Python 光滑离散二维阵列

我需要平滑二维numpy数组，其中包含离散步长处的高程。这里我有

z-value=1（高程）

在

（0，0）

位置，但是，它可以是0到1之间的任何值。我的数组如下所示：

['1.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']

['1.00', '0.99', '0.95', '0.90', '0.82', '0.72', '0.60', '0.47', '0.33', '0.18']
['0.99', '0.98', '0.94', '0.89', '0.81', '0.71', '0.60', '0.47', '0.33', '0.18']
['0.95', '0.94', '0.91', '0.85', '0.78', '0.68', '0.57', '0.45', '0.32', '0.17']
['0.90', '0.89', '0.85', '0.80', '0.73', '0.64', '0.54', '0.42', '0.29', '0.16']
['0.82', '0.81', '0.78', '0.73', '0.67', '0.59', '0.49', '0.38', '0.27', '0.14']
['0.72', '0.71', '0.68', '0.64', '0.59', '0.51', '0.43', '0.33', '0.23', '0.12']
['0.60', '0.60', '0.57', '0.54', '0.49', '0.43', '0.36', '0.28', '0.19', '0.09']
['0.47', '0.47', '0.45', '0.42', '0.38', '0.33', '0.28', '0.21', '0.14', '0.06']
['0.33', '0.33', '0.32', '0.29', '0.27', '0.23', '0.19', '0.14', '0.09', '0.03']
['0.18', '0.18', '0.17', '0.16', '0.14', '0.12', '0.09', '0.06', '0.03', '0.00']

我尝试使用

scipy

应用余弦内核，然后使用

convolve2d

。像这样：

import numpy as np
from scipy import signal

peak_array = np.array([
   [ 1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
   [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
   [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
   [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
   [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
   [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
   [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
   [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
   [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
   [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])

def elevation_grid():
    """Creates a smooth elevation-grid, from an array of peaks."""
    def gkern():
        """Returns a 2D Triangle kernel array."""
        # Decay is a cosine.
        # It is centered, so multiply by two, and add one
        # This way, we cover the entire grid, and assert
        # equal smoothing (due to an odd width)
        gkern1d_c = signal.cosine(peak_array.shape[0]*2 + 1)
        gkern1d_r = signal.cosine(peak_array.shape[1]*2 + 1)

        gkern2d = np.outer(gkern1d_c, gkern1d_r)
        return gkern2d

    kernel = gkern()
    grad = signal.convolve2d(peak_array, kernel, mode='same')

    # Normalize the grid
    grad -= np.amin(grad)
    grad /= np.amax(grad)

    return grad

def print_readable(array):
    """Prints the map to a human-readable format."""
    for row in range(0, array.shape[0]):
        # Round to two decimals
        r = ["%.2f" % array[col][row] for col in range(0, array.shape[1])]
        print(r)

smooth_array = elevation_grid()

print_readable(smooth_array)

这将导致一个如下所示的数组：

['1.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']

['1.00', '0.99', '0.95', '0.90', '0.82', '0.72', '0.60', '0.47', '0.33', '0.18']
['0.99', '0.98', '0.94', '0.89', '0.81', '0.71', '0.60', '0.47', '0.33', '0.18']
['0.95', '0.94', '0.91', '0.85', '0.78', '0.68', '0.57', '0.45', '0.32', '0.17']
['0.90', '0.89', '0.85', '0.80', '0.73', '0.64', '0.54', '0.42', '0.29', '0.16']
['0.82', '0.81', '0.78', '0.73', '0.67', '0.59', '0.49', '0.38', '0.27', '0.14']
['0.72', '0.71', '0.68', '0.64', '0.59', '0.51', '0.43', '0.33', '0.23', '0.12']
['0.60', '0.60', '0.57', '0.54', '0.49', '0.43', '0.36', '0.28', '0.19', '0.09']
['0.47', '0.47', '0.45', '0.42', '0.38', '0.33', '0.28', '0.21', '0.14', '0.06']
['0.33', '0.33', '0.32', '0.29', '0.27', '0.23', '0.19', '0.14', '0.09', '0.03']
['0.18', '0.18', '0.17', '0.16', '0.14', '0.12', '0.09', '0.06', '0.03', '0.00']

这是预期的结果。但是，如果我在每个角落放置峰值：

['1.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '1.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00']
['1.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '0.00', '1.00']

它们在中间加成，导致中心有较大的峰值，在中间……

['0.00', '0.17', '0.30', '0.39', '0.44', '0.44', '0.39', '0.30', '0.17', '0.00']
['0.17', '0.36', '0.51', '0.61', '0.66', '0.66', '0.61', '0.51', '0.36', '0.17']
['0.30', '0.51', '0.67', '0.77', '0.83', '0.83', '0.77', '0.67', '0.51', '0.30']
['0.39', '0.61', '0.77', '0.89', '0.94', '0.94', '0.89', '0.77', '0.61', '0.39']
['0.44', '0.66', '0.83', '0.94', '1.00', '1.00', '0.94', '0.83', '0.66', '0.44']
['0.44', '0.66', '0.83', '0.94', '1.00', '1.00', '0.94', '0.83', '0.66', '0.44']
['0.39', '0.61', '0.77', '0.89', '0.94', '0.94', '0.89', '0.77', '0.61', '0.39']
['0.30', '0.51', '0.67', '0.77', '0.83', '0.83', '0.77', '0.67', '0.51', '0.30']
['0.17', '0.36', '0.51', '0.61', '0.66', '0.66', '0.61', '0.51', '0.36', '0.17']
['0.00', '0.17', '0.30', '0.39', '0.44', '0.44', '0.39', '0.30', '0.17', '0.00']

我怎样才能消除我的巅峰？

---

它需要高效，因为我有大数组（高达1000x1000）。

因此，如果k是你的内核，*是卷积，v1，…v4输入矩阵就像你发布的第一个一样，你可以将它们相加，得到另一个矩阵w

w=v1+v2+v3+v4

您正在应用卷积，这是一种线性运算

输出=k*w=k*（v1+v2+v3+v4）=k*v1+k2*v2

如果你注意到，你输入的四个1在拐角处（Inp2）基本上与初始矩阵的四个1（Inp1）之和相同

您可以通过简单地在Inp1中旋转90度并求和（在numpy、transposes和fliprl中）来构建Inp2。 因此，您可以旋转第一次计算的结果并将其相加，以找到正确的最终结果

Inp1的四个旋转版本之和不太可能与应用于

Inp2

的卷积不同

---

如果是这样的话，这可能是一个数字问题（如果你用的是这些数字，就不会发生）。请仔细检查如何使用max和min重新缩放数据。您要除以max，因此请确保该值为非负，除以的值大于一个eps，这是一个浮点数组。为了便于阅读，我在print函数中将它们转换为字符串。但是所有的逻辑都是在浮点数上完成的。您的代码没有运行，因为有一堆未定义的变量：

kern\u width

，

kern\u height

，

peak\u array

…我的代码运行时，我没有包含整个文件。它们是定义的。peak_数组是包含峰值的数组。我的意思是：请提供一个代码示例，它适用于所有人，而不仅仅是你。并提供准确的参数来重现您看到的行为。无法重现您发布的结果。嗯，我明白了。我希望能把山峰放在任何地方，而不仅仅是角落。我想用插值来解决这个问题，而不是卷积。无论你把它们放在哪里，你都可以应用相同的原理，因为卷积是平移不变的