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Added sections to gallery of examples

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emmanuelle
2015-12-19 15:28:15 +01:00
parent 827e4b11c9
commit 55f5103dd8
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doc/examples/features_detection/README.txt
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Detection of features and objects
---------------------------------
doc/examples/features_detection/plot_blob.py
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"""
==============
Blob Detection
==============
Blobs are bright on dark or dark on bright regions in an image. In
this example, blobs are detected using 3 algorithms. The image used
in this case is the Hubble eXtreme Deep Field. Each bright dot in the
image is a star or a galaxy.
Laplacian of Gaussian (LoG)
-----------------------------
This is the most accurate and slowest approach. It computes the Laplacian
of Gaussian images with successively increasing standard deviation and
stacks them up in a cube. Blobs are local maximas in this cube. Detecting
larger blobs is especially slower because of larger kernel sizes during
convolution. Only bright blobs on dark backgrounds are detected. See
:py:meth:`skimage.feature.blob_log` for usage.
Difference of Gaussian (DoG)
----------------------------
This is a faster approximation of LoG approach. In this case the image is
blurred with increasing standard deviations and the difference between
two successively blurred images are stacked up in a cube. This method
suffers from the same disadvantage as LoG approach for detecting larger
blobs. Blobs are again assumed to be bright on dark. See
:py:meth:`skimage.feature.blob_dog` for usage.
Determinant of Hessian (DoH)
----------------------------
This is the fastest approach. It detects blobs by finding maximas in the
matrix of the Determinant of Hessian of the image. The detection speed is
independent of the size of blobs as internally the implementation uses
box filters instead of convolutions. Bright on dark as well as dark on
bright blobs are detected. The downside is that small blobs (<3px) are not
detected accurately. See :py:meth:`skimage.feature.blob_doh` for usage.
"""
from matplotlib import pyplot as plt
from skimage import data
from skimage.feature import blob_dog, blob_log, blob_doh
from math import sqrt
from skimage.color import rgb2gray
image = data.hubble_deep_field()[0:500, 0:500]
image_gray = rgb2gray(image)
blobs_log = blob_log(image_gray, max_sigma=30, num_sigma=10, threshold=.1)
# Compute radii in the 3rd column.
blobs_log[:, 2] = blobs_log[:, 2] * sqrt(2)
blobs_dog = blob_dog(image_gray, max_sigma=30, threshold=.1)
blobs_dog[:, 2] = blobs_dog[:, 2] * sqrt(2)
blobs_doh = blob_doh(image_gray, max_sigma=30, threshold=.01)
blobs_list = [blobs_log, blobs_dog, blobs_doh]
colors = ['yellow', 'lime', 'red']
titles = ['Laplacian of Gaussian', 'Difference of Gaussian',
'Determinant of Hessian']
sequence = zip(blobs_list, colors, titles)
fig,axes = plt.subplots(1, 3, sharex=True, sharey=True, subplot_kw={'adjustable':'box-forced'})
axes = axes.ravel()
for blobs, color, title in sequence:
ax = axes[0]
axes = axes[1:]
ax.set_title(title)
ax.imshow(image, interpolation='nearest')
for blob in blobs:
y, x, r = blob
c = plt.Circle((x, y), r, color=color, linewidth=2, fill=False)
ax.add_patch(c)
plt.show()
doc/examples/features_detection/plot_brief.py
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"""
=======================
BRIEF binary descriptor
=======================
This example demonstrates the BRIEF binary description algorithm.
The descriptor consists of relatively few bits and can be computed using
a set of intensity difference tests. The short binary descriptor results
in low memory footprint and very efficient matching based on the Hamming
distance metric.
BRIEF does not provide rotation-invariance. Scale-invariance can be achieved by
detecting and extracting features at different scales.
"""
from skimage import data
from skimage import transform as tf
from skimage.feature import (match_descriptors, corner_peaks, corner_harris,
plot_matches, BRIEF)
from skimage.color import rgb2gray
import matplotlib.pyplot as plt
img1 = rgb2gray(data.astronaut())
tform = tf.AffineTransform(scale=(1.2, 1.2), translation=(0, -100))
img2 = tf.warp(img1, tform)
img3 = tf.rotate(img1, 25)
keypoints1 = corner_peaks(corner_harris(img1), min_distance=5)
keypoints2 = corner_peaks(corner_harris(img2), min_distance=5)
keypoints3 = corner_peaks(corner_harris(img3), min_distance=5)
extractor = BRIEF()
extractor.extract(img1, keypoints1)
keypoints1 = keypoints1[extractor.mask]
descriptors1 = extractor.descriptors
extractor.extract(img2, keypoints2)
keypoints2 = keypoints2[extractor.mask]
descriptors2 = extractor.descriptors
extractor.extract(img3, keypoints3)
keypoints3 = keypoints3[extractor.mask]
descriptors3 = extractor.descriptors
matches12 = match_descriptors(descriptors1, descriptors2, cross_check=True)
matches13 = match_descriptors(descriptors1, descriptors3, cross_check=True)
fig, ax = plt.subplots(nrows=2, ncols=1)
plt.gray()
plot_matches(ax[0], img1, img2, keypoints1, keypoints2, matches12)
ax[0].axis('off')
plot_matches(ax[1], img1, img3, keypoints1, keypoints3, matches13)
ax[1].axis('off')
plt.show()
doc/examples/features_detection/plot_censure.py
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"""
========================
CENSURE feature detector
========================
The CENSURE feature detector is a scale-invariant center-surround detector
(CENSURE) that claims to outperform other detectors and is capable of real-time
implementation.
"""
from skimage import data
from skimage import transform as tf
from skimage.feature import CENSURE
from skimage.color import rgb2gray
import matplotlib.pyplot as plt
img1 = rgb2gray(data.astronaut())
tform = tf.AffineTransform(scale=(1.5, 1.5), rotation=0.5,
translation=(150, -200))
img2 = tf.warp(img1, tform)
detector = CENSURE()
fig, ax = plt.subplots(nrows=1, ncols=2)
plt.gray()
detector.detect(img1)
ax[0].imshow(img1)
ax[0].axis('off')
ax[0].scatter(detector.keypoints[:, 1], detector.keypoints[:, 0],
2 ** detector.scales, facecolors='none', edgecolors='r')
detector.detect(img2)
ax[1].imshow(img2)
ax[1].axis('off')
ax[1].scatter(detector.keypoints[:, 1], detector.keypoints[:, 0],
2 ** detector.scales, facecolors='none', edgecolors='r')
plt.show()
doc/examples/features_detection/plot_corner.py
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"""
================
Corner detection
================
Detect corner points using the Harris corner detector and determine subpixel
position of corners.
.. [1] http://en.wikipedia.org/wiki/Corner_detection
.. [2] http://en.wikipedia.org/wiki/Interest_point_detection
"""
from matplotlib import pyplot as plt
from skimage import data
from skimage.feature import corner_harris, corner_subpix, corner_peaks
from skimage.transform import warp, AffineTransform
from skimage.draw import ellipse
tform = AffineTransform(scale=(1.3, 1.1), rotation=1, shear=0.7,
translation=(210, 50))
image = warp(data.checkerboard(), tform.inverse, output_shape=(350, 350))
rr, cc = ellipse(310, 175, 10, 100)
image[rr, cc] = 1
image[180:230, 10:60] = 1
image[230:280, 60:110] = 1
coords = corner_peaks(corner_harris(image), min_distance=5)
coords_subpix = corner_subpix(image, coords, window_size=13)
fig, ax = plt.subplots()
ax.imshow(image, interpolation='nearest', cmap=plt.cm.gray)
ax.plot(coords[:, 1], coords[:, 0], '.b', markersize=3)
ax.plot(coords_subpix[:, 1], coords_subpix[:, 0], '+r', markersize=15)
ax.axis((0, 350, 350, 0))
plt.show()
doc/examples/features_detection/plot_daisy.py
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"""
===============================
Dense DAISY feature description
===============================
The DAISY local image descriptor is based on gradient orientation histograms
similar to the SIFT descriptor. It is formulated in a way that allows for fast
dense extraction which is useful for e.g. bag-of-features image
representations.
In this example a limited number of DAISY descriptors are extracted at a large
scale for illustrative purposes.
"""
from skimage.feature import daisy
from skimage import data
import matplotlib.pyplot as plt
img = data.camera()
descs, descs_img = daisy(img, step=180, radius=58, rings=2, histograms=6,
orientations=8, visualize=True)
fig, ax = plt.subplots()
ax.axis('off')
ax.imshow(descs_img)
descs_num = descs.shape[0] * descs.shape[1]
ax.set_title('%i DAISY descriptors extracted:' % descs_num)
plt.show()
doc/examples/features_detection/plot_gabor.py
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"""
=============================================
Gabor filter banks for texture classification
=============================================
In this example, we will see how to classify textures based on Gabor filter
banks. Frequency and orientation representations of the Gabor filter are
similar to those of the human visual system.
The images are filtered using the real parts of various different Gabor filter
kernels. The mean and variance of the filtered images are then used as features
for classification, which is based on the least squared error for simplicity.
"""
from __future__ import print_function
import matplotlib.pyplot as plt
import numpy as np
from scipy import ndimage as ndi
from skimage import data
from skimage.util import img_as_float
from skimage.filters import gabor_kernel
def compute_feats(image, kernels):
feats = np.zeros((len(kernels), 2), dtype=np.double)
for k, kernel in enumerate(kernels):
filtered = ndi.convolve(image, kernel, mode='wrap')
feats[k, 0] = filtered.mean()
feats[k, 1] = filtered.var()
return feats
def match(feats, ref_feats):
min_error = np.inf
min_i = None
for i in range(ref_feats.shape[0]):
error = np.sum((feats - ref_feats[i, :])**2)
if error < min_error:
min_error = error
min_i = i
return min_i
# prepare filter bank kernels
kernels = []
for theta in range(4):
theta = theta / 4. * np.pi
for sigma in (1, 3):
for frequency in (0.05, 0.25):
kernel = np.real(gabor_kernel(frequency, theta=theta,
sigma_x=sigma, sigma_y=sigma))
kernels.append(kernel)
shrink = (slice(0, None, 3), slice(0, None, 3))
brick = img_as_float(data.load('brick.png'))[shrink]
grass = img_as_float(data.load('grass.png'))[shrink]
wall = img_as_float(data.load('rough-wall.png'))[shrink]
image_names = ('brick', 'grass', 'wall')
images = (brick, grass, wall)
# prepare reference features
ref_feats = np.zeros((3, len(kernels), 2), dtype=np.double)
ref_feats[0, :, :] = compute_feats(brick, kernels)
ref_feats[1, :, :] = compute_feats(grass, kernels)
ref_feats[2, :, :] = compute_feats(wall, kernels)
print('Rotated images matched against references using Gabor filter banks:')
print('original: brick, rotated: 30deg, match result: ', end='')
feats = compute_feats(ndi.rotate(brick, angle=190, reshape=False), kernels)
print(image_names[match(feats, ref_feats)])
print('original: brick, rotated: 70deg, match result: ', end='')
feats = compute_feats(ndi.rotate(brick, angle=70, reshape=False), kernels)
print(image_names[match(feats, ref_feats)])
print('original: grass, rotated: 145deg, match result: ', end='')
feats = compute_feats(ndi.rotate(grass, angle=145, reshape=False), kernels)
print(image_names[match(feats, ref_feats)])
def power(image, kernel):
# Normalize images for better comparison.
image = (image - image.mean()) / image.std()
return np.sqrt(ndi.convolve(image, np.real(kernel), mode='wrap')**2 +
ndi.convolve(image, np.imag(kernel), mode='wrap')**2)
# Plot a selection of the filter bank kernels and their responses.
results = []
kernel_params = []
for theta in (0, 1):
theta = theta / 4. * np.pi
for frequency in (0.1, 0.4):
kernel = gabor_kernel(frequency, theta=theta)
params = 'theta=%d,\nfrequency=%.2f' % (theta * 180 / np.pi, frequency)
kernel_params.append(params)
# Save kernel and the power image for each image
results.append((kernel, [power(img, kernel) for img in images]))
fig, axes = plt.subplots(nrows=5, ncols=4, figsize=(5, 6))
plt.gray()
fig.suptitle('Image responses for Gabor filter kernels', fontsize=12)
axes[0][0].axis('off')
# Plot original images
for label, img, ax in zip(image_names, images, axes[0][1:]):
ax.imshow(img)
ax.set_title(label, fontsize=9)
ax.axis('off')
for label, (kernel, powers), ax_row in zip(kernel_params, results, axes[1:]):
# Plot Gabor kernel
ax = ax_row[0]
ax.imshow(np.real(kernel), interpolation='nearest')
ax.set_ylabel(label, fontsize=7)
ax.set_xticks([])
ax.set_yticks([])
# Plot Gabor responses with the contrast normalized for each filter
vmin = np.min(powers)
vmax = np.max(powers)
for patch, ax in zip(powers, ax_row[1:]):
ax.imshow(patch, vmin=vmin, vmax=vmax)
ax.axis('off')
plt.show()
doc/examples/features_detection/plot_gabors_from_astronaut.py
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"""
============================================================
Gabors / Primary Visual Cortex "Simple Cells" from an Image
============================================================
How to build a (bio-plausible) "sparse" dictionary (or 'codebook', or
'filterbank') for e.g. image classification without any fancy math and
with just standard python scientific libraries?
Please find below a short answer ;-)
This simple example shows how to get Gabor-like filters [1]_ using just
a simple image. In our example, we use a photograph of the astronaut Eileen
Collins. Gabor filters are good approximations of the "Simple Cells" [2]_
receptive fields [3]_ found in the mammalian primary visual cortex (V1)
(for details, see e.g. the Nobel-prize winning work of Hubel & Wiesel done
in the 60s [4]_ [5]_).
Here we use McQueen's 'kmeans' algorithm [6]_, as a simple biologically
plausible hebbian-like learning rule and we apply it (a) to patches of
the original image (retinal projection), and (b) to patches of an
LGN-like [7]_ image using a simple difference of gaussians (DoG)
approximation.
Enjoy ;-) And keep in mind that getting Gabors on natural image patches
is not rocket science.
.. [1] http://en.wikipedia.org/wiki/Gabor_filter
.. [2] http://en.wikipedia.org/wiki/Simple_cell
.. [3] http://en.wikipedia.org/wiki/Receptive_field
.. [4] http://en.wikipedia.org/wiki/K-means_clustering
.. [5] http://en.wikipedia.org/wiki/Lateral_geniculate_nucleus
.. [6] D. H. Hubel and T. N., Wiesel Receptive Fields of Single Neurones
in the Cat's Striate Cortex, J. Physiol. pp. 574-591 (148) 1959
.. [7] D. H. Hubel and T. N., Wiesel Receptive Fields, Binocular
Interaction, and Functional Architecture in the Cat's Visual Cortex,
J. Physiol. 160 pp. 106-154 1962
"""
import numpy as np
from scipy.cluster.vq import kmeans2
from scipy import ndimage as ndi
import matplotlib.pyplot as plt
from skimage import data
from skimage import color
from skimage.util.shape import view_as_windows
from skimage.util.montage import montage2d
np.random.seed(42)
patch_shape = 8, 8
n_filters = 49
astro = color.rgb2gray(data.astronaut())
# -- filterbank1 on original image
patches1 = view_as_windows(astro, patch_shape)
patches1 = patches1.reshape(-1, patch_shape[0] * patch_shape[1])[::8]
fb1, _ = kmeans2(patches1, n_filters, minit='points')
fb1 = fb1.reshape((-1,) + patch_shape)
fb1_montage = montage2d(fb1, rescale_intensity=True)
# -- filterbank2 LGN-like image
astro_dog = ndi.gaussian_filter(astro, .5) - ndi.gaussian_filter(astro, 1)
patches2 = view_as_windows(astro_dog, patch_shape)
patches2 = patches2.reshape(-1, patch_shape[0] * patch_shape[1])[::8]
fb2, _ = kmeans2(patches2, n_filters, minit='points')
fb2 = fb2.reshape((-1,) + patch_shape)
fb2_montage = montage2d(fb2, rescale_intensity=True)
# --
fig, axes = plt.subplots(2, 2, figsize=(7, 6))
ax0, ax1, ax2, ax3 = axes.ravel()
ax0.imshow(astro, cmap=plt.cm.gray)
ax0.set_title("Image (original)")
ax1.imshow(fb1_montage, cmap=plt.cm.gray, interpolation='nearest')
ax1.set_title("K-means filterbank (codebook)\non original image")
ax2.imshow(astro_dog, cmap=plt.cm.gray)
ax2.set_title("Image (LGN-like DoG)")
ax3.imshow(fb2_montage, cmap=plt.cm.gray, interpolation='nearest')
ax3.set_title("K-means filterbank (codebook)\non LGN-like DoG image")
for ax in axes.ravel():
ax.axis('off')
fig.subplots_adjust(hspace=0.3)
plt.show()
doc/examples/features_detection/plot_glcm.py
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"""
=====================
GLCM Texture Features
=====================
This example illustrates texture classification using texture
classification using grey level co-occurrence matrices (GLCMs).
A GLCM is a histogram of co-occurring greyscale values at a given
offset over an image.
In this example, samples of two different textures are extracted from
an image: grassy areas and sky areas. For each patch, a GLCM with
a horizontal offset of 5 is computed. Next, two features of the
GLCM matrices are computed: dissimilarity and correlation. These are
plotted to illustrate that the classes form clusters in feature space.
In a typical classification problem, the final step (not included in
this example) would be to train a classifier, such as logistic
regression, to label image patches from new images.
"""
import matplotlib.pyplot as plt
from skimage.feature import greycomatrix, greycoprops
from skimage import data
PATCH_SIZE = 21
# open the camera image
image = data.camera()
# select some patches from grassy areas of the image
grass_locations = [(474, 291), (440, 433), (466, 18), (462, 236)]
grass_patches = []
for loc in grass_locations:
grass_patches.append(image[loc[0]:loc[0] + PATCH_SIZE,
loc[1]:loc[1] + PATCH_SIZE])
# select some patches from sky areas of the image
sky_locations = [(54, 48), (21, 233), (90, 380), (195, 330)]
sky_patches = []
for loc in sky_locations:
sky_patches.append(image[loc[0]:loc[0] + PATCH_SIZE,
loc[1]:loc[1] + PATCH_SIZE])
# compute some GLCM properties each patch
xs = []
ys = []
for patch in (grass_patches + sky_patches):
glcm = greycomatrix(patch, [5], [0], 256, symmetric=True, normed=True)
xs.append(greycoprops(glcm, 'dissimilarity')[0, 0])
ys.append(greycoprops(glcm, 'correlation')[0, 0])
# create the figure
fig = plt.figure(figsize=(8, 8))
# display original image with locations of patches
ax = fig.add_subplot(3, 2, 1)
ax.imshow(image, cmap=plt.cm.gray, interpolation='nearest',
vmin=0, vmax=255)
for (y, x) in grass_locations:
ax.plot(x + PATCH_SIZE / 2, y + PATCH_SIZE / 2, 'gs')
for (y, x) in sky_locations:
ax.plot(x + PATCH_SIZE / 2, y + PATCH_SIZE / 2, 'bs')
ax.set_xlabel('Original Image')
ax.set_xticks([])
ax.set_yticks([])
ax.axis('image')
# for each patch, plot (dissimilarity, correlation)
ax = fig.add_subplot(3, 2, 2)
ax.plot(xs[:len(grass_patches)], ys[:len(grass_patches)], 'go',
label='Grass')
ax.plot(xs[len(grass_patches):], ys[len(grass_patches):], 'bo',
label='Sky')
ax.set_xlabel('GLCM Dissimilarity')
ax.set_ylabel('GLVM Correlation')
ax.legend()
# display the image patches
for i, patch in enumerate(grass_patches):
ax = fig.add_subplot(3, len(grass_patches), len(grass_patches)*1 + i + 1)
ax.imshow(patch, cmap=plt.cm.gray, interpolation='nearest',
vmin=0, vmax=255)
ax.set_xlabel('Grass %d' % (i + 1))
for i, patch in enumerate(sky_patches):
ax = fig.add_subplot(3, len(sky_patches), len(sky_patches)*2 + i + 1)
ax.imshow(patch, cmap=plt.cm.gray, interpolation='nearest',
vmin=0, vmax=255)
ax.set_xlabel('Sky %d' % (i + 1))
# display the patches and plot
fig.suptitle('Grey level co-occurrence matrix features', fontsize=14)
plt.show()
doc/examples/features_detection/plot_hog.py
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"""
===============================
Histogram of Oriented Gradients
===============================
The `Histogram of Oriented Gradient
<http://en.wikipedia.org/wiki/Histogram_of_oriented_gradients>`__ (HOG) feature
descriptor [1]_ is popular for object detection.
In the following example, we compute the HOG descriptor and display
a visualisation.
Algorithm overview
------------------
Compute a Histogram of Oriented Gradients (HOG) by
1. (optional) global image normalisation
2. computing the gradient image in x and y
3. computing gradient histograms
4. normalising across blocks
5. flattening into a feature vector
The first stage applies an optional global image normalisation
equalisation that is designed to reduce the influence of illumination
effects. In practice we use gamma (power law) compression, either
computing the square root or the log of each colour channel.
Image texture strength is typically proportional to the local surface
illumination so this compression helps to reduce the effects of local
shadowing and illumination variations.
The second stage computes first order image gradients. These capture
contour, silhouette and some texture information, while providing
further resistance to illumination variations. The locally dominant
colour channel is used, which provides colour invariance to a large
extent. Variant methods may also include second order image derivatives,
which act as primitive bar detectors - a useful feature for capturing,
e.g. bar like structures in bicycles and limbs in humans.
The third stage aims to produce an encoding that is sensitive to
local image content while remaining resistant to small changes in
pose or appearance. The adopted method pools gradient orientation
information locally in the same way as the SIFT [2]_
feature. The image window is divided into small spatial regions,
called "cells". For each cell we accumulate a local 1-D histogram
of gradient or edge orientations over all the pixels in the
cell. This combined cell-level 1-D histogram forms the basic
"orientation histogram" representation. Each orientation histogram
divides the gradient angle range into a fixed number of
predetermined bins. The gradient magnitudes of the pixels in the
cell are used to vote into the orientation histogram.
The fourth stage computes normalisation, which takes local groups of
cells and contrast normalises their overall responses before passing
to next stage. Normalisation introduces better invariance to illumination,
shadowing, and edge contrast. It is performed by accumulating a measure
of local histogram "energy" over local groups of cells that we call
"blocks". The result is used to normalise each cell in the block.
Typically each individual cell is shared between several blocks, but
its normalisations are block dependent and thus different. The cell
thus appears several times in the final output vector with different
normalisations. This may seem redundant but it improves the performance.
We refer to the normalised block descriptors as Histogram of Oriented
Gradient (HOG) descriptors.
The final step collects the HOG descriptors from all blocks of a dense
overlapping grid of blocks covering the detection window into a combined
feature vector for use in the window classifier.
References
----------
.. [1] Dalal, N. and Triggs, B., "Histograms of Oriented Gradients for
Human Detection," IEEE Computer Society Conference on Computer
Vision and Pattern Recognition, 2005, San Diego, CA, USA.
.. [2] David G. Lowe, "Distinctive image features from scale-invariant
keypoints," International Journal of Computer Vision, 60, 2 (2004),
pp. 91-110.
"""
import matplotlib.pyplot as plt
from skimage.feature import hog
from skimage import data, color, exposure
image = color.rgb2gray(data.astronaut())
fd, hog_image = hog(image, orientations=8, pixels_per_cell=(16, 16),
cells_per_block=(1, 1), visualise=True)
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 4), sharex=True, sharey=True)
ax1.axis('off')
ax1.imshow(image, cmap=plt.cm.gray)
ax1.set_title('Input image')
ax1.set_adjustable('box-forced')
# Rescale histogram for better display
hog_image_rescaled = exposure.rescale_intensity(hog_image, in_range=(0, 0.02))
ax2.axis('off')
ax2.imshow(hog_image_rescaled, cmap=plt.cm.gray)
ax2.set_title('Histogram of Oriented Gradients')
ax1.set_adjustable('box-forced')
plt.show()
doc/examples/features_detection/plot_holes_and_peaks.py
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"""
===============================
Filling holes and finding peaks
===============================
In this example, we fill holes (i.e. isolated, dark spots) in an image using
morphological reconstruction by erosion. Erosion expands the minimal values of
the seed image until it encounters a mask image. Thus, the seed image and mask
image represent the maximum and minimum possible values of the reconstructed
image.
We start with an image containing both peaks and holes:
"""
import matplotlib.pyplot as plt
from skimage import data
from skimage.exposure import rescale_intensity
image = data.moon()
# Rescale image intensity so that we can see dim features.
image = rescale_intensity(image, in_range=(50, 200))
fig,ax = plt.subplots(2, 2, figsize=(5, 4), sharex=True, sharey=True, subplot_kw={'adjustable':'box-forced'})
ax = ax.ravel()
ax[0].imshow(image)
ax[0].set_title('Original image')
ax[0].axis('off')
"""
.. image:: PLOT2RST.current_figure
Now we need to create the seed image, where the minima represent the starting
points for erosion. To fill holes, we initialize the seed image to the maximum
value of the original image. Along the borders, however, we use the original
values of the image. These border pixels will be the starting points for the
erosion process. We then limit the erosion by setting the mask to the values
of the original image.
"""
import numpy as np
from skimage.morphology import reconstruction
seed = np.copy(image)
seed[1:-1, 1:-1] = image.max()
mask = image
filled = reconstruction(seed, mask, method='erosion')
ax[1].imshow(filled)
ax[1].set_title('after filling holes')
ax[1].axis('off')
"""
.. image:: PLOT2RST.current_figure
As shown above, eroding inward from the edges removes holes, since (by
definition) holes are surrounded by pixels of brighter value. Finally, we can
isolate the dark regions by subtracting the reconstructed image from the
original image.
"""
ax[2].imshow(image-filled)
ax[2].set_title('holes')
ax[2].axis('off')
"""
.. image:: PLOT2RST.current_figure
Alternatively, we can find bright spots in an image using morphological
reconstruction by dilation. Dilation is the inverse of erosion and expands the
*maximal* values of the seed image until it encounters a mask image. Since this
is an inverse operation, we initialize the seed image to the minimum image
intensity instead of the maximum. The remainder of the process is the same.
"""
seed = np.copy(image)
seed[1:-1, 1:-1] = image.min()
rec = reconstruction(seed, mask, method='dilation')
ax[3].imshow(image-rec)
ax[3].set_title('peaks')
ax[3].axis('off')
plt.show()
"""
.. image:: PLOT2RST.current_figure
"""
doc/examples/features_detection/plot_local_binary_pattern.py
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"""
===============================================
Local Binary Pattern for texture classification
===============================================
In this example, we will see how to classify textures based on LBP (Local
Binary Pattern). LBP looks at points surrounding a central point and tests
whether the surrounding points are greater than or less than the central point
(i.e. gives a binary result).
Before trying out LBP on an image, it helps to look at a schematic of LBPs.
The below code is just used to plot the schematic.
"""
from __future__ import print_function
import numpy as np
import matplotlib.pyplot as plt
METHOD = 'uniform'
plt.rcParams['font.size'] = 9
def plot_circle(ax, center, radius, color):
circle = plt.Circle(center, radius, facecolor=color, edgecolor='0.5')
ax.add_patch(circle)
def plot_lbp_model(ax, binary_values):
"""Draw the schematic for a local binary pattern."""
# Geometry spec
theta = np.deg2rad(45)
R = 1
r = 0.15
w = 1.5
gray = '0.5'
# Draw the central pixel.
plot_circle(ax, (0, 0), radius=r, color=gray)
# Draw the surrounding pixels.
for i, facecolor in enumerate(binary_values):
x = R * np.cos(i * theta)
y = R * np.sin(i * theta)
plot_circle(ax, (x, y), radius=r, color=str(facecolor))
# Draw the pixel grid.
for x in np.linspace(-w, w, 4):
ax.axvline(x, color=gray)
ax.axhline(x, color=gray)
# Tweak the layout.
ax.axis('image')
ax.axis('off')
size = w + 0.2
ax.set_xlim(-size, size)
ax.set_ylim(-size, size)
fig, axes = plt.subplots(ncols=5, figsize=(7, 2))
titles = ['flat', 'flat', 'edge', 'corner', 'non-uniform']
binary_patterns = [np.zeros(8),
np.ones(8),
np.hstack([np.ones(4), np.zeros(4)]),
np.hstack([np.zeros(3), np.ones(5)]),
[1, 0, 0, 1, 1, 1, 0, 0]]
for ax, values, name in zip(axes, binary_patterns, titles):
plot_lbp_model(ax, values)
ax.set_title(name)
"""
.. image:: PLOT2RST.current_figure
The figure above shows example results with black (or white) representing
pixels that are less (or more) intense than the central pixel. When surrounding
pixels are all black or all white, then that image region is flat (i.e.
featureless). Groups of continuous black or white pixels are considered
"uniform" patterns that can be interpreted as corners or edges. If pixels
switch back-and-forth between black and white pixels, the pattern is considered
"non-uniform".
When using LBP to detect texture, you measure a collection of LBPs over an
image patch and look at the distribution of these LBPs. Lets apply LBP to
a brick texture.
"""
from skimage.transform import rotate
from skimage.feature import local_binary_pattern
from skimage import data
from skimage.color import label2rgb
# settings for LBP
radius = 3
n_points = 8 * radius
def overlay_labels(image, lbp, labels):
mask = np.logical_or.reduce([lbp == each for each in labels])
return label2rgb(mask, image=image, bg_label=0, alpha=0.5)
def highlight_bars(bars, indexes):
for i in indexes:
bars[i].set_facecolor('r')
image = data.load('brick.png')
lbp = local_binary_pattern(image, n_points, radius, METHOD)
def hist(ax, lbp):
n_bins = lbp.max() + 1
return ax.hist(lbp.ravel(), normed=True, bins=n_bins, range=(0, n_bins),
facecolor='0.5')
# plot histograms of LBP of textures
fig, (ax_img, ax_hist) = plt.subplots(nrows=2, ncols=3, figsize=(9, 6))
plt.gray()
titles = ('edge', 'flat', 'corner')
w = width = radius - 1
edge_labels = range(n_points // 2 - w, n_points // 2 + w + 1)
flat_labels = list(range(0, w + 1)) + list(range(n_points - w, n_points + 2))
i_14 = n_points // 4 # 1/4th of the histogram
i_34 = 3 * (n_points // 4) # 3/4th of the histogram
corner_labels = (list(range(i_14 - w, i_14 + w + 1)) +
list(range(i_34 - w, i_34 + w + 1)))
label_sets = (edge_labels, flat_labels, corner_labels)
for ax, labels in zip(ax_img, label_sets):
ax.imshow(overlay_labels(image, lbp, labels))
for ax, labels, name in zip(ax_hist, label_sets, titles):
counts, _, bars = hist(ax, lbp)
highlight_bars(bars, labels)
ax.set_ylim(ymax=np.max(counts[:-1]))
ax.set_xlim(xmax=n_points + 2)
ax.set_title(name)
ax_hist[0].set_ylabel('Percentage')
for ax in ax_img:
ax.axis('off')
"""
.. image:: PLOT2RST.current_figure
The above plot highlights flat, edge-like, and corner-like regions of the
image.
The histogram of the LBP result is a good measure to classify textures. Here,
we test the histogram distributions against each other using the
Kullback-Leibler-Divergence.
"""
# settings for LBP
radius = 2
n_points = 8 * radius
def kullback_leibler_divergence(p, q):
p = np.asarray(p)
q = np.asarray(q)
filt = np.logical_and(p != 0, q != 0)
return np.sum(p[filt] * np.log2(p[filt] / q[filt]))
def match(refs, img):
best_score = 10
best_name = None
lbp = local_binary_pattern(img, n_points, radius, METHOD)
n_bins = lbp.max() + 1
hist, _ = np.histogram(lbp, normed=True, bins=n_bins, range=(0, n_bins))
for name, ref in refs.items():
ref_hist, _ = np.histogram(ref, normed=True, bins=n_bins,
range=(0, n_bins))
score = kullback_leibler_divergence(hist, ref_hist)
if score < best_score:
best_score = score
best_name = name
return best_name
brick = data.load('brick.png')
grass = data.load('grass.png')
wall = data.load('rough-wall.png')
refs = {
'brick': local_binary_pattern(brick, n_points, radius, METHOD),
'grass': local_binary_pattern(grass, n_points, radius, METHOD),
'wall': local_binary_pattern(wall, n_points, radius, METHOD)
}
# classify rotated textures
print('Rotated images matched against references using LBP:')
print('original: brick, rotated: 30deg, match result: ',
match(refs, rotate(brick, angle=30, resize=False)))
print('original: brick, rotated: 70deg, match result: ',
match(refs, rotate(brick, angle=70, resize=False)))
print('original: grass, rotated: 145deg, match result: ',
match(refs, rotate(grass, angle=145, resize=False)))
# plot histograms of LBP of textures
fig, ((ax1, ax2, ax3), (ax4, ax5, ax6)) = plt.subplots(nrows=2, ncols=3,
figsize=(9, 6))
plt.gray()
ax1.imshow(brick)
ax1.axis('off')
hist(ax4, refs['brick'])
ax4.set_ylabel('Percentage')
ax2.imshow(grass)
ax2.axis('off')
hist(ax5, refs['grass'])
ax5.set_xlabel('Uniform LBP values')
ax3.imshow(wall)
ax3.axis('off')
hist(ax6, refs['wall'])
"""
.. image:: PLOT2RST.current_figure
"""
plt.show()
doc/examples/features_detection/plot_multiblock_local_binary_pattern.py
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"""
===========================================================
Multi-Block Local Binary Pattern for texture classification
===========================================================
This example shows how to compute multi-block local binary pattern (MB-LBP)
features as well as how to visualize them.
The features are calculated similarly to local binary patterns (LBPs), except
that summed blocks are used instead of individual pixel values.
MB-LBP is an extension of LBP that can be computed on multiple scales in
constant time using the integral image. 9 equally-sized rectangles are used to
compute a feature. For each rectangle, the sum of the pixel intensities is
computed. Comparisons of these sums to that of the central rectangle determine
the feature, similarly to LBP (See `LBP <plot_local_binary_pattern.html>`_).
First, we generate an image to illustrate the functioning of MB-LBP: consider
a (9, 9) rectangle and divide it into (3, 3) block, upon which we then apply
MB-LBP.
"""
from __future__ import print_function
from skimage.feature import multiblock_lbp
import numpy as np
from numpy.testing import assert_equal
from skimage.transform import integral_image
# Create test matrix where first and fifth rectangles starting
# from top left clockwise have greater value than the central one.
test_img = np.zeros((9, 9), dtype='uint8')
test_img[3:6, 3:6] = 1
test_img[:3, :3] = 50
test_img[6:, 6:] = 50
# First and fifth bits should be filled. This correct value will
# be compared to the computed one.
correct_answer = 0b10001000
int_img = integral_image(test_img)
lbp_code = multiblock_lbp(int_img, 0, 0, 3, 3)
assert_equal(correct_answer, lbp_code)
"""
Now let's apply the operator to a real image and see how the
visualization works.
"""
from skimage import data
from matplotlib import pyplot as plt
from skimage.feature import draw_multiblock_lbp
test_img = data.coins()
int_img = integral_image(test_img)
lbp_code = multiblock_lbp(int_img, 0, 0, 90, 90)
img = draw_multiblock_lbp(test_img, 0, 0, 90, 90,
lbp_code=lbp_code, alpha=0.5)
plt.imshow(img, interpolation='nearest')
plt.show()
"""
.. image:: PLOT2RST.current_figure
On the above plot we see the result of computing a MB-LBP and visualization of
the computed feature. The rectangles that have less intensities' sum than the
central rectangle are marked in cyan. The ones that have higher intensity
values are marked in white. The central rectangle is left untouched.
"""
doc/examples/features_detection/plot_orb.py
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"""
==========================================
ORB feature detector and binary descriptor
==========================================
This example demonstrates the ORB feature detection and binary description
algorithm. It uses an oriented FAST detection method and the rotated BRIEF
descriptors.
Unlike BRIEF, ORB is comparatively scale- and rotation-invariant while still
employing the very efficient Hamming distance metric for matching. As such, it
is preferred for real-time applications.
"""
from skimage import data
from skimage import transform as tf
from skimage.feature import (match_descriptors, corner_harris,
corner_peaks, ORB, plot_matches)
from skimage.color import rgb2gray
import matplotlib.pyplot as plt
img1 = rgb2gray(data.astronaut())
img2 = tf.rotate(img1, 180)
tform = tf.AffineTransform(scale=(1.3, 1.1), rotation=0.5,
translation=(0, -200))
img3 = tf.warp(img1, tform)
descriptor_extractor = ORB(n_keypoints=200)
descriptor_extractor.detect_and_extract(img1)
keypoints1 = descriptor_extractor.keypoints
descriptors1 = descriptor_extractor.descriptors
descriptor_extractor.detect_and_extract(img2)
keypoints2 = descriptor_extractor.keypoints
descriptors2 = descriptor_extractor.descriptors
descriptor_extractor.detect_and_extract(img3)
keypoints3 = descriptor_extractor.keypoints
descriptors3 = descriptor_extractor.descriptors
matches12 = match_descriptors(descriptors1, descriptors2, cross_check=True)
matches13 = match_descriptors(descriptors1, descriptors3, cross_check=True)
fig, ax = plt.subplots(nrows=2, ncols=1)
plt.gray()
plot_matches(ax[0], img1, img2, keypoints1, keypoints2, matches12)
ax[0].axis('off')
plot_matches(ax[1], img1, img3, keypoints1, keypoints3, matches13)
ax[1].axis('off')
plt.show()
doc/examples/features_detection/plot_template.py
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"""
=================
Template Matching
=================
In this example, we use template matching to identify the occurrence of an
image patch (in this case, a sub-image centered on a single coin). Here, we
return a single match (the exact same coin), so the maximum value in the
``match_template`` result corresponds to the coin location. The other coins
look similar, and thus have local maxima; if you expect multiple matches, you
should use a proper peak-finding function.
The ``match_template`` function uses fast, normalized cross-correlation [1]_
to find instances of the template in the image. Note that the peaks in the
output of ``match_template`` correspond to the origin (i.e. top-left corner) of
the template.
.. [1] J. P. Lewis, "Fast Normalized Cross-Correlation", Industrial Light and
Magic.
"""
import numpy as np
import matplotlib.pyplot as plt
from skimage import data
from skimage.feature import match_template
image = data.coins()
coin = image[170:220, 75:130]
result = match_template(image, coin)
ij = np.unravel_index(np.argmax(result), result.shape)
x, y = ij[::-1]
fig = plt.figure(figsize=(8, 3))
ax1 = plt.subplot(1, 3, 1)
ax2 = plt.subplot(1, 3, 2, adjustable='box-forced')
ax3 = plt.subplot(1, 3, 3, sharex=ax2, sharey=ax2, adjustable='box-forced')
ax1.imshow(coin)
ax1.set_axis_off()
ax1.set_title('template')
ax2.imshow(image)
ax2.set_axis_off()
ax2.set_title('image')
# highlight matched region
hcoin, wcoin = coin.shape
rect = plt.Rectangle((x, y), wcoin, hcoin, edgecolor='r', facecolor='none')
ax2.add_patch(rect)
ax3.imshow(result)
ax3.set_axis_off()
ax3.set_title('`match_template`\nresult')
# highlight matched region
ax3.autoscale(False)
ax3.plot(x, y, 'o', markeredgecolor='r', markerfacecolor='none', markersize=10)
plt.show()
doc/examples/features_detection/plot_windowed_histogram.py
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from __future__ import division
"""
========================
Sliding window histogram
========================
Histogram matching can be used for object detection in images [1]_. This
example extracts a single coin from the `skimage.data.coins` image and uses
histogram matching to attempt to locate it within the original image.
First, a box-shaped region of the image containing the target coin is
extracted and a histogram of its greyscale values is computed.
Next, for each pixel in the test image, a histogram of the greyscale values in
a region of the image surrounding the pixel is computed.
`skimage.filters.rank.windowed_histogram` is used for this task, as it employs
an efficient sliding window based algorithm that is able to compute these
histograms quickly [2]_. The local histogram for the region surrounding each
pixel in the image is compared to that of the single coin, with a similarity
measure being computed and displayed.
The histogram of the single coin is computed using `numpy.histogram` on a box
shaped region surrounding the coin, while the sliding window histograms are
computed using a disc shaped structural element of a slightly different size.
This is done in aid of demonstrating that the technique still finds similarity
in spite of these differences.
To demonstrate the rotational invariance of the technique, the same test is
performed on a version of the coins image rotated by 45 degrees.
References
----------
.. [1] Porikli, F. "Integral Histogram: A Fast Way to Extract Histograms
in Cartesian Spaces" CVPR, 2005. Vol. 1. IEEE, 2005
.. [2] S.Perreault and P.Hebert. Median filtering in constant time.
Trans. Image Processing, 16(9):2389-2394, 2007.
"""
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from skimage import data, transform
from skimage.util import img_as_ubyte
from skimage.morphology import disk
from skimage.filters import rank
matplotlib.rcParams['font.size'] = 9
def windowed_histogram_similarity(image, selem, reference_hist, n_bins):
# Compute normalized windowed histogram feature vector for each pixel
px_histograms = rank.windowed_histogram(image, selem, n_bins=n_bins)
# Reshape coin histogram to (1,1,N) for broadcast when we want to use it in
# arithmetic operations with the windowed histograms from the image
reference_hist = reference_hist.reshape((1, 1) + reference_hist.shape)
# Compute Chi squared distance metric: sum((X-Y)^2 / (X+Y));
# a measure of distance between histograms
X = px_histograms
Y = reference_hist
num = (X - Y) ** 2
denom = X + Y
denom[denom == 0] = np.infty
frac = num / denom
chi_sqr = 0.5 * np.sum(frac, axis=2)
# Generate a similarity measure. It needs to be low when distance is high
# and high when distance is low; taking the reciprocal will do this.
# Chi squared will always be >= 0, add small value to prevent divide by 0.
similarity = 1 / (chi_sqr + 1.0e-4)
return similarity
# Load the `skimage.data.coins` image
img = img_as_ubyte(data.coins())
# Quantize to 16 levels of greyscale; this way the output image will have a
# 16-dimensional feature vector per pixel
quantized_img = img // 16
# Select the coin from the 4th column, second row.
# Co-ordinate ordering: [x1,y1,x2,y2]
coin_coords = [184, 100, 228, 148] # 44 x 44 region
coin = quantized_img[coin_coords[1]:coin_coords[3],
coin_coords[0]:coin_coords[2]]
# Compute coin histogram and normalize
coin_hist, _ = np.histogram(coin.flatten(), bins=16, range=(0, 16))
coin_hist = coin_hist.astype(float) / np.sum(coin_hist)
# Compute a disk shaped mask that will define the shape of our sliding window
# Example coin is ~44px across, so make a disk 61px wide (2 * rad + 1) to be
# big enough for other coins too.
selem = disk(30)
# Compute the similarity across the complete image
similarity = windowed_histogram_similarity(quantized_img, selem, coin_hist,
coin_hist.shape[0])
# Now try a rotated image
rotated_img = img_as_ubyte(transform.rotate(img, 45.0, resize=True))
# Quantize to 16 levels as before
quantized_rotated_image = rotated_img // 16
# Similarity on rotated image
rotated_similarity = windowed_histogram_similarity(quantized_rotated_image,
selem, coin_hist,
coin_hist.shape[0])
fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(10, 10))
axes[0, 0].imshow(quantized_img, cmap='gray')
axes[0, 0].set_title('Quantized image')
axes[0, 0].axis('off')
axes[0, 1].imshow(coin, cmap='gray')
axes[0, 1].set_title('Coin from 2nd row, 4th column')
axes[0, 1].axis('off')
axes[1, 0].imshow(img, cmap='gray')
axes[1, 0].imshow(similarity, cmap='hot', alpha=0.5)
axes[1, 0].set_title('Original image with overlaid similarity')
axes[1, 0].axis('off')
axes[1, 1].imshow(rotated_img, cmap='gray')
axes[1, 1].imshow(rotated_similarity, cmap='hot', alpha=0.5)
axes[1, 1].set_title('Rotated image with overlaid similarity')
axes[1, 1].axis('off')
plt.show()