rand.py

# coding=utf-8

import numpy as np
import scipy.sparse as sparse

# Evaluation code courtesy of Juan Nunez-Iglesias, taken from
# https://github.com/janelia-flyem/gala/blob/master/gala/evaluate.py

def adapted_rand(seg, gt, all_stats=False):
    """Compute Adapted Rand error as defined by the SNEMI3D contest [1]

    Formula is given as 1 - the maximal F-score of the Rand index 
    (excluding the zero component of the original labels). Adapted 
    from the SNEMI3D MATLAB script, hence the strange style.

    Parameters
    ----------
    seg : np.ndarray
        the segmentation to score, where each value is the label at that point
    gt : np.ndarray, same shape as seg
        the groundtruth to score against, where each value is a label
    all_stats : boolean, optional
        whether to also return precision and recall as a 3-tuple with rand_error

    Returns
    -------
    are : float
        The adapted Rand error; equal to $1 - \frac{2pr}{p + r}$,
        where $p$ and $r$ are the precision and recall described below.
    prec : float, optional
        The adapted Rand precision. (Only returned when `all_stats` is ``True``.)
    rec : float, optional
        The adapted Rand recall.  (Only returned when `all_stats` is ``True``.)

    References
    ----------
    [1]: http://brainiac2.mit.edu/SNEMI3D/evaluation
    """
    # segA is truth, segB is query
    segA = np.ravel(gt)
    segB = np.ravel(seg)
    n = segA.size

    n_labels_A = np.amax(segA) + 1
    n_labels_B = np.amax(segB) + 1

    ones_data = np.ones(n)

    p_ij = sparse.csr_matrix((ones_data, (segA[:], segB[:])), shape=(n_labels_A, n_labels_B))

    a = p_ij[1:n_labels_A,:]
    b = p_ij[1:n_labels_A,1:n_labels_B]
    c = p_ij[1:n_labels_A,0].todense()
    d = b.multiply(b)

    a_i = np.array(a.sum(1))
    b_i = np.array(b.sum(0))

    sumA = np.sum(a_i * a_i)
    sumB = np.sum(b_i * b_i) + (np.sum(c) / n)
    sumAB = np.sum(d) + (np.sum(c) / n)

    precision = sumAB / sumB
    recall = sumAB / sumA

    fScore = 2.0 * precision * recall / (precision + recall)
    are = 1.0 - fScore

    if all_stats:
        return (are, precision, recall)
    else:
        return are