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Mean IoU (mIoU)

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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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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Python 3.13

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