如何在Keras中使用Hausdorff度量？

Question

我想使用Hausdorff Distance作为度量来进行训练，但我只是发现[Weighted_Hausdorff_loss](https:/github.comN0velweighted-hausdorff-distance-tensorflow-keras-lossblobmasterweighted_hausdorff_loss.py。)，并将其作为医疗图像分割的度量标准。

import math

import numpy as np
import tensorflow as tf
from sklearn.utils.extmath import cartesian

resized_height = 192  
resized_width  = 192
max_dist = math.sqrt(resized_height**2 + resized_width**2)
n_pixels = resized_height * resized_width
all_img_locations = tf.convert_to_tensor(cartesian([np.arange(resized_height), np.arange(resized_width)]),
                                                   tf.float32)
batch_size = 1

def tf_repeat(tensor, repeats):
    """
    Args:
    input: A Tensor. 1-D or higher.
    repeats: A list. Number of repeat for each dimension, length must be the same as the number of dimensions in input
    Returns:

    A Tensor. Has the same type as input. Has the shape of tensor.shape * repeats
    """
    with tf.variable_scope("repeat"):
        expanded_tensor = tf.expand_dims(tensor, -1)
        multiples = [1] + repeats
        tiled_tensor = tf.tile(expanded_tensor, multiples = multiples)
        repeated_tesnor = tf.reshape(tiled_tensor, tf.shape(tensor) * repeats)
    return repeated_tesnor



def Weighted_Hausdorff_loss(y_true, y_pred):
    # https://arxiv.org/pdf/1806.07564.pdf
    #prob_map_b - y_pred
    #gt_b - y_true

    terms_1 = []
    terms_2 = []
    y_true = tf.squeeze(y_true, axis=-1)
    y_pred = tf.squeeze(y_pred, axis=-1)
#     y_true = tf.reduce_mean(y_true, axis=-1)
#     y_pred = tf.reduce_mean(y_pred, axis=-1)
    for b in range(batch_size):
        gt_b = y_true[b]
        prob_map_b = y_pred[b]
        # Pairwise distances between all possible locations and the GTed locations
        n_gt_pts = tf.reduce_sum(gt_b)
        gt_b = tf.where(tf.cast(gt_b, tf.bool))
        gt_b = tf.cast(gt_b, tf.float32)
        d_matrix = tf.sqrt(tf.maximum(tf.reshape(tf.reduce_sum(gt_b*gt_b, axis=1), (-1, 1)) + tf.reduce_sum(all_img_locations*all_img_locations, axis=1)-2*(tf.matmul(gt_b, tf.transpose(all_img_locations))), 0.0))
        d_matrix = tf.transpose(d_matrix)
        # Reshape probability map as a long column vector,
        # and prepare it for multiplication
        p = tf.reshape(prob_map_b, (n_pixels, 1))
        n_est_pts = tf.reduce_sum(p)
        p_replicated = tf_repeat(tf.reshape(p, (-1, 1)), [1, n_gt_pts])
        eps = 1e-6
        alpha = 4
        # Weighted Hausdorff Distance
        term_1 = (1 / (n_est_pts + eps)) * tf.reduce_sum(p * tf.reshape(tf.reduce_min(d_matrix, axis=1), (-1, 1)))
        d_div_p = tf.reduce_min((d_matrix + eps) / (p_replicated**alpha + eps / max_dist), axis=0)
        d_div_p = tf.clip_by_value(d_div_p, 0, max_dist)
        term_2 = tf.reduce_mean(d_div_p, axis=0)
        terms_1.append(term_1)
        terms_2.append(term_2)
    terms_1 = tf.stack(terms_1)
    terms_2 = tf.stack(terms_2)
    terms_1 = tf.Print(tf.reduce_mean(terms_1), [tf.reduce_mean(terms_1)], "term 1")
    terms_2 = tf.Print(tf.reduce_mean(terms_2), [tf.reduce_mean(terms_2)], "term 2")
    res = terms_1 + terms_2
    return res
model.compile(optimizer=optimizers.Adam(lr=1e-3), 
             loss=bce_dice_loss, metrics=['accuracy',iou_metric,specificity,sensitivity,Weighted_Hausdorff_loss])

它在一个数据集上成功了，但在另一个数据集上没有成功，它返回了val_Weighted_Hausdorff_loss: nan。

你想告诉我如何使用豪斯多夫距离作为公制？我认为问题是 tf.reduce_mean 和 tf.reduce_min 因为它是一个LOSSBut我不知道如何解决它。你能不能给我一些提示？

    term_1 = (1 / (n_est_pts + eps)) * tf.reduce_sum(p * tf.reshape(tf.reduce_min(d_matrix, axis=1), (-1, 1)))
    d_div_p = tf.reduce_min((d_matrix + eps) / (p_replicated**alpha + eps / max_dist), axis=0)
    d_div_p = tf.clip_by_value(d_div_p, 0, max_dist)
    term_2 = tf.reduce_mean(d_div_p, axis=0)
    terms_1.append(term_1)
    terms_2.append(term_2)
terms_1 = tf.stack(terms_1)
terms_2 = tf.stack(terms_2)
terms_1 = tf.Print(tf.reduce_mean(terms_1), [tf.reduce_mean(terms_1)], "term 1")
terms_2 = tf.Print(tf.reduce_mean(terms_2), [tf.reduce_mean(terms_2)], "term 2")