Question

An image analyst classifies an image into three classes, namely, water, vegetation and urban, using a simple classification technique. Using the reference data (ground truth) and classified data, the analyst prepares an error matrix, as shown in the table, and calculates accuracy values (Rounded off to the nearest integer value). Which of the following options is/are CORRECT?

		Reference data
	Land-cover classes	Water	Vegetation	Urban
Classification data	Water	48	12	10
	Vegetation	8	16	16
	Urban	14	12	84

• A. Overall accuracy is 67%
• B. Producer's and User's accuracy values in case of water class are equal
• C. In case of urban class, Producer's accuracy is 20% and User's accuracy is 13%
• D. In case of vegetation class, Producer's accuracy is 20% and User's accuracy is 11%

Hint:

Overall accuracy = diagonal sum / N; Producer's accuracy = diagonal/column total; User's accuracy = diagonal/row total.

Answer 1

The Correct Option is A, B

Step 1: Read the error matrix and compute the row and column totals.
Row totals: Water = 48+12+10 = 70, Vegetation = 8+16+16 = 40, Urban = 14+12+84 = 110. Column totals: Water = 48+8+14 = 70, Vegetation = 12+16+12 = 40, Urban = 10+16+84 = 110. Grand total \(N=70+40+110=220\), consistent from both directions.
Step 2: Compute overall accuracy and check option (A).
Diagonal sum = 48+16+84 = 148. \[ OA=\dfrac{148}{220}\times100\%=67.27\%\approx67\% \] matching option (A), so (A) is correct.
Step 3: Compute Producer's and User's accuracy for water and check option (B).
Producer's accuracy = diagonal/column total = \(48/70=68.57\%\approx69\%\). User's accuracy = diagonal/row total = \(48/70=68.57\%\approx69\%\). Since the water row total and column total are both 70, the two accuracies are numerically identical, so option (B) is correct.
Step 4: Compute for urban and check option (C).
Producer's accuracy = \(84/110=76.36\%\approx76\%\); User's accuracy = \(84/110=76.36\%\approx76\%\). Option (C)'s claimed 20% and 13% match neither, so (C) is incorrect.
Step 5: Compute for vegetation and check option (D).
Producer's accuracy = \(16/40=40\%\); User's accuracy = \(16/40=40\%\). Option (D)'s claimed 20% and 11% do not match the correct 40%, so (D) is incorrect.
Step 6: Conclusion.
Overall accuracy is 67% and the water class has equal Producer's and User's accuracy.\[ \boxed{\text{(A) and (B) are correct}} \]