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.