$: ``` 72 0 84 26 Show more…

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5 Template Matching (20 points) 26 3 184 75 80 128 72 0 84 89 65 0 200 224 18 170 26 54 47 75 127 52 94 26 68 43 199 81 87 86 0 97 3 9 208 218 23 12 188 176 180 1 2 6 3 0 80 54 39 31 22 40 9 2 5 21 9 12 98 176 211 105 9 3 10 20 18 1 5 2 30 3 Figure 1: Left: gray scale values of a 7 × 9 image. Right: gray scale values of a 3 × 3 template. As shown in Figure 1, we have an image and a template. To determine which one of the three positions in the image indicated by the shaded pixels best matches the template, we can use either Sum of squared difference (SSD) or Normalized cross correlation (NCC). Do zero padding at the border if necessary. 1. Compute the sum of squared difference (SSD) at the three positions indicated by the shaded pixels. Explain which position is the best match. (10 points) 2. Compute the normalized cross correlation (NCC) at the three positions indicated by the shaded pixels. Explain which position is the best match. (10 points)

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Transcript

00:01 So, we have been given f is equals to in the matrix form 9 9 9 0 0 9 0 0 9 and g is equals to 0 0 0 9 9 0 9 9 0.

00:23 Let us find out a part.

00:25 So, we have to find correlation between the two patches.

00:29 So, correlation between the two patches would be equals to submission from i comma j belongs to real numbers f of i j multiplied by g of i f sorry i j i comma j.

00:51 So, when we substitute in the values in the submission we get the answer to be c of f g or we can say correlation between the patches and g is equals to 0 and that would be our answer for part a.

01:10 Now, let us talk about part b.

01:12 So, when we talk about part b we have to find the ssd score.

01:17 So, to find for finding the ssd score ssd is equals to submission of where i comma j belongs to real numbers and inside submission we have f of i j minus g of i j whole square.

01:39 So, again we substitute in the values.

01:42 So, our ssd comes out to be equals to 720 and that would be our answer for ssd score.

01:51 Now, let us find the normal correlation coefficient.

01:57 So, our normal correlation coefficient will be coefficient will be basically we are denoting it the mcc.

02:13 So, mcc of f comma j would be equal to c of f g of f cap and g cap is equals to submission of i comma j belongs to real numbers f cap i of j i comma j and g cap i comma j...

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