# IoU (Intersection over Union)

How well does a prediction fit the ground truth?

IoU is used to estimate how well a predicted mask or bounding box matches the ground truth data.

IoU also known as Jaccard index or Jaccard similarity coefficient.

# Interpretation / calculation

The IoU is calculated by dividing the overlap between the prediction and ground truth label by the union of these.

The output is a percentage indicating the overlap between the two labels.

# Code implementation

Numpy
PyTorch
Numpy
`import numpy as np​SMOOTH = 1e-6​def iou_numpy(outputs: np.array, labels: np.array):    outputs = outputs.squeeze(1)        intersection = (outputs & labels).sum((1, 2))    union = (outputs | labels).sum((1, 2))        iou = (intersection + SMOOTH) / (union + SMOOTH)        thresholded = np.ceil(np.clip(20 * (iou - 0.5), 0, 10)) / 10        return thresholded  # Or thresholded.mean()`
PyTorch
`import torch​SMOOTH = 1e-6​def iou_pytorch(outputs: torch.Tensor, labels: torch.Tensor):    # You can comment out this line if you are passing tensors of equal shape    # But if you are passing output from UNet or something it will most probably    # be with the BATCH x 1 x H x W shape    outputs = outputs.squeeze(1)  # BATCH x 1 x H x W => BATCH x H x W        intersection = (outputs & labels).float().sum((1, 2))  # Will be zero if Truth=0 or Prediction=0    union = (outputs | labels).float().sum((1, 2))         # Will be zzero if both are 0        iou = (intersection + SMOOTH) / (union + SMOOTH)  # We smooth our devision to avoid 0/0        thresholded = torch.clamp(20 * (iou - 0.5), 0, 10).ceil() / 10  # This is equal to comparing with thresolds        return thresholded  # Or thresholded.mean() if you are interested in average across the batch`