# Houghova transformace¶

Vstup: obraz

Výstup: pozice hledaných objektu

Cíl: nalézt v obraze objekty popsané mat. funkcí

In [1]:
%pylab inline --no-import-all

Populating the interactive namespace from numpy and matplotlib

In [2]:
from skimage.transform import (hough_line, hough_line_peaks,
probabilistic_hough_line)
from skimage.feature import canny
from skimage import data

import numpy as np
import matplotlib.pyplot as plt
import skimage
import skimage.transform
import numpy as np
import matplotlib.pyplot as plt

from skimage.transform import hough_line
from skimage.draw import line


# Akumulátor¶

In [3]:
img = np.zeros((100, 150), dtype=bool)
img[30, :] = 1
img[:, 65] = 1
img[35:45, 35:50] = 1
rr, cc = line(60, 130, 80, 10)
img[rr, cc] = 1
img += np.random.random(img.shape) > 0.95

hspace, angles, dists = hough_line(img)

plt.figure(figsize=(15,15))
plt.subplot(1, 2, 1)

plt.imshow(img, cmap=plt.cm.gray)
plt.title('Input image')

plt.subplot(1, 2, 2)
plt.imshow(hspace,
#            cmap=plt.cm.bone,
dists[-1], dists[0]))
plt.title('Hough transform')
plt.xlabel('Angle (degree)')
plt.ylabel('Distance (pixel)')

plt.show()


## Nalezení vrcholů v Houghově transformaci¶

dokumentace k hough_line_peaks

In [4]:
#from skimage.transform import hough_peaks

#d#ir(skimage.transform)

lhspace, langles, ldists = skimage.transform.hough_line_peaks(hspace, angles, dists)
print(lhspace)
print(langles)
print(ldists)

[150  94]
[1.57079633 1.41283915]
[30.58448753 80.72299169]


In [5]:
# Construct test image

image = np.zeros((100, 100))

# Classic straight-line Hough transform

idx = np.arange(25, 75)
image[idx[::-1], idx] = 255
image[idx, idx] = 255

h, theta, d = hough_line(image)

plt.figure(figsize=(15, 15))

plt.subplot(131)
plt.imshow(image,
cmap=plt.cm.gray
)
plt.title('Input image')

plt.subplot(132)
plt.imshow(np.log(1 + h),
d[-1], d[0]],
#            cmap=plt.cm.gray,
aspect=1/1.5)
plt.title('Hough transform')
plt.xlabel('Angles (degrees)')
plt.ylabel('Distance (pixels)')

plt.subplot(133)
plt.imshow(image, cmap=plt.cm.gray)
rows, cols = image.shape
for _, angle, dist in zip(*hough_line_peaks(h, theta, d)):
y0 = (dist - 0 * np.cos(angle)) / np.sin(angle)
y1 = (dist - cols * np.cos(angle)) / np.sin(angle)
plt.plot((0, cols), (y0, y1), '-r')
plt.axis((0, cols, rows, 0))
plt.title('Detected lines')
plt.show()


In [6]:
# Line finding, using the Probabilistic Hough Transform

image = data.camera()
edges = canny(image, 2, 1, 25)
lines = probabilistic_hough_line(edges, threshold=100, line_length=5, line_gap=3)

plt.figure(figsize=(15, 15))

plt.subplot(131)
plt.imshow(image, cmap=plt.cm.gray)
plt.title('Input image')

plt.subplot(132)
plt.imshow(edges,
cmap=plt.cm.gray
)
plt.title('Canny edges')

plt.subplot(133)
plt.imshow(edges * 0)

for line in lines:
p0, p1 = line
plt.plot((p0[0], p1[0]), (p0[1], p1[1]))

plt.title('Probabilistic Hough')
plt.axis('image')
plt.show()


## Kruhová Houghova transformace¶

In [7]:
import numpy as np
import matplotlib.pyplot as plt

from skimage import data, feature, color
from skimage.transform import hough_circle
from skimage.feature import peak_local_max
from skimage.draw import circle_perimeter
from skimage.util import img_as_ubyte

# Load picture and detect edges
image = img_as_ubyte(data.coins()[0:95, 70:370])
edges = feature.canny(image, sigma=3, low_threshold=10, high_threshold=50)

fig, ax = plt.subplots(ncols=1, nrows=1, figsize=(6, 6))

centers = []
accums = []

# For each radius, extract two circles
peaks = peak_local_max(h, num_peaks=2)
centers.extend(peaks)
accums.extend(h[peaks[:, 0], peaks[:, 1]])

# Draw the most prominent 5 circles
image = color.gray2rgb(image)
for idx in np.argsort(accums)[::-1][:5]:
center_x, center_y = centers[idx]
cx, cy = circle_perimeter(center_y, center_x, radius)
image[cy, cx] = (220, 20, 20)

ax.imshow(image, cmap=plt.cm.gray)

Out[7]:
<matplotlib.image.AxesImage at 0x2be496365f8>
In [18]:
"""
Ellipse detection
=================

In this second example, the aim is to detect the edge of a coffee cup.
Basically, this is a projection of a circle, i.e. an ellipse.
The problem to solve is much more difficult because five parameters have to be
determined, instead of three for circles.

Algorithm overview
------------------

The algorithm takes two different points belonging to the ellipse. It assumes
that it is the main axis. A loop on all the other points determines how much
an ellipse passes to them. A good match corresponds to high accumulator values.

A full description of the algorithm can be found in reference [1]_.

References
----------
.. [1] Xie, Yonghong, and Qiang Ji. "A new efficient ellipse detection
method." Pattern Recognition, 2002. Proceedings. 16th International
Conference on. Vol. 2. IEEE, 2002
"""

import matplotlib.pyplot as plt

from skimage import data, feature, color
from skimage.transform import hough_ellipse
from skimage.draw import ellipse_perimeter

# Load picture, convert to grayscale and detect edges
image_rgb = data.coffee()[0:220, 160:420]
image_gray = color.rgb2gray(image_rgb)
edges = feature.canny(image_gray, sigma=2.0,
low_threshold=0.55, high_threshold=0.8)

# Perform a Hough Transform
# The accuracy corresponds to the bin size of a major axis.
# The value is chosen in order to get a single high accumulator.
# The threshold eliminates low accumulators
result = hough_ellipse(edges, accuracy=20, threshold=250,
min_size=100, max_size=120)
result.sort(order='accumulator')

# Estimated parameters for the ellipse
best = result[-1]
yc = int(best[1])
xc = int(best[2])
a = int(best[3])
b = int(best[4])
orientation = best[5]

# Draw the ellipse on the original image
cy, cx = ellipse_perimeter(yc, xc, a, b, orientation)
image_rgb[cy, cx] = (0, 0, 255)
# Draw the edge (white) and the resulting ellipse (red)
edges = color.gray2rgb(edges)
edges[cy, cx] = (250, 0, 0)

fig2, (ax1, ax2) = plt.subplots(ncols=2, nrows=1, figsize=(10, 6))

ax1.set_title('Original picture')
ax1.imshow(image_rgb)

ax2.set_title('Edge (white) and result (red)')
ax2.imshow(edges.astype(float))

plt.show()


# Zpětná projekce¶

In [9]:
from __future__ import print_function, division

import numpy as np
import matplotlib.pyplot as plt

from skimage import data_dir

image = rescale(image, scale=0.4)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 4.5))

ax1.set_title("Original")
ax1.imshow(image, cmap=plt.cm.Greys_r)

theta = np.linspace(0., 180., max(image.shape), endpoint=False)
ax2.set_xlabel("Projection angle (deg)")
ax2.set_ylabel("Projection position (pixels)")
ax2.imshow(sinogram, cmap=plt.cm.Greys_r,
extent=(0, 180, 0, sinogram.shape[0]), aspect='auto')

plt.show()

C:\Users\miros\Miniconda3\envs\animalwatch\lib\site-packages\skimage\transform\_warps.py:84: UserWarning: The default mode, 'constant', will be changed to 'reflect' in skimage 0.15.
warn("The default mode, 'constant', will be changed to 'reflect' in "

In [10]:
from skimage.transform import iradon

error = reconstruction_fbp - image
print('FBP rms reconstruction error: %.3g' % np.sqrt(np.mean(error**2)))

imkwargs = dict(vmin=-0.2, vmax=0.2)
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 4.5), sharex=True, sharey=True, subplot_kw={'adjustable':'box-forced'})
ax1.set_title("Reconstruction\nFiltered back projection")
ax1.imshow(reconstruction_fbp, cmap=plt.cm.Greys_r)
ax2.set_title("Reconstruction error\nFiltered back projection")
ax2.imshow(reconstruction_fbp - image, cmap=plt.cm.Greys_r, **imkwargs)
plt.show()

FBP rms reconstruction error: 0.0547

C:\Users\miros\Miniconda3\envs\animalwatch\lib\site-packages\matplotlib\axes\_base.py:1400: MatplotlibDeprecationWarning: The 'box-forced' keyword argument is deprecated since 2.2.
" since 2.2.", cbook.mplDeprecation)

In [11]:
kolik = 10
theta = np.linspace(0., 180., kolik , endpoint=False)
# theta = [0, 45, 90]

plt.axis('off')
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 5))
ax1.imshow(image, cmap='gray')
ax2.imshow(sinogram, cmap='gray')
plt.figure(figsize=(15,5))
plt.axis('off')
for i in range(1, kolik+1):
plt.subplot(2,kolik / 2,i)
plt.axis('off')