Bounding box handling in PyTorch - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of bounding box area calculation

What is the output of the following code that calculates the area of bounding boxes stored as (x_min, y_min, x_max, y_max)?

PyTorch

import torch
boxes = torch.tensor([[1, 2, 4, 6], [0, 0, 3, 3], [2, 2, 5, 5]])
widths = boxes[:, 2] - boxes[:, 0]
heights = boxes[:, 3] - boxes[:, 1]
areas = widths * heights
print(areas.tolist())

A [15, 9, 12]

B [12, 9, 9]

C [12, 6, 9]

D [9, 9, 9]

💡 Hint

Remember area = width * height, where width = x_max - x_min and height = y_max - y_min.

The widths are [3, 3, 3] and heights are [4, 3, 3]. Multiplying element-wise gives areas [12, 9, 9].

❓ Model Choice

intermediate

Choosing the right bounding box format for IoU calculation

Which bounding box format is best suited for calculating Intersection over Union (IoU) directly without conversion?

A Top-left and bottom-right corners (x_min, y_min, x_max, y_max)

B Top-left corner with width and height (x_min, y_min, w, h)

C Center coordinates with corner points (cx, cy, x_min, y_min)

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

💡 Hint

IoU requires overlapping area calculation which is easier with corner coordinates.

The (x_min, y_min, x_max, y_max) format directly gives the corners needed to find intersection areas without extra conversion.

❓ Hyperparameter

advanced

Effect of IoU threshold on Non-Maximum Suppression (NMS)

What is the effect of increasing the IoU threshold parameter in Non-Maximum Suppression when filtering bounding boxes?

A Boxes are sorted by confidence score instead of IoU

B Fewer boxes are kept, resulting in stricter suppression

C No change in number of boxes kept

D More boxes are kept, allowing more overlapping detections

💡 Hint

Higher IoU threshold means boxes must overlap more to be suppressed.

Increasing IoU threshold means boxes with less overlap are not suppressed, so more boxes remain after NMS.

🔧 Debug

advanced

Debugging incorrect bounding box clipping

Given bounding boxes and image size, which option correctly clips boxes to image boundaries without errors?

PyTorch

import torch
boxes = torch.tensor([[50, 30, 200, 180], [-10, 20, 100, 150], [30, 40, 500, 400]])
image_size = (300, 300)  # height, width
# Clip boxes so coordinates stay within image boundaries

A

boxes[:, 0] = boxes[:, 0].clamp(0, image_size[1])
boxes[:, 1] = boxes[:, 1].clamp(0, image_size[0])
boxes[:, 2] = boxes[:, 2].clamp(0, image_size[1])
boxes[:, 3] = boxes[:, 3].clamp(0, image_size[0])

B

boxes[:, 0] = boxes[:, 0].clamp(0, image_size[0])
boxes[:, 1] = boxes[:, 1].clamp(0, image_size[1])
boxes[:, 2] = boxes[:, 2].clamp(0, image_size[0])
boxes[:, 3] = boxes[:, 3].clamp(0, image_size[1])

C

boxes[:, 0] = boxes[:, 0].clamp(0, image_size[1]-1)
boxes[:, 1] = boxes[:, 1].clamp(0, image_size[0]-1)
boxes[:, 2] = boxes[:, 2].clamp(0, image_size[1]-1)
boxes[:, 3] = boxes[:, 3].clamp(0, image_size[0]-1)

D

boxes[:, 0] = boxes[:, 0].clamp(0, image_size[0]-1)
boxes[:, 1] = boxes[:, 1].clamp(0, image_size[0]-1)
boxes[:, 2] = boxes[:, 2].clamp(0, image_size[1]-1)
boxes[:, 3] = boxes[:, 3].clamp(0, image_size[1]-1)

💡 Hint

Remember image_size is (height, width). x coordinates clamp to width, y coordinates clamp to height.

x coordinates (0 and 2) clamp to width (image_size[1]-1), y coordinates (1 and 3) clamp to height (image_size[0]-1).

🧠 Conceptual

expert

Understanding bounding box regression targets in object detection

In object detection, bounding box regression predicts offsets relative to anchor boxes. Which statement correctly describes why offsets are predicted instead of absolute coordinates?

A Offsets normalize the prediction space, making training more stable and easier to learn

B Absolute coordinates are always better because they are direct and simpler

C Offsets reduce the number of bounding boxes needed during inference

D Absolute coordinates allow the model to ignore anchor boxes completely

💡 Hint

Think about how predicting relative changes helps the model focus on small adjustments.

Predicting offsets relative to anchors normalizes the scale and position differences, improving training stability and convergence.

Practice

1. What do the four numbers in a bounding box usually represent in PyTorch object detection tasks?

easy

A. Width, height, depth, and color

B. Center x, center y, width, height

C. Top-left corner x and y, width, height

D. Left, top, right, bottom coordinates of the box

Solution

1. Step 1: Understand bounding box format

   Bounding boxes in PyTorch detection models are often represented by four numbers indicating the edges: left (x_min), top (y_min), right (x_max), and bottom (y_max).

2. Step 2: Compare options with standard format

   Left, top, right, bottom coordinates of the box matches this format exactly, while others describe different formats or unrelated values.

3. Final Answer:

   Left, top, right, bottom coordinates of the box -> Option D

4. Quick Check:

   Bounding box = left, top, right, bottom [OK]

Hint: Remember bounding box edges are left, top, right, bottom [OK]

Common Mistakes:

• Confusing center coordinates with edges
• Mixing width and height with coordinates
• Assuming depth or color are part of bounding box

2. Which PyTorch tensor shape correctly represents a batch of 5 bounding boxes, each with 4 coordinates?

easy

A. torch.Size([5, 4])

B. torch.Size([4, 5])

C. torch.Size([5])

D. torch.Size([4])

Solution

1. Step 1: Identify bounding box tensor shape

   Each bounding box has 4 coordinates. For 5 boxes, the tensor shape should be (5, 4), meaning 5 rows (boxes) and 4 columns (coordinates).

2. Step 2: Match options with correct shape

   torch.Size([5, 4]) matches (5, 4). torch.Size([4, 5]) reverses dimensions, and C and D are one-dimensional, which is incorrect.

3. Final Answer:

   torch.Size([5, 4]) -> Option A

4. Quick Check:

   Batch size 5 and 4 coords = (5, 4) [OK]

Hint: Batch size first, coordinates second in tensor shape [OK]

Common Mistakes:

• Swapping batch and coordinate dimensions
• Using 1D tensor for multiple boxes
• Confusing number of boxes with number of coordinates

3. Given the following PyTorch code, what is the output?

import torch
boxes = torch.tensor([[1, 2, 4, 6], [0, 0, 3, 3]])
widths = boxes[:, 2] - boxes[:, 0]
heights = boxes[:, 3] - boxes[:, 1]
areas = widths * heights
print(areas.tolist())

medium

A. [10, 9]

B. [15, 9]

C. [12, 9]

D. [12, 6]

Solution

1. Step 1: Calculate widths and heights

   For box 1: width = 4 - 1 = 3, height = 6 - 2 = 4. For box 2: width = 3 - 0 = 3, height = 3 - 0 = 3.

2. Step 2: Calculate areas

   Area box 1 = 3 * 4 = 12, area box 2 = 3 * 3 = 9.

3. Final Answer:

   [12, 9] -> Option C

4. Quick Check:

   Area = width * height = [12, 9] [OK]

Hint: Area = (right-left) * (bottom-top) for each box [OK]

Common Mistakes:

• Subtracting coordinates in wrong order
• Mixing width with height values
• Forgetting to multiply widths and heights

4. Identify the error in this PyTorch code snippet for checking if points lie inside bounding boxes:

import torch
boxes = torch.tensor([1, 1, 5, 5])
points = torch.tensor([[3, 3], [6, 6]])
inside = (points[:, 0] >= boxes[:, 0]) & (points[:, 0] <= boxes[:, 2]) & (points[:, 1] >= boxes[:, 1]) & (points[:, 1] <= boxes[:, 3])
print(inside)

medium

A. The comparison between points and boxes tensors will fail due to shape mismatch

B. The logical AND operator '&' cannot be used with tensors

C. The code should use .all() to combine conditions

D. Points coordinates are reversed in the comparisons

Solution

1. Step 1: Check tensor shapes for broadcasting

   Boxes shape is (4,), points shape is (2,2). Comparing points[:, 0] (shape 2) with boxes[:, 0] causes shape mismatch as boxes is 1D.

2. Step 2: Understand broadcasting rules

   Direct element-wise comparison fails because points and boxes dimensions don't align for broadcasting in this code.

3. Final Answer:

   The comparison between points and boxes tensors will fail due to shape mismatch -> Option A

4. Quick Check:

   Shape mismatch causes error in element-wise comparison [OK]

Hint: Check tensor shapes before element-wise comparisons [OK]

Common Mistakes:

• Assuming PyTorch auto-broadcasts all shapes
• Using bitwise operators incorrectly
• Mixing coordinate order in comparisons

5. You want to convert bounding boxes from (left, top, right, bottom) format to (center_x, center_y, width, height) in PyTorch. Which code snippet correctly performs this conversion for a tensor boxes of shape (N, 4)?

hard

A. centers = boxes[:, :2] - boxes[:, 2:]
sizes = boxes[:, 2:] + boxes[:, :2]
converted = torch.cat([centers, sizes], dim=1)

B. centers = (boxes[:, :2] + boxes[:, 2:]) / 2
sizes = boxes[:, 2:] - boxes[:, :2]
converted = torch.cat([centers, sizes], dim=1)

C. centers = boxes[:, 2:] - boxes[:, :2]
sizes = (boxes[:, :2] + boxes[:, 2:]) / 2
converted = torch.cat([sizes, centers], dim=1)

D. centers = boxes[:, :2] * boxes[:, 2:]
sizes = boxes[:, 2:] / boxes[:, :2]
converted = torch.cat([centers, sizes], dim=1)

Solution

1. Step 1: Calculate center coordinates

   Center x and y are the average of left and right, top and bottom: (left + right)/2, (top + bottom)/2, which is (boxes[:, :2] + boxes[:, 2:]) / 2.

2. Step 2: Calculate width and height

   Width and height are right - left and bottom - top: boxes[:, 2:] - boxes[:, :2].

3. Step 3: Concatenate centers and sizes

   Combine centers and sizes along dimension 1 to get (center_x, center_y, width, height).

4. Final Answer:

   centers = (boxes[:, :2] + boxes[:, 2:]) / 2 sizes = boxes[:, 2:] - boxes[:, :2] converted = torch.cat([centers, sizes], dim=1) -> Option B

5. Quick Check:

   Center = avg edges, size = difference edges [OK]

Hint: Center = average edges; size = difference edges [OK]

Common Mistakes:

• Swapping center and size calculations
• Using addition instead of subtraction for sizes
• Concatenating in wrong order