Segmentation Metrics - CNNs & Computer Vision

Segmentation Metrics

What you'll build

Three standard scores for a binary segmentation mask: IoU (Jaccard index), pixel accuracy and the Dice coefficient.

Background

Segmentation models (U-Net, DeepLab, Mask R-CNN's mask head) predict a label for every pixel. Pixel accuracy is easy to read but misleading when the object is small: predicting "background everywhere" on an image that is 95% background scores 0.95. IoU and Dice only look at the foreground, so they are the metrics reported in papers and medical-imaging challenges. Dice also exists as a training loss (1 - soft Dice).

Formula

Treat each mask as the set of pixels equal to 1. With TP = |P ∩ T| (both 1), |P| = number of predicted foreground pixels, |T| = number of target foreground pixels:

IoU            = |P ∩ T| / |P ∪ T|          = TP / (|P| + |T| - TP)
Dice           = 2 |P ∩ T| / (|P| + |T|)     = 2 TP / (2 TP + FP + FN)
Pixel accuracy = (number of pixels where prediction == target) / (total pixels)

Dice is the F1 score over pixels, and the two overlap scores are linked by Dice = 2 IoU / (1 + IoU), so Dice >= IoU.

Inputs

• prediction, target: 2D arrays of the same shape (H, W) containing only 0 and 1 (any integer or float dtype).

Expected return format

A dictionary with exactly these keys, each a Python float rounded to 4 decimal places:

• 'iou': foreground intersection over union
• 'pixel_accuracy': fraction of pixels that agree (foreground and background)
• 'dice': Dice coefficient

Edge cases and conventions

• If both masks are empty (no foreground at all), the IoU and Dice denominators are 0: return 0.0 for 'iou' and 'dice' here. Pixel accuracy is then 1.0. (Some libraries return 1.0 for an empty-vs-empty match; be explicit about which you use.)
• Disjoint masks give IoU and Dice of 0.0.

Constraints

NumPy only, vectorised (no loops over pixels).

Follow-up

• How do you extend these to K classes (per-class IoU, then mean IoU)?
• Write a differentiable soft Dice loss on predicted probabilities.

Input: prediction = [[1, 1], [0, 0]], target = [[1, 0], [0, 1]]
Output: {'iou': 0.3333, 'pixel_accuracy': 0.5, 'dice': 0.5}

Input: prediction = [[1, 1, 0], [1, 1, 0], [0, 0, 0]], target = [[1, 1, 1], [1, 0, 0], [0, 0, 0]]
Output: {'iou': 0.6, 'pixel_accuracy': 0.7778, 'dice': 0.75}

import numpy as np

def segmentation_metrics(prediction, target):
    """
    Binary segmentation metrics.

    Args:
        prediction: Predicted mask, shape (H, W), values 0 or 1
        target: Ground-truth mask, shape (H, W), values 0 or 1

    Returns:
        dict with Python floats rounded to 4 decimals:
            'iou': foreground IoU (0.0 if both masks are empty)
            'pixel_accuracy': fraction of matching pixels
            'dice': Dice coefficient (0.0 if both masks are empty)
    """
    # Your code here
    pass