形態學蛇形

形態學蛇形 [1] 是一系列用於影像分割的方法。它們的行為類似於活動輪廓（例如，測地活動輪廓 [2] 或無邊緣活動輪廓 [3]）。然而，形態學蛇形 在二元陣列上使用形態學運算子（例如，擴張或侵蝕），而不是在浮點數陣列上求解偏微分方程式，這是活動輪廓的標準方法。這使得形態學蛇形 比傳統的對應物更快且數值更穩定。

在此實作中有兩種形態學蛇形 方法可用：形態學測地活動輪廓（MorphGAC，在 morphological_geodesic_active_contour 函式中實作）和無邊緣形態學活動輪廓（MorphACWE，在 morphological_chan_vese 函式中實作）。

MorphGAC 適用於具有可見輪廓的影像，即使這些輪廓可能嘈雜、混亂或部分不明確。然而，它需要預處理影像以突顯輪廓。這可以使用 inverse_gaussian_gradient 函式完成，儘管使用者可能想要定義自己的版本。MorphGAC 分割的品質很大程度上取決於此預處理步驟。

相反地，當要分割的物件的內部和外部區域的像素值具有不同的平均值時，MorphACWE 運作良好。與 MorphGAC 不同，MorphACWE 不需要物件的輪廓明確定義，並且它可以對原始影像執行，而無需任何先前的處理。這使得 MorphACWE 比 MorphGAC 更容易使用和調整。

參考文獻

[1]

A Morphological Approach to Curvature-based Evolution of Curves and Surfaces, Pablo Márquez-Neila, Luis Baumela and Luis Álvarez. In IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 2014, DOI:10.1109/TPAMI.2013.106

[2]

Geodesic Active Contours, Vicent Caselles, Ron Kimmel and Guillermo Sapiro. In International Journal of Computer Vision (IJCV), 1997, DOI:10.1023/A:1007979827043

[3]

Active Contours without Edges, Tony Chan and Luminita Vese. In IEEE Transactions on Image Processing, 2001, DOI:10.1109/83.902291

/home/runner/work/scikit-image/scikit-image/doc/examples/segmentation/plot_morphsnakes.py:95: MatplotlibDeprecationWarning:

The collections attribute was deprecated in Matplotlib 3.8 and will be removed in 3.10.

/home/runner/work/scikit-image/scikit-image/doc/examples/segmentation/plot_morphsnakes.py:97: MatplotlibDeprecationWarning:

The collections attribute was deprecated in Matplotlib 3.8 and will be removed in 3.10.

/home/runner/work/scikit-image/scikit-image/doc/examples/segmentation/plot_morphsnakes.py:99: MatplotlibDeprecationWarning:

The collections attribute was deprecated in Matplotlib 3.8 and will be removed in 3.10.

/home/runner/work/scikit-image/scikit-image/doc/examples/segmentation/plot_morphsnakes.py:133: MatplotlibDeprecationWarning:

The collections attribute was deprecated in Matplotlib 3.8 and will be removed in 3.10.

/home/runner/work/scikit-image/scikit-image/doc/examples/segmentation/plot_morphsnakes.py:135: MatplotlibDeprecationWarning:

The collections attribute was deprecated in Matplotlib 3.8 and will be removed in 3.10.

/home/runner/work/scikit-image/scikit-image/doc/examples/segmentation/plot_morphsnakes.py:137: MatplotlibDeprecationWarning:

The collections attribute was deprecated in Matplotlib 3.8 and will be removed in 3.10.

import numpy as np
import matplotlib.pyplot as plt
from skimage import data, img_as_float
from skimage.segmentation import (
    morphological_chan_vese,
    morphological_geodesic_active_contour,
    inverse_gaussian_gradient,
    checkerboard_level_set,
)


def store_evolution_in(lst):
    """Returns a callback function to store the evolution of the level sets in
    the given list.
    """

    def _store(x):
        lst.append(np.copy(x))

    return _store


# Morphological ACWE
image = img_as_float(data.camera())

# Initial level set
init_ls = checkerboard_level_set(image.shape, 6)
# List with intermediate results for plotting the evolution
evolution = []
callback = store_evolution_in(evolution)
ls = morphological_chan_vese(
    image, num_iter=35, init_level_set=init_ls, smoothing=3, iter_callback=callback
)

fig, axes = plt.subplots(2, 2, figsize=(8, 8))
ax = axes.flatten()

ax[0].imshow(image, cmap="gray")
ax[0].set_axis_off()
ax[0].contour(ls, [0.5], colors='r')
ax[0].set_title("Morphological ACWE segmentation", fontsize=12)

ax[1].imshow(ls, cmap="gray")
ax[1].set_axis_off()
contour = ax[1].contour(evolution[2], [0.5], colors='g')
contour.collections[0].set_label("Iteration 2")
contour = ax[1].contour(evolution[7], [0.5], colors='y')
contour.collections[0].set_label("Iteration 7")
contour = ax[1].contour(evolution[-1], [0.5], colors='r')
contour.collections[0].set_label("Iteration 35")
ax[1].legend(loc="upper right")
title = "Morphological ACWE evolution"
ax[1].set_title(title, fontsize=12)


# Morphological GAC
image = img_as_float(data.coins())
gimage = inverse_gaussian_gradient(image)

# Initial level set
init_ls = np.zeros(image.shape, dtype=np.int8)
init_ls[10:-10, 10:-10] = 1
# List with intermediate results for plotting the evolution
evolution = []
callback = store_evolution_in(evolution)
ls = morphological_geodesic_active_contour(
    gimage,
    num_iter=230,
    init_level_set=init_ls,
    smoothing=1,
    balloon=-1,
    threshold=0.69,
    iter_callback=callback,
)

ax[2].imshow(image, cmap="gray")
ax[2].set_axis_off()
ax[2].contour(ls, [0.5], colors='r')
ax[2].set_title("Morphological GAC segmentation", fontsize=12)

ax[3].imshow(ls, cmap="gray")
ax[3].set_axis_off()
contour = ax[3].contour(evolution[0], [0.5], colors='g')
contour.collections[0].set_label("Iteration 0")
contour = ax[3].contour(evolution[100], [0.5], colors='y')
contour.collections[0].set_label("Iteration 100")
contour = ax[3].contour(evolution[-1], [0.5], colors='r')
contour.collections[0].set_label("Iteration 230")
ax[3].legend(loc="upper right")
title = "Morphological GAC evolution"
ax[3].set_title(title, fontsize=12)

fig.tight_layout()
plt.show()