IoU (Intersection over Union) in Computer Vision - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the area of a bounding box given its coordinates.

Computer Vision

def box_area(x1, y1, x2, y2):
    return (x2 - x1) [1] (y2 - y1)

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

A*

B-

C+

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition instead of multiplication.

Subtracting the coordinates incorrectly.

The area of a rectangle is width times height, so we multiply the width (x2 - x1) by the height (y2 - y1).

2fill in blank

medium

Complete the code to find the coordinates of the intersection box between two bounding boxes.

Computer Vision

def intersection_box(boxA, boxB):
    x_left = max(boxA[0], boxB[0])
    y_top = max(boxA[1], boxB[1])
    x_right = min(boxA[2], boxB[2])
    y_bottom = [1](boxA[3], boxB[3])
    return x_left, y_top, x_right, y_bottom

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

Amax

Bsum

Cabs

Dmin

Attempts:

3 left

💡 Hint

Common Mistakes

Using max instead of min for bottom coordinate.

Mixing up x and y coordinates.

The bottom coordinate of the intersection is the minimum of the two boxes' bottom y-coordinates.

3fill in blank

hard

Fix the error in the code that calculates the intersection area of two bounding boxes.

Computer Vision

def intersection_area(boxA, boxB):
    x_left, y_top, x_right, y_bottom = intersection_box(boxA, boxB)
    if x_right < x_left or y_bottom < y_top:
        return 0
    return (x_right - x_left) [1] (y_bottom - y_top)

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

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition instead of multiplication.

Returning negative area values.

The intersection area is width times height, so multiply the differences in x and y.

4fill in blank

hard

Fill both blanks to compute the union area of two bounding boxes.

Computer Vision

def union_area(boxA, boxB):
    areaA = box_area(*boxA)
    areaB = box_area(*boxB)
    inter_area = intersection_area(boxA, boxB)
    return areaA [1] areaB [2] inter_area

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

A+

B-

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Adding intersection area instead of subtracting.

Multiplying areas instead of adding.

The union area is the sum of both areas minus the intersection area to avoid double counting.

5fill in blank

hard

Fill all three blanks to complete the IoU calculation function.

Computer Vision

def iou(boxA, boxB):
    inter_area = intersection_area(boxA, boxB)
    union = union_area(boxA, boxB)
    if union == 0:
        return 0
    return [3](inter_area [1] union [2] 1.0)

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

A/

B*

C==

Dfloat

Attempts:

3 left

💡 Hint

Common Mistakes

Using equality (==) instead of division (/).

Not converting to float causing integer division.

IoU is intersection area divided by union area. Multiplying by 1.0 and converting to float ensures a float result.

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