Semantic segmentation metrics in Keras and Numpy. IoU, Dice in both soft and hard variants. Mean metrics for multiclass prediction. See https://ilmonteux.github.io/2019/05/10/segmentation-metrics.html for discussion

segmentation_metrics.py

import numpy as np
import keras.backend as K
import tensorflow as tf

def metrics_np(y_true, y_pred, metric_name, metric_type='standard', drop_last = True, mean_per_class=False, verbose=False):
    """ 
    Compute mean metrics of two segmentation masks, via numpy.
    
    IoU(A,B) = |A & B| / (| A U B|)
    Dice(A,B) = 2*|A & B| / (|A| + |B|)
    
    Args:
        y_true: true masks, one-hot encoded.
        y_pred: predicted masks, either softmax outputs, or one-hot encoded.
        metric_name: metric to be computed, either 'iou' or 'dice'.
        metric_type: one of 'standard' (default), 'soft', 'naive'.
          In the standard version, y_pred is one-hot encoded and the mean
          is taken only over classes that are present (in y_true or y_pred).
          The 'soft' version of the metrics are computed without one-hot 
          encoding y_pred.
          The 'naive' version return mean metrics where absent classes contribute
          to the class mean as 1.0 (instead of being dropped from the mean).
        drop_last = True: boolean flag to drop last class (usually reserved
          for background class in semantic segmentation)
        mean_per_class = False: return mean along batch axis for each class.
        verbose = False: print intermediate results such as intersection, union
          (as number of pixels).
    Returns:
        IoU/Dice of y_true and y_pred, as a float, unless mean_per_class == True
          in which case it returns the per-class metric, averaged over the batch.
    
    Inputs are B*W*H*N tensors, with
        B = batch size,
        W = width,
        H = height,
        N = number of classes
    """
    
    assert y_true.shape == y_pred.shape, 'Input masks should be same shape, instead are {}, {}'.format(y_true.shape, y_pred.shape)
    assert len(y_pred.shape) == 4, 'Inputs should be B*W*H*N tensors, instead have shape {}'.format(y_pred.shape)
    
    flag_soft = (metric_type == 'soft')
    flag_naive_mean = (metric_type == 'naive')
    
    num_classes = y_pred.shape[-1]
    # if only 1 class, there is no background class and it should never be dropped
    drop_last = drop_last and num_classes>1
    
    if not flag_soft:
        if num_classes>1:
            # get one-hot encoded masks from y_pred (true masks should already be in correct format, do it anyway)
            y_pred = np.array([ np.argmax(y_pred, axis=-1)==i for i in range(num_classes) ]).transpose(1,2,3,0)
            y_true = np.array([ np.argmax(y_true, axis=-1)==i for i in range(num_classes) ]).transpose(1,2,3,0)
        else:
            y_pred = (y_pred > 0).astype(int)
            y_true = (y_true > 0).astype(int)
    
    # intersection and union shapes are batch_size * n_classes (values = area in pixels)
    axes = (1,2) # W,H axes of each image
    intersection = np.sum(np.abs(y_pred * y_true), axis=axes) # or, np.logical_and(y_pred, y_true) for one-hot
    mask_sum = np.sum(np.abs(y_true), axis=axes) + np.sum(np.abs(y_pred), axis=axes)
    union = mask_sum  - intersection # or, np.logical_or(y_pred, y_true) for one-hot
    
    if verbose:
        print('intersection (pred*true), intersection (pred&true), union (pred+true-inters), union (pred|true)')
        print(intersection, np.sum(np.logical_and(y_pred, y_true), axis=axes), union, np.sum(np.logical_or(y_pred, y_true), axis=axes))
    
    smooth = .001
    iou = (intersection + smooth) / (union + smooth)
    dice = 2*(intersection + smooth)/(mask_sum + smooth)
    
    metric = {'iou': iou, 'dice': dice}[metric_name]
    
    # define mask to be 0 when no pixels are present in either y_true or y_pred, 1 otherwise
    mask =  np.not_equal(union, 0).astype(int)
    # mask = 1 - np.equal(union, 0).astype(int) # True = 1
    
    if drop_last:
        metric = metric[:,:-1]
        mask = mask[:,:-1]
    
    # return mean metrics: remaining axes are (batch, classes)
    # if mean_per_class, average over batch axis only
    # if flag_naive_mean, average over absent classes too
    if mean_per_class:
        if flag_naive_mean:
            return np.mean(metric, axis=0)
        else:
            # mean only over non-absent classes in batch (still return 1 if class absent for whole batch)
            return (np.sum(metric * mask, axis=0) + smooth)/(np.sum(mask, axis=0) + smooth)
    else:
        if flag_naive_mean:
            return np.mean(metric)
        else:
            # mean only over non-absent classes
            class_count = np.sum(mask, axis=0)
            return np.mean(np.sum(metric * mask, axis=0)[class_count!=0]/(class_count[class_count!=0]))
        
def mean_iou_np(y_true, y_pred, **kwargs):
    """
    Compute mean Intersection over Union of two segmentation masks, via numpy.
    
    Calls metrics_np(y_true, y_pred, metric_name='iou'), see there for allowed kwargs.
    """
    return metrics_np(y_true, y_pred, metric_name='iou', **kwargs)

def mean_dice_np(y_true, y_pred, **kwargs):
    """
    Compute mean Dice coefficient of two segmentation masks, via numpy.
    
    Calls metrics_np(y_true, y_pred, metric_name='dice'), see there for allowed kwargs.
    """
    return metrics_np(y_true, y_pred, metric_name='dice', **kwargs)
  
  
  
  
  # keras version
def seg_metrics(y_true, y_pred, metric_name, metric_type='standard', drop_last = True, mean_per_class=False, verbose=False):
    """ 
    Compute mean metrics of two segmentation masks, via Keras.
    
    IoU(A,B) = |A & B| / (| A U B|)
    Dice(A,B) = 2*|A & B| / (|A| + |B|)
    
    Args:
        y_true: true masks, one-hot encoded.
        y_pred: predicted masks, either softmax outputs, or one-hot encoded.
        metric_name: metric to be computed, either 'iou' or 'dice'.
        metric_type: one of 'standard' (default), 'soft', 'naive'.
          In the standard version, y_pred is one-hot encoded and the mean
          is taken only over classes that are present (in y_true or y_pred).
          The 'soft' version of the metrics are computed without one-hot 
          encoding y_pred.
          The 'naive' version return mean metrics where absent classes contribute
          to the class mean as 1.0 (instead of being dropped from the mean).
        drop_last = True: boolean flag to drop last class (usually reserved
          for background class in semantic segmentation)
        mean_per_class = False: return mean along batch axis for each class.
        verbose = False: print intermediate results such as intersection, union
          (as number of pixels).
    Returns:
        IoU/Dice of y_true and y_pred, as a float, unless mean_per_class == True
          in which case it returns the per-class metric, averaged over the batch.
    
    Inputs are B*W*H*N tensors, with
        B = batch size,
        W = width,
        H = height,
        N = number of classes
    """
    
    flag_soft = (metric_type == 'soft')
    flag_naive_mean = (metric_type == 'naive')
    
    # always assume one or more classes
    num_classes = K.shape(y_true)[-1]
        
    if not flag_soft:
        # get one-hot encoded masks from y_pred (true masks should already be one-hot)
        y_pred = K.one_hot(K.argmax(y_pred), num_classes)
        y_true = K.one_hot(K.argmax(y_true), num_classes)

    # if already one-hot, could have skipped above command
    # keras uses float32 instead of float64, would give error down (but numpy arrays or keras.to_categorical gives float64)
    y_true = K.cast(y_true, 'float32')
    y_pred = K.cast(y_pred, 'float32')

    # intersection and union shapes are batch_size * n_classes (values = area in pixels)
    axes = (1,2) # W,H axes of each image
    intersection = K.sum(K.abs(y_true * y_pred), axis=axes)
    mask_sum = K.sum(K.abs(y_true), axis=axes) + K.sum(K.abs(y_pred), axis=axes)
    union = mask_sum  - intersection # or, np.logical_or(y_pred, y_true) for one-hot

    smooth = .001
    iou = (intersection + smooth) / (union + smooth)
    dice = 2 * (intersection + smooth)/(mask_sum + smooth)

    metric = {'iou': iou, 'dice': dice}[metric_name]

    # define mask to be 0 when no pixels are present in either y_true or y_pred, 1 otherwise
    mask =  K.cast(K.not_equal(union, 0), 'float32')
    
    if drop_last:
        metric = metric[:,:-1]
        mask = mask[:,:-1]
    
    if verbose:
        print('intersection, union')
        print(K.eval(intersection), K.eval(union))
        print(K.eval(intersection/union))
    
    # return mean metrics: remaining axes are (batch, classes)
    if flag_naive_mean:
        return K.mean(metric)

    # take mean only over non-absent classes
    class_count = K.sum(mask, axis=0)
    non_zero = tf.greater(class_count, 0)
    non_zero_sum = tf.boolean_mask(K.sum(metric * mask, axis=0), non_zero)
    non_zero_count = tf.boolean_mask(class_count, non_zero)
    
    if verbose:
        print('Counts of inputs with class present, metrics for non-absent classes')
        print(K.eval(class_count), K.eval(non_zero_sum / non_zero_count))
        
    return K.mean(non_zero_sum / non_zero_count)

def mean_iou(y_true, y_pred, **kwargs):
    """
    Compute mean Intersection over Union of two segmentation masks, via Keras.

    Calls metrics_k(y_true, y_pred, metric_name='iou'), see there for allowed kwargs.
    """
    return seg_metrics(y_true, y_pred, metric_name='iou', **kwargs)

def mean_dice(y_true, y_pred, **kwargs):
    """
    Compute mean Dice coefficient of two segmentation masks, via Keras.

    Calls metrics_k(y_true, y_pred, metric_name='iou'), see there for allowed kwargs.
    """
    return seg_metrics(y_true, y_pred, metric_name='dice', **kwargs)

segmentation_metrics_playground.ipynb

Hi and thank you very much for the article and your code. I would like to use this snippet within my current work. Do you have any (Bibtex) reference that I can refer to? Thank you!

Hi, I have color maps available , can I use your code directly? without one hot encoding? just reading through cv2?

hi, you'll have to one-hot encode