Bounding box representation in Computer Vision - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding bounding box formats

Which of the following bounding box representations uses the coordinates of the top-left corner and the width and height of the box?

A XYWH format

B XYXY format

C Center coordinates with width and height

D Normalized coordinates between 0 and 1

💡 Hint

Think about which format explicitly mentions width and height.

The XYWH format specifies the bounding box by the top-left corner coordinates (X, Y) and the width (W) and height (H) of the box.

❓ Predict Output

intermediate

Output of bounding box conversion code

What is the output of this Python code converting a bounding box from XYWH to XYXY format? box_xywh = [50, 30, 100, 200] box_xyxy = [box_xywh[0], box_xywh[1], box_xywh[0] + box_xywh[2], box_xywh[1] + box_xywh[3]] print(box_xyxy)

Computer Vision

box_xywh = [50, 30, 100, 200]
box_xyxy = [box_xywh[0], box_xywh[1], box_xywh[0] + box_xywh[2], box_xywh[1] + box_xywh[3]]
print(box_xyxy)

A [0, 0, 150, 230]

B [50, 30, 100, 200]

C [50, 30, 150, 230]

D [50, 30, 50, 30]

💡 Hint

Add width to x and height to y to get bottom-right corner.

The bottom-right corner is calculated by adding width to x and height to y, so (50+100, 30+200) = (150, 230).

❓ Model Choice

advanced

Choosing bounding box format for object detection model

You are designing an object detection model that predicts bounding boxes. Which bounding box representation is most suitable for regression output in a neural network?

A Top-left and bottom-right corners (x1, y1, x2, y2)

B Center coordinates with width and height (cx, cy, w, h)

C Polygon points around the object

D Binary mask of the object

💡 Hint

Think about what is easier for a network to predict smoothly.

Center coordinates with width and height are continuous and easier for regression, making them suitable for neural network outputs.

❓ Metrics

advanced

Evaluating bounding box predictions with IoU

What does an Intersection over Union (IoU) score of 0.75 between a predicted bounding box and the ground truth indicate?

A The predicted box overlaps 75% with the ground truth box

B The predicted box is 75% larger than the ground truth box

C The predicted box is 75% smaller than the ground truth box

D The predicted box and ground truth box do not overlap

💡 Hint

IoU measures overlap area divided by union area.

IoU is the ratio of the overlapping area to the combined area of both boxes. A score of 0.75 means 75% overlap.

🔧 Debug

expert

Debugging bounding box normalization error

Given an image of size 200x100 pixels and a bounding box [50, 20, 150, 80] in XYXY format, a developer tries to normalize the box coordinates by dividing by image width and height as follows: normalized_box = [50/100, 20/200, 150/100, 80/200] What is the main issue with this normalization approach?

A The box coordinates are not in XYXY format

B The box coordinates exceed image dimensions

C The width and height are swapped in division

D The normalization should use width for x-coordinates and height for y-coordinates

💡 Hint

Check which coordinates correspond to width and height axes.

The code incorrectly divides x-coordinates by image height (100) and y-coordinates by image width (200). X-coordinates should be divided by image width (200), and y-coordinates by image height (100).

Practice

1. What does a bounding box represent in computer vision?

easy

A. The location of an object in an image using four numbers

B. The color of an object in an image

C. The texture pattern of an object

D. The size of the entire image

Solution

1. Step 1: Understand bounding box purpose

   A bounding box is used to locate objects visually in an image.

2. Step 2: Identify bounding box representation

   It uses four numbers to mark the top-left and bottom-right corners of the object.

3. Final Answer:

   The location of an object in an image using four numbers -> Option A

4. Quick Check:

   Bounding box = object location [OK]

Hint: Bounding box = 4 numbers marking object edges [OK]

Common Mistakes:

• Confusing bounding box with color or texture
• Thinking bounding box covers the whole image
• Believing bounding box uses only two numbers

2. Which of the following is the correct order of values in a bounding box representation?

easy

A. (bottom-left x, bottom-left y, top-right x, top-right y)

B. (center x, center y, width, height)

C. (width, height, top-left x, top-left y)

D. (top-left x, top-left y, bottom-right x, bottom-right y)

Solution

1. Step 1: Recall bounding box corner points

   The bounding box is defined by the top-left and bottom-right corners.

2. Step 2: Match the correct order

   The order is (top-left x, top-left y, bottom-right x, bottom-right y).

3. Final Answer:

   (top-left x, top-left y, bottom-right x, bottom-right y) -> Option D

4. Quick Check:

   Bounding box corners = top-left and bottom-right [OK]

Hint: Bounding box uses top-left then bottom-right coordinates [OK]

Common Mistakes:

• Mixing center coordinates with corner points
• Swapping bottom-left with top-left
• Using width and height before coordinates

3. Given a bounding box with coordinates (10, 20, 50, 80), what is the width and height of the box?

medium

A. Width = 40, Height = 60

B. Width = 60, Height = 40

C. Width = 50, Height = 80

D. Width = 30, Height = 50

Solution

1. Step 1: Calculate width from x-coordinates

   Width = bottom-right x - top-left x = 50 - 10 = 40.

2. Step 2: Calculate height from y-coordinates

   Height = bottom-right y - top-left y = 80 - 20 = 60.

3. Final Answer:

   Width = 40, Height = 60 -> Option A

4. Quick Check:

   Width = 50-10, Height = 80-20 [OK]

Hint: Width = x2 - x1, Height = y2 - y1 [OK]

Common Mistakes:

• Swapping width and height values
• Adding coordinates instead of subtracting
• Using top-left y for width calculation

4. Identify the error in this bounding box definition: bbox = (x1=30, y1=40, x2=20, y2=70)

medium

A. y2 should be less than y1

B. x2 is less than x1, which is invalid for bounding boxes

C. Coordinates must be strings, not integers

D. Bounding box must have five values, not four

Solution

1. Step 1: Check coordinate order validity

   Bounding box requires bottom-right x (x2) to be greater than top-left x (x1).

2. Step 2: Identify the error

   Here, x2=20 is less than x1=30, which is invalid and would cause errors in drawing or calculations.

3. Final Answer:

   x2 is less than x1, which is invalid for bounding boxes -> Option B

4. Quick Check:

   x2 must be > x1 for valid box [OK]

Hint: Bottom-right x must be greater than top-left x [OK]

Common Mistakes:

• Ignoring coordinate order rules
• Thinking y2 must be less than y1
• Assuming bounding box needs 5 values

5. You have bounding boxes in the format (center_x, center_y, width, height). How do you convert them to (top-left x, top-left y, bottom-right x, bottom-right y)?

hard

A. top-left x = center_x; top-left y = center_y; bottom-right x = width; bottom-right y = height

B. top-left x = center_x + width/2; top-left y = center_y + height/2; bottom-right x = center_x - width/2; bottom-right y = center_y - height/2

C. top-left x = center_x - width/2; top-left y = center_y - height/2; bottom-right x = center_x + width/2; bottom-right y = center_y + height/2

D. top-left x = width/2; top-left y = height/2; bottom-right x = center_x; bottom-right y = center_y

Solution

1. Step 1: Understand center to corner conversion

   Center coordinates are in the middle of the box; to get corners, subtract half width/height for top-left.

2. Step 2: Calculate corners from center and size

   Top-left x = center_x - width/2; top-left y = center_y - height/2; bottom-right x = center_x + width/2; bottom-right y = center_y + height/2.

3. Final Answer:

   top-left x = center_x - width/2; top-left y = center_y - height/2; bottom-right x = center_x + width/2; bottom-right y = center_y + height/2 -> Option C

4. Quick Check:

   Center ± half size = corners [OK]

Hint: Corners = center ± half width/height [OK]

Common Mistakes:

• Adding half width to top-left instead of subtracting
• Swapping top-left and bottom-right calculations
• Using width and height as coordinates directly