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

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