Morphological operations

These methods perform morphological filtering operations such as dilation and erosion on binary and greyscale images.

class machinevisiontoolbox.ImageMorph.ImageMorphMixin[source]

Image processing morphological operations on the Image class

erode(se, n=1, border='replicate', bordervalue=0, **kwargs)[source]

Morphological erosion

Parameters

  • se (ndarray(N,M)) – structuring element

  • n (int, optional) – number of times to apply the erosion, defaults to 1

  • border (str, optional) – option for boundary handling, see convolve, defaults to ‘replicate’

  • bordervalue (scalar, optional) – padding value, defaults to 0

  • kwargs – addition options passed to opencv.erode

Returns

eroded image

Return type

Image

Returns the image after morphological erosion with the structuring element se applied n times.

Example:

>>> from machinevisiontoolbox import Image
>>> import numpy as np
>>> img = Image.Squares(1,7)
>>> img.print()
 0 0 0 0 0 0 0
 0 1 1 1 0 0 0
 0 1 1 1 0 0 0
 0 1 1 1 0 0 0
 0 0 0 0 0 0 0
 0 0 0 0 0 0 0
 0 0 0 0 0 0 0
>>> img.erode(np.ones((3,3))).print()
 0 0 0 0 0 0 0
 0 0 0 0 0 0 0
 0 0 1 0 0 0 0
 0 0 0 0 0 0 0
 0 0 0 0 0 0 0
 0 0 0 0 0 0 0
 0 0 0 0 0 0 0

Note

  • It is cheaper to apply a smaller structuring element multiple times than one large one, the effective structuing element is the Minkowski sum of the structuring element with itself N times.

  • The structuring element typically has odd side lengths.

  • For a greyscale image this is the maximum value over the structuring element.

References

  • Robotics, Vision & Control for Python, Section 11.6, P. Corke, Springer 2023.

Seealso

dilate opencv.erode

dilate(se, n=1, border='replicate', bordervalue=0, **kwargs)[source]

Morphological dilation

Parameters

  • se (ndarray(N,M)) – structuring element

  • n (int, optional) – number of times to apply the dilation, defaults to 1

  • border (str, optional) – option for boundary handling, see convolve, defaults to ‘replicate’

  • bordervalue (scalar, optional) – padding value, defaults to 0

  • kwargs – addition options passed to opencv.dilate

Returns

dilated image

Return type

Image

Returns the image after morphological dilation with the structuring element se applied n times.

Example:

>>> from machinevisiontoolbox import Image
>>> import numpy as np
>>> pixels = np.zeros((7,7)); pixels[3,3] = 1
>>> img = Image(pixels)
>>> img.print()
 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 1.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00
 0.00 0.00 0.00 0.00 0.00 0.00 0.00
>>> img.dilate(np.ones((3,3))).print()
   0   0   0   0   0   0   0
   0   0   0   0   0   0   0
   0   0 255 255 255   0   0
   0   0 255 255 255   0   0
   0   0 255 255 255   0   0
   0   0   0   0   0   0   0
   0   0   0   0   0   0   0

Note

  • It is cheaper to apply a smaller structuring element multiple times than one large one, the effective structuing element is the Minkowski sum of the structuring element with itself N times.

  • The structuring element typically has odd side lengths.

  • For a greyscale image this is the minimum value over the structuring element.

References

  • Robotics, Vision & Control for Python, Section 11.6, P. Corke, Springer 2023.

Seealso

erode opencv.dilate

morph(se, op, n=1, border='replicate', bordervalue=0, **kwargs)[source]

Morphological neighbourhood processing

Parameters

  • se (ndarray(N,M)) – structuring element

  • op (str) – morphological operation, one of: ‘min’, ‘max’, ‘diff’

  • n (int, optional) – number of times to apply the operation, defaults to 1

  • border (str, optional) – option for boundary handling, see ve, defaults to ‘replicate’

  • bordervalue (scalar, optional) – padding value, defaults to 0

  • kwargs – addition options passed to opencv.morphologyEx

Returns

morphologically transformed image

Return type

Image

Apply the morphological operation oper with structuring element se to the image n times.

'oper'

description

'min'

minimum value over the structuring element

'max'

maximum value over the structuring element

'diff'

maximum - minimum value over the structuring element

Note

  • It is cheaper to apply a smaller structuring element multiple times than one large one, the effective structuing element is the Minkowski sum of the structuring element with itself N times.

  • Performs greyscale morphology

  • The structuring element should have an odd side length.

  • For a binary image, min = erosion, max = dilation.

References

  • Robotics, Vision & Control for Python, Section 11.6, P. Corke, Springer 2023.

Seealso

erode dilate opencv.morphologyEx

open(se, n=1, border='replicate', bordervalue=0, **kwargs)[source]

Morphological opening

Parameters

  • se (ndarray(N,M)) – structuring element

  • n (int, optional) – number of times to apply the erosion then dilation, defauts to 1

  • border (str, optional) – option for boundary handling, see convolve, defaults to ‘replicate’

  • bordervalue (scalar, optional) – padding value, defaults to 0

  • kwargs – addition options passed to opencv.morphologyEx

Returns

dilated image

Return type

Image

Returns the image after morphological opening with the structuring element se applied as n erosions followed by n dilations.

Example:

>>> from machinevisiontoolbox import Image
>>> import numpy as np
>>> img = Image.Read("eg-morph1.png")
>>> img.print('{:1d}')
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
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00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000010000000000000000000000001100000000
00000000000000010000000000000000000000001100000000
00000000001111111111000000000000000000001100000000
00000000001111111111000000000000000000001100000000
00000000001111111111000001111100000000001100000000
00000000001111111111000001111100000000001100000000
00000000001111111111111111111100000000001100000000
00000000111111111111000001111100000000001100000000
00000000001111111111000001111100000000001100000000
00000000001111111111000000000000000000001100000000
00000000001111111111000000000000000000001100000000
00000000001111111111000000000000000000001100000000
00000000000000000000000000000000000000001100000000
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00000111111111111111111110000000000000000000000000
00000111111111111111111110000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
>>> img.open(np.ones((5,5))).print('{:1d}')
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
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00000000001111111111000000000000000000000000000000
00000000001111111111000000000000000000000000000000
00000000001111111111000001111100000000000000000000
00000000001111111111000001111100000000000000000000
00000000001111111111000001111100000000000000000000
00000000001111111111000001111100000000000000000000
00000000001111111111000001111100000000000000000000
00000000001111111111000000000000000000000000000000
00000000001111111111000000000000000000000000000000
00000000001111111111000000000000000000000000000000
00000000000000000000000000000000000000000000000000
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Note

  • For binary image an opening operation can be used to eliminate small white noise regions.

  • It is cheaper to apply a smaller structuring element multiple times than one large one, the effective structuing element is the Minkowski sum of the structuring element with itself N times.

  • The structuring element typically has odd side lengths.

References

  • Robotics, Vision & Control for Python, Section 11.6, P. Corke, Springer 2023.

Seealso

close :meth:`morph opencv.morphologyEx

close(se, n=1, border='replicate', bordervalue=0, **kwargs)[source]

Morphological closing

Parameters

  • se (ndarray(N,M)) – structuring element

  • n (int, optional) – number of times to apply the dilation then erosion, defauts to 1

  • border (str, optional) – option for boundary handling, see convolve, defaults to ‘replicate’

  • bordervalue (scalar, optional) – padding value, defaults to 0

  • kwargs – addition options passed to opencv.morphologyEx

Returns

dilated image

Return type

Image

Returns the image after morphological opening with the structuring element se applied as n dilations followed by n erosions.

Example:

>>> from machinevisiontoolbox import Image
>>> import numpy as np
>>> img = Image.Read("eg-morph2.png")
>>> img.print('{:1d}')
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000010000000000000000000000001100000000
00000000000000010000000000000000000000001100000000
00000000001111111111000000000000000000001100000000
00000000001111111111000000000000000000001100000000
00000000001111111111000001111100000000001100000000
00000000001111111111000001111100000000001100000000
00000000001111001111111111111100000000001100000000
00000000111111001111000001111100000000001100000000
00000000001111111111000001111100000000001100000000
00000000001111111111000000000000000000001100000000
00000000001111111111000000000000000000001100000000
00000000001111111111000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000000000000000
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00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
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00000111111111111111111110000000000000000000000000
00000111111111111111111110000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
>>> img.close(np.ones((5,5))).print('{:1d}')
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000010000000000000000000000001100000000
00000000000000010000000000000000000000001100000000
00000000001111111111000000000000000000001100000000
00000000001111111111000000000000000000001100000000
00000000001111111111000001111100000000001100000000
00000000001111111111000001111100000000001100000000
00000000001111111111111111111100000000001100000000
00000000111111111111000001111100000000001100000000
00000000001111111111000001111100000000001100000000
00000000001111111111000000000000000000001100000000
00000000001111111111000000000000000000001100000000
00000000001111111111000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000001100000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
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00000000000000000000000000000000000000000000000000
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00000111111111111111111110000000000000000000000000
00000111111111111111111110000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000

Note

  • For binary image a closing operation can be used to eliminate joins between regions.

  • It is cheaper to apply a smaller structuring element multiple times than one large one, the effective structuing element is the Minkowski sum of the structuring element with itself N times.

  • The structuring element typically has odd side lengths.

References

  • Robotics, Vision & Control for Python, Section 11.6, P. Corke, Springer 2023.

Seealso

open morph opencv.morphologyEx

hitormiss(s1, s2=None, border='replicate', bordervalue=0, **kwargs)[source]

Hit or miss transform

Parameters

  • s1 (ndarray(N,M)) – structuring element 1

  • s2 (ndarray(N,M)) – structuring element 2

  • kwargs – arguments passed to opencv.morphologyEx

Returns

transformed image

Return type

Image

Return the hit-or-miss transform of the binary image which is defined by two structuring elements structuring elements

\[Y = (X \ominus S_1) \cap (X \ominus S_2)\]

which is the logical-and of the binary image and its complement, eroded by two different structuring elements. This preserves pixels where ones in the window are consistent with \(S_1\) and zeros in the window are consistent with \(S_2\).

If only s1 is provided it has three possible values:

  • 1, must match a non-zero value

  • -1, must match a zero value

  • 0, don’t care, matches any value.

Example:

Note

For the single argument case s1 \(=S_1 - S_2\).

References

  • Robotics, Vision & Control for Python, Section 11.6.3, P. Corke, Springer 2023.

Seealso

thin endpoint triplepoint opencv.morphologyEx

thin(**kwargs)[source]

Morphological skeletonization

Parameters

kwargs – options passed to hitormiss

Returns

Image

Return type

Image instance

Return the thinned version (skeleton) of the binary image as another binary image. Any non-zero region is replaced by a network of single-pixel wide lines.

Example:

>>> from machinevisiontoolbox import Image
>>> img = Image.String('000000|011110|011110|000000')
>>> img.print()
 0 0 0 0 0 0
 0 1 1 1 1 0
 0 1 1 1 1 0
 0 0 0 0 0 0
>>> img.thin().print()
 0 0 0 0 0 0
 0 1 0 0 1 0
 0 0 1 1 0 0
 0 0 0 0 0 0
>>> img = Image.Read("shark2.png")
>>> skeleton = img.thin()
References

  • Robotics, Vision & Control for Python, Section 11.6.3, P. Corke, Springer 2023.

Seealso

thin_animate hitormiss endpoint triplepoint

thin_animate(delay=0.5, **kwargs)[source]

Morphological skeletonization with animation

Parameters

  • delay (float, optional) – time in seconds between each iteration of display, default to 0.5

  • kwargs – options passed to hitormiss

Returns

Image

Return type

Image instance

Return the thinned version (skeleton) of the binary image as another binary image. Any non-zero region is replaced by a network of single-pixel wide lines.

The algorithm is iterative, and the result of of each iteration is displayed using Matplotlib.

Example:

>>> from machinevisiontoolbox import Image
>>> img = Image.Read("shark2.png")
>>> img.thin_animate()
Image: 500 x 500 (uint8)
References

  • Robotics, Vision & Control for Python, Section 11.6.3, P. Corke, Springer 2023.

Seealso

thin hitormiss endpoint triplepoint

endpoint(**kwargs)[source]

Find end points on a binary skeleton image

Parameters

kwargs – options passed to hitormiss

Returns

Image

Return type

Image instance

Return a binary image where pixels are True if the corresponding pixel in the binary image is the end point of a single-pixel wide line such as found in an image skeleton.

Example:

>>> from machinevisiontoolbox import Image
>>> img = Image.String('000000|011110|000000')
>>> img.print()
 0 0 0 0 0 0
 0 1 1 1 1 0
 0 0 0 0 0 0
>>> img.endpoint().print()
 0 0 0 0 0 0
 0 1 0 0 1 0
 0 0 0 0 0 0

Note

Computed using the hit-or-miss morphological operator.

References

  • Robotics, Vision & Control for Python, Section 11.6.3, P. Corke, Springer 2023.

Seealso

hitormiss thin triplepoint

triplepoint(**kwargs)[source]

Find triple points

Parameters

kwargs – options passed to hitormiss

Returns

Image

Return type

Image instance

Return a binary image where pixels are True if the corresponding pixel in the binary image is a triple point, that is where three single-pixel wide line intersect. These are the Voronoi points in an image skeleton.

Example:

>>> from machinevisiontoolbox import Image
>>> img = Image.String('000000|011110|001000|001000|000000')
>>> img.print()
 0 0 0 0 0 0
 0 1 1 1 1 0
 0 0 1 0 0 0
 0 0 1 0 0 0
 0 0 0 0 0 0
>>> img.triplepoint().print()
 0 0 0 0 0 0
 0 0 1 0 0 0
 0 0 0 0 0 0
 0 0 0 0 0 0
 0 0 0 0 0 0

Note

Computed using the hit-or-miss morphological operator.

References

  • Robotics, Vision & Control for Python, Section 11.6.3, P. Corke, Springer 2023.

Seealso

hitormiss thin endpoint