Scipy/Sklearn中基于自定义度量的高维图像距离矩阵计算问询

你可以通过两种方式实现对(n_samples, width, height)格式图像的自定义度量距离矩阵计算：

1. 适配Sklearn/Scipy的现有函数（推荐） #

Sklearn的pairwise_distances和Scipy的cdist确实仅接受(n_samples, n_features)的2D输入，但你可以先将每张图像flatten为1D数组，再在自定义度量函数中重新reshape回2D格式计算。

示例代码（Sklearn版） #

import numpy as np
from sklearn.metrics import pairwise_distances

ksize = 3

# 封装自定义度量，通过闭包传入图像尺寸
def create_image_metric(img_shape, ksize=3):
    w, h = img_shape
    def metric(a_flat, b_flat):
        # 将flatten后的数组恢复为2D图像
        a = a_flat.reshape(w, h)
        b = b_flat.reshape(w, h)
        
        ratio = []
        for i in range(w // ksize):
            for j in range(h // ksize):
                kernel_a = a[i*ksize:(i+1)*ksize, j*ksize:(j+1)*ksize]
                kernel_b = b[i*ksize:(i+1)*ksize, j*ksize:(j+1)*ksize]
                ratio.append(np.mean(kernel_a == kernel_b))
        return 1 - max(ratio)
    return metric

# 构造样本集：(n_samples, width, height)
a = np.array([
    [1,0,0,0,0,1],
    [0,0,1,0,0,0],
    [0,0,0,0,0,0],
    [0,0,0,0,1,0],
    [0,1,0,0,0,1],
    [0,0,0,0,0,0]
])

b = np.array([
    [0,1,0,0,0,0],
    [0,0,1,0,0,1],
    [1,0,0,0,1,0],
    [0,0,0,0,1,0],
    [0,0,0,1,0,1],
    [0,0,0,1,1,1]
])
samples = np.array([a, b])

# 转换为(n_samples, n_features)格式
samples_flat = samples.reshape(samples.shape[0], -1)

# 创建适配的度量函数
img_metric = create_image_metric(img_shape=(6,6))

# 计算距离矩阵
distance_matrix = pairwise_distances(samples_flat, metric=img_metric)
print(distance_matrix)

2. 手动构建距离矩阵 #

如果样本量不大，也可以直接遍历所有样本对，调用原自定义度量函数生成距离矩阵，无需flatten操作：

import numpy as np

ksize = 3

def custom_metric(a, b):
    w, h = a.shape
    ratio = []
    for i in range(w // ksize):
        for j in range(h // ksize):
            kernel_a = a[i*ksize:(i+1)*ksize, j*ksize:(j+1)*ksize]
            kernel_b = b[i*ksize:(i+1)*ksize, j*ksize:(j+1)*ksize]
            ratio.append(np.mean(kernel_a == kernel_b))
    return 1 - max(ratio)

def compute_distance_matrix(samples):
    n_samples = samples.shape[0]
    dist_matrix = np.zeros((n_samples, n_samples))
    # 遍历所有样本对（利用对称性减少计算量）
    for i in range(n_samples):
        for j in range(i, n_samples):
            dist = custom_metric(samples[i], samples[j])
            dist_matrix[i, j] = dist
            dist_matrix[j, i] = dist
    return dist_matrix

# 输入为(n_samples, width, height)格式
samples = np.array([a, b])
distance_matrix = compute_distance_matrix(samples)
print(distance_matrix)

关键说明 #

• Sklearn/Scipy的官方距离函数不直接支持高维输入，flatten是最通用的适配方案，不会影响度量计算的结果。
• 手动构建矩阵适合小样本场景，避免了数组reshape的开销，代码更直观。

内容的提问来源于stack exchange，提问作者Tartempion