Thresholding

Thresholding is used to create a binary image from a grayscale image [1]. It is the simplest way to segment objects from a background.

Thresholding algorithms implemented in scikit-image can be separated in two categories:

• Histogram-based. The histogram of the pixels’ intensity is used and certain assumptions are made on the properties of this histogram (e.g. bimodal).

• Local. To process a pixel, only the neighboring pixels are used. These algorithms often require more computation time.

If you are not familiar with the details of the different algorithms and the underlying assumptions, it is often difficult to know which algorithm will give the best results. Therefore, Scikit-image includes a function to evaluate thresholding algorithms provided by the library. At a glance, you can select the best algorithm for you data without a deep understanding of their mechanisms.

[1]

https://en.wikipedia.org/wiki/Thresholding_%28image_processing%29

See also

Presentation on Rank filters.

import matplotlib.pyplot as plt

import skimage as ski

img = ski.data.page()

fig, ax = ski.filters.try_all_threshold(img, figsize=(10, 8), verbose=False)

plt.show()

How to apply a threshold?

Now, we illustrate how to apply one of these thresholding algorithms. This example uses the mean value of pixel intensities. It is a simple and naive threshold value, which is sometimes used as a guess value.

image = ski.data.camera()
thresh = ski.filters.threshold_mean(image)
binary = image > thresh

fig, axes = plt.subplots(ncols=2, figsize=(8, 3))
ax = axes.ravel()

ax[0].imshow(image, cmap=plt.cm.gray)
ax[0].set_title('Original image')

ax[1].imshow(binary, cmap=plt.cm.gray)
ax[1].set_title('Result')

for a in ax:
    a.set_axis_off()

plt.show()

Bimodal histogram

For pictures with a bimodal histogram, more specific algorithms can be used. For instance, the minimum algorithm takes a histogram of the image and smooths it repeatedly until there are only two peaks in the histogram.

image = ski.data.camera()

thresh_min = ski.filters.threshold_minimum(image)
binary_min = image > thresh_min

fig, ax = plt.subplots(2, 2, figsize=(10, 10))

ax[0, 0].imshow(image, cmap=plt.cm.gray)
ax[0, 0].set_title('Original')

ax[0, 1].hist(image.ravel(), bins=256)
ax[0, 1].set_title('Histogram')

ax[1, 0].imshow(binary_min, cmap=plt.cm.gray)
ax[1, 0].set_title('Thresholded (min)')

ax[1, 1].hist(image.ravel(), bins=256)
ax[1, 1].axvline(thresh_min, color='r')

for a in ax[:, 0]:
    a.set_axis_off()

plt.show()

Otsu’s method [2] calculates an “optimal” threshold (marked by a red line in the histogram below) by maximizing the variance between two classes of pixels, which are separated by the threshold. Equivalently, this threshold minimizes the intra-class variance.

[2] (1,2)

https://en.wikipedia.org/wiki/Otsu’s_method

image = ski.data.camera()
thresh = ski.filters.threshold_otsu(image)
binary = image > thresh

fig, ax = plt.subplots(ncols=3, figsize=(8, 2.5))

ax[0].imshow(image, cmap=plt.cm.gray)
ax[0].set_title('Original')
ax[0].axis('off')

ax[1].hist(image.ravel(), bins=256)
ax[1].set_title('Histogram')
ax[1].axvline(thresh, color='r')

ax[2].imshow(binary, cmap=plt.cm.gray)
ax[2].set_title('Thresholded')
ax[2].set_axis_off()

plt.show()

Local thresholding

If the image background is relatively uniform, then you can use a global threshold value as presented above. However, if there is large variation in the background intensity, adaptive thresholding (a.k.a. local or dynamic thresholding) may produce better results. Note that local is much slower than global thresholding.

Here, we binarize an image using the threshold_local function, which calculates thresholds in regions with a characteristic size block_size surrounding each pixel (i.e. local neighborhoods). Each threshold value is the weighted mean of the local neighborhood minus an offset value.

image = ski.data.page()

global_thresh = ski.filters.threshold_otsu(image)
binary_global = image > global_thresh

block_size = 35
local_thresh = ski.filters.threshold_local(image, block_size, offset=10)
binary_local = image > local_thresh

fig, axes = plt.subplots(nrows=3, figsize=(7, 8))
ax = axes.ravel()
plt.gray()

ax[0].imshow(image)
ax[0].set_title('Original')

ax[1].imshow(binary_global)
ax[1].set_title('Global thresholding')

ax[2].imshow(binary_local)
ax[2].set_title('Local thresholding')

for a in ax:
    a.set_axis_off()

plt.show()

Now, we show how Otsu’s threshold [2] method can be applied locally. For each pixel, an “optimal” threshold is determined by maximizing the variance between two classes of pixels of the local neighborhood defined by a structuring element.

The example compares the local threshold with the global threshold.

img = ski.util.img_as_ubyte(ski.data.page())

radius = 15
footprint = ski.morphology.disk(radius)

local_otsu = ski.filters.rank.otsu(img, footprint)
threshold_global_otsu = ski.filters.threshold_otsu(img)
global_otsu = img >= threshold_global_otsu

fig, axes = plt.subplots(2, 2, figsize=(8, 5), sharex=True, sharey=True)
ax = axes.ravel()
fig.tight_layout()

fig.colorbar(ax[0].imshow(img, cmap=plt.cm.gray), ax=ax[0], orientation='horizontal')
ax[0].set_title('Original')
ax[0].set_axis_off()

fig.colorbar(
    ax[1].imshow(local_otsu, cmap=plt.cm.gray), ax=ax[1], orientation='horizontal'
)
ax[1].set_title(f'Local Otsu (radius={radius})')
ax[1].set_axis_off()

ax[2].imshow(img >= local_otsu, cmap=plt.cm.gray)
ax[2].set_title('Original >= Local Otsu')
ax[2].set_axis_off()

ax[3].imshow(global_otsu, cmap=plt.cm.gray)
ax[3].set_title('Global Otsu (threshold = {threshold_global_otsu})')
ax[3].set_axis_off()

plt.show()