IoU (Intersection over Union) in Computer Vision - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding IoU Calculation

Given two bounding boxes, what does the Intersection over Union (IoU) metric measure?

A The sum of the areas of the two boxes without considering overlap.

B The ratio of the overlapping area of the two boxes to the total area covered by both boxes combined.

C The difference between the areas of the two boxes.

D The ratio of the smaller box area to the larger box area.

💡 Hint

Think about how much two boxes overlap compared to their combined size.

IoU measures how much two bounding boxes overlap by dividing the area of their intersection by the area of their union.

❓ Predict Output

intermediate

Calculate IoU for Two Boxes

What is the output of the following Python code that calculates IoU for two bounding boxes?

Computer Vision

def iou(box1, box2):
    x_left = max(box1[0], box2[0])
    y_top = max(box1[1], box2[1])
    x_right = min(box1[2], box2[2])
    y_bottom = min(box1[3], box2[3])

    if x_right < x_left or y_bottom < y_top:
        return 0.0

    intersection_area = (x_right - x_left) * (y_bottom - y_top)

    box1_area = (box1[2] - box1[0]) * (box1[3] - box1[1])
    box2_area = (box2[2] - box2[0]) * (box2[3] - box2[1])

    iou_value = intersection_area / float(box1_area + box2_area - intersection_area)
    return round(iou_value, 2)

box1 = [1, 1, 4, 4]
box2 = [2, 2, 5, 5]
print(iou(box1, box2))

A 0.14

B 0.25

C 0.11

D 0.29

💡 Hint

Calculate intersection and union areas carefully.

The intersection area is 2x2=4, box1 area is 3x3=9, box2 area is 3x3=9, so IoU = 4 / (9+9-4) = 4/14 ≈ 0.2857 rounded to 0.29.

❓ Model Choice

advanced

Choosing IoU Threshold for Object Detection

In object detection, which IoU threshold is commonly used to decide if a predicted bounding box is a true positive?

A 0.1

B 0.75

C 0.5

D 0.9

💡 Hint

Think about a balance between strictness and leniency in overlap.

An IoU threshold of 0.5 is commonly used to consider a predicted box as a correct detection, balancing precision and recall.

❓ Metrics

advanced

Effect of IoU Threshold on Precision and Recall

What happens to precision and recall when the IoU threshold for true positive detection is increased from 0.5 to 0.75?

A Precision increases, recall decreases

B Precision decreases, recall increases

C Both precision and recall increase

D Both precision and recall decrease

💡 Hint

Higher IoU threshold means stricter matching.

Increasing IoU threshold makes it harder for predictions to count as true positives, so recall drops but precision improves because fewer false positives are counted.

🔧 Debug

expert

Debugging IoU Calculation Code

What error does the following IoU calculation code produce when run, and why?

Computer Vision

def iou(box1, box2):
    x_left = min(box1[0], box2[0])
    y_top = min(box1[1], box2[1])
    x_right = max(box1[2], box2[2])
    y_bottom = max(box1[3], box2[3])

    if x_right < x_left or y_bottom < y_top:
        return 0.0

    intersection_area = (x_right - x_left) * (y_bottom - y_top)

    box1_area = (box1[2] - box1[0]) * (box1[3] - box1[1])
    box2_area = (box2[2] - box2[0]) * (box2[3] - box2[1])

    iou_value = intersection_area / float(box1_area + box2_area - intersection_area)
    return iou_value

box1 = [1, 1, 4, 4]
box2 = [2, 2, 5, 5]
print(iou(box1, box2))

A The code returns IoU greater than 1 because it uses min and max incorrectly for intersection coordinates.

B The code raises a ZeroDivisionError because intersection_area is zero.

C The code returns zero because the boxes do not overlap.

D The code runs correctly and returns the correct IoU.

💡 Hint

Check how intersection coordinates are calculated.

The code uses min for left and top and max for right and bottom, which calculates the union box, not the intersection. This causes intersection_area to be larger than actual intersection, leading to IoU > 1 which is invalid.

Practice

1. What does IoU (Intersection over Union) measure in computer vision?

easy

A. The overlap between two bounding boxes

B. The distance between two points

C. The brightness of an image

D. The number of pixels in an image

Solution

1. Step 1: Understand IoU definition

   IoU measures how much two areas overlap compared to their total combined area.

2. Step 2: Identify what IoU compares

   It compares two bounding boxes or regions to see how well they match.

3. Final Answer:

   The overlap between two bounding boxes -> Option A

4. Quick Check:

   IoU = Overlap / Union [OK]

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

Common Mistakes:

• Confusing IoU with distance metrics
• Thinking IoU measures brightness or color
• Assuming IoU can be greater than 1

2. Which of the following is the correct formula for IoU between two boxes A and B?

easy

A. Area(A) + Area(B)

B. Area(A ∩ B) / Area(A ∪ B)

C. Area(A ∪ B) / Area(A ∩ B)

D. Area(A) - Area(B)

Solution

1. Step 1: Recall IoU formula

   IoU is defined as the intersection area divided by the union area of two boxes.

2. Step 2: Match formula to options

   Area(A ∩ B) / Area(A ∪ B) correctly shows IoU = Area of intersection over area of union.

3. Final Answer:

   Area(A ∩ B) / Area(A ∪ B) -> Option B

4. Quick Check:

   IoU = Intersection / Union [OK]

Hint: IoU = Intersection area ÷ Union area [OK]

Common Mistakes:

• Swapping numerator and denominator
• Adding areas instead of dividing
• Subtracting areas instead of dividing

3. Given two bounding boxes: Box A with area 20, Box B with area 30, and their intersection area is 10, what is the IoU?

medium

A. 0.25

B. 0.33

C. 0.5

D. 0.67

Solution

1. Step 1: Calculate union area

   Union = Area(A) + Area(B) - Intersection = 20 + 30 - 10 = 40.

2. Step 2: Calculate IoU

   IoU = Intersection / Union = 10 / 40 = 0.25.

3. Final Answer:

   0.25 -> Option A

4. Quick Check:

   IoU = 10/40 = 0.25 [OK]

Hint: IoU = Intersection ÷ (A + B - Intersection) [OK]

Common Mistakes:

• Forgetting to subtract intersection in union
• Using sum of areas as union
• Mixing up intersection and union values

4. Consider this Python code to compute IoU:

def iou(area_a, area_b, intersection):
    union = area_a + area_b + intersection
    return intersection / union

print(iou(15, 25, 5))

What is the error in this code?

medium

A. Function should return union instead of IoU

B. Intersection should be added twice in union

C. Division should be union divided by intersection

D. Union is calculated incorrectly by adding intersection instead of subtracting

Solution

1. Step 1: Check union calculation

   Union should be area_a + area_b - intersection, not plus intersection.

2. Step 2: Identify impact on IoU

   Adding intersection inflates union, making IoU smaller than correct value.

3. Final Answer:

   Union is calculated incorrectly by adding intersection instead of subtracting -> Option D

4. Quick Check:

   Union = A + B - Intersection [OK]

Hint: Union = sum of areas minus intersection [OK]

Common Mistakes:

• Adding intersection instead of subtracting
• Swapping numerator and denominator
• Returning union instead of IoU

5. You have two predicted bounding boxes and one ground truth box. Box1 IoU with ground truth is 0.6, Box2 IoU is 0.4. If the threshold for a correct detection is 0.5, which box is considered a correct detection and why?

hard

A. Both boxes are correct because any IoU > 0 counts

B. Only Box2 is correct because it has lower IoU

C. Only Box1 is correct because its IoU is above 0.5

D. Neither box is correct because threshold is 0.7

Solution

1. Step 1: Understand IoU threshold meaning

   Threshold 0.5 means IoU must be at least 0.5 to count as correct detection.

2. Step 2: Compare IoU values to threshold

   Box1 IoU = 0.6 > 0.5 (correct), Box2 IoU = 0.4 < 0.5 (incorrect).

3. Final Answer:

   Only Box1 is correct because its IoU is above 0.5 -> Option C

4. Quick Check:

   IoU ≥ 0.5 means correct detection [OK]

Hint: IoU must meet threshold to be correct detection [OK]

Common Mistakes:

• Ignoring threshold and accepting all IoUs
• Confusing higher IoU as incorrect
• Using wrong threshold value