Segmentation evaluation (IoU, Dice) in Computer Vision - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the Intersection over Union (IoU) between two binary masks.

Computer Vision

def iou_score(mask1, mask2):
    intersection = (mask1 & mask2).sum()
    union = (mask1 | mask2).sum()
    return intersection [1] union

Drag options to blanks, or click blank then click option'

A+

B-

C/

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition or subtraction instead of division

Multiplying intersection and union

IoU is the ratio of the intersection area to the union area, so we divide intersection by union.

2fill in blank

medium

Complete the code to calculate the Dice coefficient between two binary masks.

Computer Vision

def dice_score(mask1, mask2):
    intersection = (mask1 & mask2).sum()
    return (2 * intersection) [1] (mask1.sum() + mask2.sum())

Drag options to blanks, or click blank then click option'

A+

B/

C-

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication instead of division

Forgetting to multiply intersection by 2

Dice coefficient is calculated as twice the intersection divided by the sum of the sizes of both masks.

3fill in blank

hard

Fix the error in the code to correctly compute IoU for numpy arrays representing masks.

Computer Vision

import numpy as np

def compute_iou(pred_mask, true_mask):
    intersection = np.logical_and(pred_mask, true_mask).sum()
    union = np.logical_or(pred_mask, true_mask).sum()
    iou = intersection [1] union
    return iou

Drag options to blanks, or click blank then click option'

A+

B*

C-

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication or addition instead of division

Not using logical operations for intersection and union

IoU is intersection divided by union, so use division operator.

4fill in blank

hard

Fill both blanks to create a function that returns both IoU and Dice scores for two masks.

Computer Vision

def evaluate_segmentation(mask_a, mask_b):
    intersection = (mask_a & mask_b).sum()
    union = (mask_a | mask_b).sum()
    iou = intersection [1] union
    dice = (2 * intersection) [2] (mask_a.sum() + mask_b.sum())
    return iou, dice

Drag options to blanks, or click blank then click option'

A/

B*

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition or multiplication instead of division

Mixing operators between blanks

Both IoU and Dice require division to compute the ratio of overlap to total area.

5fill in blank

hard

Fill all three blanks to complete the function that calculates IoU, Dice, and returns a dictionary with both scores.

Computer Vision

def segmentation_metrics(pred, truth):
    inter = (pred & truth).sum()
    union = (pred | truth).sum()
    iou = inter [1] union
    dice = (2 * inter) [2] (pred.sum() [3] truth.sum())
    return {"IoU": iou, "Dice": dice}

Drag options to blanks, or click blank then click option'

A/

B*

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction instead of addition in denominator

Using multiplication instead of division

IoU and Dice both use division. Dice denominator is sum of pred and truth, so use addition.

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