Segmentation evaluation (IoU, Dice) in Computer Vision - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Calculate IoU for two binary masks

Given two binary masks representing segmentation results, what is the output of the following code calculating the Intersection over Union (IoU)?

Computer Vision

import numpy as np
mask1 = np.array([[1, 0, 1], [0, 1, 0], [1, 0, 0]])
mask2 = np.array([[1, 1, 0], [0, 1, 0], [1, 0, 1]])
intersection = np.logical_and(mask1, mask2).sum()
union = np.logical_or(mask1, mask2).sum()
iou = intersection / union
print(round(iou, 2))

A 0.43

B 0.50

C 0.57

D 0.67

💡 Hint

Count how many pixels overlap and how many pixels are in either mask.

IoU is the ratio of overlapping pixels (intersection) to total pixels covered by either mask (union). Here, intersection is 3 and union is 6, so IoU = 3/6 = 0.50.

🧠 Conceptual

intermediate

Understanding Dice coefficient properties

Which of the following statements about the Dice coefficient is TRUE?

A Dice coefficient can be negative if masks have no overlap.

B Dice coefficient measures the difference between masks, not overlap.

C Dice coefficient is always smaller than IoU for the same masks.

D Dice coefficient equals 1 when two masks are identical.

💡 Hint

Think about what perfect overlap means for Dice.

Dice coefficient ranges from 0 to 1, with 1 meaning perfect overlap (identical masks). It cannot be negative. Dice is usually larger than IoU for the same masks.

❓ Metrics

advanced

Calculate Dice coefficient from confusion matrix values

Given true positives (TP)=30, false positives (FP)=10, and false negatives (FN)=20, what is the Dice coefficient?

A 0.67

B 0.60

C 0.75

D 0.80

💡 Hint

Dice = 2 * TP / (2 * TP + FP + FN)

Dice = 2*30 / (2*30 + 10 + 20) = 60 / 90 = 0.67

🔧 Debug

advanced

Identify the error in IoU calculation code

What error does the following code produce when calculating IoU for two numpy arrays mask1 and mask2?

Computer Vision

intersection = (mask1 & mask2).sum()
union = (mask1 | mask2).sum()
iou = intersection / union
print(iou)

A ZeroDivisionError if union is zero

B ValueError due to shape mismatch of mask1 and mask2

C TypeError because bitwise operators cannot be used on numpy arrays

D No error, code runs correctly and prints IoU

💡 Hint

Consider what happens if both masks are empty.

If both masks are empty, union is zero causing division by zero error.

❓ Model Choice

expert

Choosing the best metric for imbalanced segmentation

You have a segmentation task where the object occupies only 1% of the image pixels. Which metric is most reliable to evaluate your model's performance?

A IoU, because it balances false positives and false negatives

B Accuracy, because it measures overall pixel correctness

C Dice coefficient, because it is sensitive to small object overlap

D Mean Squared Error, because it measures pixel intensity differences

💡 Hint

Think about which metric handles small object sizes better.

Dice coefficient is more sensitive to overlap in small objects and less biased by large background pixels than accuracy or MSE.

Practice

1. What does the Intersection over Union (IoU) metric measure in image segmentation?

easy

A. The overlap between predicted and true masks divided by their union

B. The difference between predicted and true masks

C. The total number of pixels in the predicted mask

D. The ratio of true positives to false negatives

Solution

1. Step 1: Understand IoU definition

   IoU measures how much the predicted mask and true mask overlap compared to their combined area.

2. Step 2: Apply IoU formula

   IoU = (Area of Overlap) / (Area of Union) between predicted and true masks.

3. Final Answer:

   The overlap between predicted and true masks divided by their union -> Option A

4. Quick Check:

   IoU = Overlap / Union [OK]

Hint: IoU = Overlap divided by combined area [OK]

Common Mistakes:

• Confusing IoU with difference or subtraction
• Using only predicted mask area
• Mixing IoU with accuracy or precision

2. Which of the following is the correct formula for Dice coefficient between predicted mask P and true mask T?

easy

A. Dice = |P| / |T|

B. Dice = (2 * |P ∩ T|) / (|P| + |T|)

C. Dice = |P ∪ T| / (|P| + |T|)

D. Dice = |P ∩ T| / |P ∪ T|

Solution

1. Step 1: Recall Dice coefficient formula

   Dice coefficient is defined as twice the overlap divided by the sum of sizes of predicted and true masks.

2. Step 2: Match formula to options

   Dice = (2 * |P ∩ T|) / (|P| + |T|) matches Dice = (2 * intersection) / (sum of areas).

3. Final Answer:

   Dice = (2 * |P ∩ T|) / (|P| + |T|) -> Option B

4. Quick Check:

   Dice = 2*Overlap / (Sum areas) [OK]

Hint: Dice doubles overlap, divides by sum of mask sizes [OK]

Common Mistakes:

• Confusing Dice with IoU formula
• Using union instead of sum of areas
• Forgetting to multiply overlap by 2

3. Given predicted mask pixels: {1,2,3,4} and true mask pixels: {3,4,5,6}, what is the IoU score?

medium

A. 0.33

B. 0.25

C. 0.5

D. 0.4

Solution

1. Step 1: Calculate intersection and union

   Intersection = {3,4} size = 2; Union = {1,2,3,4,5,6} size = 6.

2. Step 2: Compute IoU

   IoU = Intersection / Union = 2 / 6 = 0.3333 (approx). Check options carefully.

3. Step 3: Re-check options

   0.33 is 0.33, closest to calculation. But 0.4 is 0.4, which is incorrect.

4. Final Answer:

   0.33 -> Option A

5. Quick Check:

   IoU = 2/6 = 0.33 [OK]

Hint: IoU = intersection size / union size [OK]

Common Mistakes:

• Counting union incorrectly
• Mixing intersection with union
• Rounding IoU incorrectly

4. You have this Python code to compute Dice score but it returns 0. Identify the error:

def dice_score(pred, true):
    intersection = len(pred & true)
    return intersection / (len(pred) + len(true))

pred = {1,2,3}
true = {2,3,4}
print(dice_score(pred, true))

medium

A. Wrong variable names in function

B. Using set intersection instead of union

C. Incorrect data type for masks

D. Missing multiplication by 2 in numerator

Solution

1. Step 1: Review Dice formula

   Dice = 2 * intersection / (sum of sizes). The code misses multiplying intersection by 2.

2. Step 2: Check code calculation

   Code returns intersection / sum, which is half the correct Dice score.

3. Final Answer:

   Missing multiplication by 2 in numerator -> Option D

4. Quick Check:

   Dice needs 2*intersection [OK]

Hint: Dice numerator must be 2 times intersection [OK]

Common Mistakes:

• Forgetting to multiply intersection by 2
• Confusing intersection with union
• Using wrong data types for masks

5. A segmentation model predicts a mask with 80 pixels, the true mask has 100 pixels, and their overlap is 60 pixels. What is the Dice score and IoU score respectively?

hard

A. Dice = 0.8, IoU = 0.7

B. Dice = 0.75, IoU = 0.6

C. Dice = 0.67, IoU = 0.5

D. Dice = 0.6, IoU = 0.75

Solution

1. Step 1: Calculate Dice score

   Dice = 2 * overlap / (predicted + true) = 2*60 / (80+100) = 120/180 = 0.6667 (approx). Check options carefully.

2. Step 2: Calculate IoU score

   IoU = overlap / union = 60 / (80 + 100 - 60) = 60 / 120 = 0.5.

3. Step 3: Re-check options

   Dice = 0.67, IoU = 0.5 matches Dice ~0.67 and IoU 0.5 exactly.

4. Final Answer:

   Dice = 0.67, IoU = 0.5 -> Option C

5. Quick Check:

   Dice = 2*60/180=0.67, IoU=60/120=0.5 [OK]

Hint: Dice doubles overlap; IoU divides by union [OK]

Common Mistakes:

• Using sum instead of union for IoU denominator
• Forgetting to multiply overlap by 2 for Dice
• Mixing Dice and IoU formulas