Mean IoU (mIoU)

mediumPROSemantic SegmentationSegmentationCV: Recognition

You are given predicted and ground truth segmentation masks and need to calculate the mean Intersection over Union across all classes.

For each class c, IoU is computed as:

$IoU_c = \frac{TP_c}{TP_c + FP_c + FN_c}$

Where for class c:

TP (True Positive): pixels correctly predicted as class c
FP (False Positive): pixels incorrectly predicted as class c
FN (False Negative): pixels of class c predicted as something else

Mean IoU averages over all classes:

$mIoU = \frac{1}{C}\sum_{c=0}^{C-1} IoU_c$

Only include classes that appear in either pred or gt (skip classes with TP=FP=FN=0).

Example

Input

pred = [[0, 1], [1, 0]]
gt = [[0, 1], [0, 0]]
num_classes = 2

Output

0.5833

Reasoning

For class 0:

TP: pixels where pred=0 AND gt=0 → positions (0,0), (1,1) → 2
FP: pixels where pred=0 AND gt≠0 → none → 0
FN: pixels where pred≠0 AND gt=0 → position (1,0) → 1
IoU_0 = 2/(2+0+1) = 2/3 = 0.6667

For class 1:

TP: pixels where pred=1 AND gt=1 → position (0,1) → 1
FP: pixels where pred=1 AND gt≠1 → position (1,0) → 1
FN: pixels where pred≠1 AND gt=1 → none → 0
IoU_1 = 1/(1+1+0) = 1/2 = 0.5

mIoU = (0.6667 + 0.5) / 2 = 0.5833

Constraints

pred and gt are 2D lists of class indices
num_classes is the total number of possible classes
Return mIoU rounded to 4 decimal places
If no valid classes exist, return 0.0

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Concept primerPREVIEW

You are computing mean Intersection over Union (mIoU) over class labels for semantic segmentation masks.

1. Background Knowledge

In semantic segmentation, each pixel in an image is assigned a class label (e.g., background, road, car). A model outputs a predicted mask, and we compare it to the ground truth mask to evaluate how well it identified each class.

Intersection over Union (IoU) for a class $c$ measures how well the predicted region for that class overlaps with the true region. It is defined as:

IoU_c = \frac{| \text{prediction}_c \cap \text{ground\_truth}_c |}{| \text{prediction}_c \cup \text{ground\_truth}_c |}

This can be rewritten using TP, FP, FN counts for pixels of class $c$ :

IoU_c = \frac{TP_c}{TP_c + FP_c + FN_c}

Mean IoU (mIoU) is the average IoU over all classes being evaluated:

mIoU = \frac{1}{C'} \sum_{c \in \mathcal{S}} IoU_c

where $\mathcal{S}$ is the set of classes that actually appear in either prediction or ground truth (you skip classes where $TP_c = FP_c = FN_c = 0$ ).

2. Algorithm / General Approach

High-level pattern:

Loop over classes $c \in \{0, \dots, C-1\}$ .
For each class, compute TP, FP, FN by comparing pred and gt pixel-wise.
If all of TP, FP, FN are zero, skip this class (it doesn’t appear at all).
Otherwise, compute:

IoU_c = \frac{TP_c}{TP_c + FP_c + FN_c}

Collect all valid $IoU_c$ values and average them to get mIoU.

This is essentially building a per-class confusion summary (TP/FP/FN) from the full confusion matrix and then turning those into IoUs.

3. Step-by-Step Strategy

Assume pred and gt are same shape arrays of integer class labels (e.g., H x W or N x H x W).

Identify number of classes

Either given as C, or infer as max(pred.max(), gt.max()) + 1.

Optional: flatten arrays

For convenience, convert masks to 1D arrays:

pred_flat = pred.reshape(-1)
gt_flat = gt.reshape(-1)

Initialize accumulators

Arrays or dicts for TP, FP, FN per class:

TP = * C
FP = * C
FN = * C

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solution.py

Python 3.13

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