第一个问题是meshgrid生成不正确-它使用0..1范围，而代码的其余部分假设它持有大图的坐标（0..hm_width/height范围）。即使我们在归一化空间中操作，0..1也只能捕获曲线的一小部分。
解决方案：我会保留规范化的空间，因为它将简化以下代码。我会把范围扩大到-3..3标准差请随意调整。

x, y = np.meshgrid(
    np.linspace(-3, 3, blob_width), 
    np.linspace(-3, 3, blob_height), 
)

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第二个问题：这是一个2D分布，你不能分别计算x和y的结果（在一般情况下，正如Chris指出的那样-在这里，你可以）。通常，the formula为

sigma = ...  # covariance matrix
pos = np.array([x - blob_center_x, y - blob_center_y])
# I don't want to figure out proper axes here, but I hope you get the idea
gaussian_blob = const * np.exp(-0.5 * np.tensordot(np.tensordot(pos, np.inv(sigma), axes=...), pos, axes=...).sum(axis=...))

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但由于我们现在在归一化空间中操作，平均值为零，sigma为[[1, 0], [0, 1]]，因此可以简化为：

# we dont care about const as it will be normalized later
gaussian_blob = np.exp(-0.5 * (x**2 + y**2))

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最后，注意缩放时忽略的常量：

gaussian_blob =  (255.0 * (gaussian_blob - gaussian_blob.min()) / gaussian_blob.max()).astype(np.uint8)

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UPD

正如Chris所指出的，你可以通过这样做来保存一毫秒左右的时间：

X = np.linspace(-3, 3, blob_width)[None, :]
Y = np.linspace(-3, 3, blob_height)[:, None]
gaussian_blob = np.exp(-0.5*X**2) * np.exp(-0.5*Y**2)
gaussian_blob =  255.0 * (gaussian_blob - gaussian_blob.min()) / gaussian_blob.max()

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这里是一个复制/粘贴可运行的示例，包括制作高斯的代码（由@马拉特提供）和将高斯添加到OpenCV图像的代码，包括高斯部分重叠的情况。我不会把这个作为解决方案，这样@马拉特就能得到信任。
在代码中有一个轻微的缺陷，将高斯添加到热图中，因为在高斯重叠的情况下，结果图像中有一个轻微的接缝，请参见下面的截图。我将在稍后的时间尝试解决这个问题。

# heatmap_drawing_test.py

import numpy as np
import cv2
from termcolor import colored

# ref:
# https://stackoverflow.com/questions/76723027/how-to-draw-2d-gaussian-blob-on-an-opencv-image/76724003#76724003

HEATMAP_WIDTH = 1600
HEATMAP_HEIGHT = 1000

def main():
    # suppress numpy printing in scientific notation
    np.set_printoptions(suppress=True)

    # create blank heatmap (OpenCV image)
    heatmap = np.zeros((HEATMAP_HEIGHT, HEATMAP_WIDTH), dtype=np.uint8)

    blob_1_center_x = 1000
    blob_1_center_y = 400
    blob_1_width = 451
    blob_1_height = 201

    gaussian_blob_1 = make_gaussian_blob(blob_1_width, blob_1_height)

    blob_2_center_x = 1100
    blob_2_center_y = 500
    blob_2_width = 451
    blob_2_height = 201

    gaussian_blob_2 = make_gaussian_blob(blob_2_width, blob_2_height)

    # show the blob via OpenCV
    cv2.imshow('gaussian blob 1', gaussian_blob_1)
    cv2.imshow('gaussian blob 2', gaussian_blob_2)

    heatmap = add_gaussian_blob_to_heatmap(gaussian_blob_1, blob_1_center_x, blob_1_center_y, heatmap)
    heatmap = add_gaussian_blob_to_heatmap(gaussian_blob_2, blob_2_center_x, blob_2_center_y, heatmap)

    print('\n' + 'final heatmap: ')
    print(heatmap.dtype)
    print(heatmap.shape)
    print('min = ' + str(np.min(heatmap)) + ' (s/b 0)')
    print('max = ' + str(np.max(heatmap)) + ' (s/b 255)')
    print(heatmap)

    # show the heatmap
    cv2.imshow('heatmap', heatmap)

    cv2.waitKey()
# end function

def make_gaussian_blob(blob_width, blob_height):
    assert blob_height % 2 == 1 and blob_width % 2 == 1, \
        colored('\n\n' + 'in make_gaussian_blob, blob_height and blob_width must be odd numbers !!' + '\n', color='red', attrs=['bold'])

    # Create a 2D Gaussian blob
    # +-2.5 was derived from experimentation
    x, y = np.meshgrid(np.linspace(-2.5, 2.5, blob_width), np.linspace(-2.5, 2.5, blob_height))

    print('\n' + 'x: ')
    print(x.dtype)
    print(x.shape)
    print('min = ' + str(np.min(x)) + ' (s/b 0.0)')
    print('max = ' + str(np.max(x)) + ' (s/b 1.0)')
    print(x)

    print('\n' + 'y: ')
    print(y.dtype)
    print(y.shape)
    print('min = ' + str(np.min(y)) + ' (s/b 0.0)')
    print('max = ' + str(np.max(y)) + ' (s/b 1.0)')
    print(y)

    gaussian_blob = np.exp(-0.5 * (x**2 + y**2))

    print('\n' + 'gaussian_blob before: ')
    print(gaussian_blob.dtype)
    print(gaussian_blob.shape)
    print('min = ' + str(np.min(gaussian_blob)) + ' (s/b 0.0)')
    print('max = ' + str(np.max(gaussian_blob)) + ' (s/b 1.0)')
    print(gaussian_blob)

    # scale up the gaussian blob from the 0.0 to 1.0 range to the 0 to 255 range
    gaussian_blob = gaussian_blob * 255.0
    gaussian_blob = np.clip(gaussian_blob, a_min=0.0, a_max=255.0)
    gaussian_blob = np.rint(gaussian_blob).astype(np.uint8)

    print('\n' + 'gaussian_blob after: ')
    print(gaussian_blob.dtype)
    print(gaussian_blob.shape)
    print('min = ' + str(np.min(gaussian_blob)) + ' (s/b 0)')
    print('max = ' + str(np.max(gaussian_blob)) + ' (s/b 255)')
    print(gaussian_blob)

    return gaussian_blob
# end function

def add_gaussian_blob_to_heatmap(gaussian_blob, blob_center_x, blob_center_y, heatmap):
    # ToDo: this function is not perfect, there is a slight seam when two blobs overlap each other, eventually should resolve this

    blob_height, blob_width = gaussian_blob.shape[0:2]
    blob_left_edge_loc = round(blob_center_x - ((blob_width - 1) * 0.5))
    blob_right_edge_loc = round(blob_center_x + ((blob_width - 1) * 0.5))

    print('\n' + 'blob_left_edge_loc = ' + str(blob_left_edge_loc))
    print('\n' + 'blob_right_edge_loc = ' + str(blob_right_edge_loc))

    blob_top_edge_loc = round(blob_center_y - ((blob_height - 1) * 0.5))
    blob_bottom_edge_loc = round(blob_center_y + ((blob_height - 1) * 0.5))

    print('\n' + 'blob_top_edge_loc = ' + str(blob_top_edge_loc))
    print('\n' + 'blob_bottom_edge_loc = ' + str(blob_bottom_edge_loc))

    heatmap = heatmap.astype(np.uint16)
    gaussian_blob = gaussian_blob.astype(np.uint16)

    heatmap[blob_top_edge_loc:blob_bottom_edge_loc+1, blob_left_edge_loc:blob_right_edge_loc+1] += gaussian_blob

    heatmap = np.where(heatmap > 255, 255, heatmap).astype(np.uint8)

    return heatmap
# end function

if __name__ == '__main__':
    main()

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结果：x1c 0d1x