IoU (Intersection over Union)

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