segmentation_metric.py

import torch
import torch.nn.functional as F
import ipdb
st = ipdb.set_trace


def adjusted_rand_index(true_mask, pred_mask, name='ari_score'):
    r"""Computes the adjusted Rand index (ARI), a clustering similarity score.
    This implementation ignores points with no cluster label in `true_mask` (i.e.
    those points for which `true_mask` is a zero vector). In the context of
    segmentation, that means this function can ignore points in an image
    corresponding to the background (i.e. not to an object).
    Args:
    true_mask: `Tensor` of shape [batch_size, n_points, n_true_groups].
      The true cluster assignment encoded as one-hot.
    pred_mask: `Tensor` of shape [batch_size, n_points, n_pred_groups].
      The predicted cluster assignment encoded as categorical probabilities.
      This function works on the argmax over axis 2.
    name: str. Name of this operation (defaults to "ari_score").
    Returns:
    ARI scores as a tf.float32 `Tensor` of shape [batch_size].
    Raises:
    ValueError: if n_points <= n_true_groups and n_points <= n_pred_groups.
      We've chosen not to handle the special cases that can occur when you have
      one cluster per datapoint (which would be unusual).
    References:
    Lawrence Hubert, Phipps Arabie. 1985. "Comparing partitions"
      https://link.springer.com/article/10.1007/BF01908075
    Wikipedia
      https://en.wikipedia.org/wiki/Rand_index
    Scikit Learn
      http://scikit-learn.org/stable/modules/generated/\
      sklearn.metrics.adjusted_rand_score.html
    """
    _, n_points, n_true_groups = true_mask.shape
    n_pred_groups = pred_mask.shape[-1]
    if n_points <= n_true_groups and n_points <= n_pred_groups:
      # This rules out the n_true_groups == n_pred_groups == n_points
      # corner case, and also n_true_groups == n_pred_groups == 0, since
      # that would imply n_points == 0 too.
      # The sklearn implementation has a corner-case branch which does
      # handle this. We chose not to support these cases to avoid counting
      # distinct clusters just to check if we have one cluster per datapoint.
      raise ValueError(
          "adjusted_rand_index requires n_groups < n_points. We don't handle "
          "the special cases that can occur when you have one cluster "
          "per datapoint.")

    true_group_ids = torch.argmax(true_mask, -1)
    pred_group_ids = torch.argmax(pred_mask, -1)
    # We convert true and predicted clusters to one-hot ('oh') representations.
    true_mask_oh = true_mask.to(torch.float32)  # already one-hot
    pred_mask_oh = F.one_hot(pred_group_ids, n_pred_groups)  # returns float32

    n_points = torch.sum(true_mask_oh, axis=[1, 2]).to(torch.float32)

    nij = torch.einsum('bji,bjk->bki', pred_mask_oh.float(), true_mask_oh.float())
    a = torch.sum(nij, axis=1)
    b = torch.sum(nij, axis=2)

    rindex = torch.sum(nij * (nij - 1), axis=[1, 2])
    aindex = torch.sum(a * (a - 1), axis=1)
    bindex = torch.sum(b * (b - 1), axis=1)
    expected_rindex = aindex * bindex / (n_points*(n_points-1))
    max_rindex = (aindex + bindex) / 2
    ari = (rindex - expected_rindex) / (max_rindex - expected_rindex)

    # The case where n_true_groups == n_pred_groups == 1 needs to be
    # special-cased (to return 1) as the above formula gives a divide-by-zero.
    # This might not work when true_mask has values that do not sum to one:
    both_single_cluster = torch.logical_and(
        _all_equal(true_group_ids), _all_equal(pred_group_ids))
    return torch.where(both_single_cluster, torch.ones_like(ari), ari)


def _all_equal(values):
    """Whether values are all equal along the final axis."""
    return (values == values[..., :1]).all(axis=-1)