脊線運算子

脊線濾鏡可用於偵測脊狀結構，例如神經突 [1]、管狀結構 [2]、血管 [3]、皺紋 [4] 或河流。

不同的脊線濾鏡可能適合偵測不同的結構，例如，取決於對比度或雜訊程度。

目前的脊線濾鏡類別依賴於影像強度的 Hessian 矩陣的特徵值，來偵測強度垂直於結構變化但沿結構不變化的脊線結構。

參考文獻

[1]

Meijering, E., Jacob, M., Sarria, J. C., Steiner, P., Hirling, H., Unser, M. (2004). Design and validation of a tool for neurite tracing and analysis in fluorescence microscopy images. Cytometry Part A, 58(2), 167-176. DOI:10.1002/cyto.a.20022

[2]

Sato, Y., Nakajima, S., Shiraga, N., Atsumi, H., Yoshida, S., Koller, T., …, Kikinis, R. (1998). Three-dimensional multi-scale line filter for segmentation and visualization of curvilinear structures in medical images. Medical image analysis, 2(2), 143-168. DOI:10.1016/S1361-8415(98)80009-1

[3]

Frangi, A. F., Niessen, W. J., Vincken, K. L., & Viergever, M. A. (1998, October). Multiscale vessel enhancement filtering. In International Conference on Medical Image Computing and Computer-Assisted Intervention (pp. 130-137). Springer Berlin Heidelberg. DOI:10.1007/BFb0056195

[4]

Ng, C. C., Yap, M. H., Costen, N., & Li, B. (2014, November). Automatic wrinkle detection using hybrid Hessian filter. In Asian Conference on Computer Vision (pp. 609-622). Springer International Publishing. DOI:10.1007/978-3-319-16811-1_40

from skimage import data
from skimage import color
from skimage.filters import meijering, sato, frangi, hessian
import matplotlib.pyplot as plt


def original(image, **kwargs):
    """Return the original image, ignoring any kwargs."""
    return image


image = color.rgb2gray(data.retina())[300:700, 700:900]
cmap = plt.cm.gray

plt.rcParams["axes.titlesize"] = "medium"
axes = plt.figure(figsize=(10, 4)).subplots(2, 9)
for i, black_ridges in enumerate([True, False]):
    for j, (func, sigmas) in enumerate(
        [
            (original, None),
            (meijering, [1]),
            (meijering, range(1, 5)),
            (sato, [1]),
            (sato, range(1, 5)),
            (frangi, [1]),
            (frangi, range(1, 5)),
            (hessian, [1]),
            (hessian, range(1, 5)),
        ]
    ):
        result = func(image, black_ridges=black_ridges, sigmas=sigmas)
        axes[i, j].imshow(result, cmap=cmap)
        if i == 0:
            title = func.__name__
            if sigmas:
                title += f"\n\N{GREEK SMALL LETTER SIGMA} = {list(sigmas)}"
            axes[i, j].set_title(title)
        if j == 0:
            axes[i, j].set_ylabel(f'{black_ridges = }')
        axes[i, j].set_xticks([])
        axes[i, j].set_yticks([])

plt.tight_layout()
plt.show()