If we threshold an image to try to isolate an object, the pixels that are 'selected' by our threshold may or may not be part of the desired object. Given the confusion matrix below... If we threshold an image to try to isolate an object, the pixels that are 'selected' by our threshold may or may not be part of the desired object. Given the confusion matrix below, indicate the percentage of correctly labelled pixels (enter your answer to 2 decimal places). Read more

Steps to Solve

1. Identify True Positives and True Negatives

From the confusion matrix, we have:

• True Positives (TP): Pixels correctly labeled as part of the object = 66
• True Negatives (TN): Pixels correctly labeled as not part of the object = 52

2. Calculate Total Correctly Labeled Pixels

Add the true positives and true negatives:
$$ \text{Total Correct} = TP + TN = 66 + 52 = 118 $$

3. Calculate Total Pixels

Calculate the total number of pixels by adding all values in the confusion matrix:

• Total pixels = TP + False Positives (FP) + False Negatives (FN) + TN
• False Positives (FP): 21 (selected but not part of the object)
• False Negatives (FN): 70 (not selected but part of the object)
• Total = $66 + 21 + 70 + 52 = 209$

4. Calculate Percentage of Correctly Labeled Pixels

Using the total correctly labeled pixels and the total pixels, the percentage is calculated as follows:
$$ \text{Percentage} = \left( \frac{\text{Total Correct}}{\text{Total Pixels}} \right) \times 100 $$ Substituting the values:
$$ \text{Percentage} = \left( \frac{118}{209} \right) \times 100 \approx 56.49 $$

5. Round to Two Decimal Places

The final answer should be rounded to two decimal places:
$$ \text{Percentage} \approx 56.49% $$