Opening

✖
`Opening`

✖

Opening[image,ker]

gives the morphological opening of image with respect to the structuring element ker.

✖

Opening[image,r]

gives the opening with respect to a range-r square.

✖

Opening[data,…]

applies opening to an array of data.

Details

Opening works with arbitrary 2D and 3D images, operating separately on each channel, as well as data arrays of any rank.
The structuring element ker is a matrix containing 0s and 1s.
Opening automatically pads structuring elements to have odd dimensions.
Opening[image,r] is equivalent to Opening[image,BoxMatrix[r]].

Examples

open allclose all

Basic Examples (4)Summary of the most common use cases

Opening of a binary image using a disk-shaped structuring element:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-b7pzxp

Out[1]=1

Opening of a grayscale image using a disk-shaped structuring element:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-0c1z44

Out[1]=1

Opening of a color photo with a diamond-shaped structuring element:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-400cb1

Out[1]=1

Opening of a 3D image using a cubic structuring element:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-i5rj8x

Out[1]=1

Scope (9)Survey of the scope of standard use cases

Data (6)

Use Opening to remove short sequences of 1s from a numeric vector:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-fp0vsp

Out[1]=1

Opening of a numeric vector:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-om08hy

In[2]:=2

✖

https://wolfram.com/xid/0j48joz2-6i5x1p

Out[2]=2

Opening of a 2D binary array:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-kyjez3

Opening of a binary image with a disk-shaped structuring element:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-et46vr

Out[1]=1

Opening of a grayscale image:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-dr2m0j

Out[1]=1

Opening of a symbolic array of data:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-ioqpw6

Out[1]=1

Kernel (3)

Open horizontally:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-clylnb

Out[1]=1

Open vertically:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-peee

Out[1]=1

Open using a uniform, square structuring element:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-jb1l3g

Out[1]=1

Applications (2)Sample problems that can be solved with this function

Use morphological opening to extract objects larger than the structuring element:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-ciu754

Out[1]=1

Extract 3D objects larger than the structuring element:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-nr1bsl

Out[1]=1

Properties & Relations (3)Properties of the function, and connections to other functions

Even-length kernels get right-padded with zeros:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-ewcmkp

In[2]:=2

✖

https://wolfram.com/xid/0j48joz2-8vhv1l

Out[2]=2

For symmetric kernels, Opening corresponds to an Erosion followed by a Dilation:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-r7e5yo

Out[1]=1

For non-symmetric kernels, Opening corresponds to Erosion followed by a Dilation with a reflected structuring element:

In[1]:=1

✖

https://wolfram.com/xid/0j48joz2-7vnmet

In[2]:=2

✖

https://wolfram.com/xid/0j48joz2-s5yjnk

Out[2]=2

Top