Bounding box representation in Computer Vision - Model Metrics & Evaluation

Metrics & Evaluation - Bounding box representation

Which metric matters for Bounding Box Representation and WHY

In object detection, bounding boxes show where objects are in images. The key metric is Intersection over Union (IoU). It measures how much the predicted box overlaps the true box. A higher IoU means better prediction. IoU helps us know if the box is placed well and sized correctly.

Confusion matrix or equivalent visualization

Bounding box evaluation uses IoU threshold to decide if a prediction is correct (True Positive) or wrong (False Positive). For example:

    Ground Truth Box: [x1=30, y1=40, x2=70, y2=80]
    Predicted Box:    [x1=35, y1=45, x2=75, y2=85]

    IoU = Area of Overlap / Area of Union

    If IoU >= 0.5, count as True Positive (TP)
    Else, count as False Positive (FP)

    Confusion counts:
    TP = 1
    FP = 0
    FN = 0 (missed boxes)
    TN = Not used in bounding box detection
    

Precision vs Recall tradeoff with concrete examples

Precision means how many predicted boxes are correct. High precision means few false boxes.

Recall means how many true boxes are found. High recall means few missed objects.

Example:

• If you want to avoid false alarms (like detecting a cat where there is none), focus on high precision.
• If you want to find all objects (like spotting every car in traffic), focus on high recall.

Usually, increasing recall lowers precision and vice versa. IoU threshold tuning affects this tradeoff.

What "good" vs "bad" metric values look like for Bounding Box Representation

Good: IoU >= 0.7 means boxes overlap well. Precision and recall above 0.8 show reliable detection.

Bad: IoU < 0.5 means poor overlap. Precision or recall below 0.5 means many wrong or missed boxes.

Example: IoU = 0.3 means predicted box barely covers the object, so detection is poor.

Metrics pitfalls

• Ignoring IoU threshold: Counting all predicted boxes as correct without overlap check leads to falsely high accuracy.
• Data leakage: Testing on images seen during training inflates metrics.
• Overfitting: Model predicts training boxes perfectly but fails on new images, causing low recall.
• Confusing precision and recall: High precision but low recall means many objects missed.

Self-check

Your model has 98% accuracy but average IoU of 0.4 and recall of 30%. Is it good?

Answer: No. High accuracy here is misleading because accuracy does not reflect bounding box quality. IoU of 0.4 is low, meaning boxes poorly overlap objects. Recall of 30% means many objects are missed. The model needs improvement to detect objects correctly and completely.

Key Result

Intersection over Union (IoU) is the key metric to measure bounding box quality, balancing precision and recall for good object detection.

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