bwmorph3
Morphological operations on binary volume
Description
Examples
Compare the Clean and Majority Operations
Load 3-D MRI volumetric data and create a binary volume. Use volshow to view the volumetric data with a gray color.
load mristack;
BW1 = mristack > 127;
cmap = [0.6 0.6 0.6];
volshow(BW1,Colormap=cmap);
To remove voxels that are set to 1 and that are also surrounded by voxels set to 0, perform the "clean" operation on the volumetric data. When determining which voxels to remove, the "clean" operation considers 26 neighboring voxels. Use volshow to view the results.
BW2 = bwmorph3(BW1,"clean");
volshow(BW2,Colormap=cmap);
For comparison, perform the "majority" operation on the volumetric data. The "majority" operation performs a similar task to the "clean" operation but only retains voxels if more than half (the majority) of the voxels in the neighborhood of the target voxel are set to 1. When determining which voxels to retain, the "majority" operation also considers 26 neighboring voxels. Use volshow to view the results.
BW3 = bwmorph3(BW1,"majority");
volshow(BW3,Colormap=cmap); 
Illustrations of Morphological Operations
This example shows how each of the morphological operations supported by bwmorph3 works on simple volumes.
Make a 9-by-9-by-3 cuboid of 0s that contains a 3-by-3-by-3 cube of 1s at its center.
innercube = ones(3,3,3);
cube_center = padarray(innercube,[3 3],0,'both')cube_center =
cube_center(:,:,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 1 1 1 0 0 0
0 0 0 1 1 1 0 0 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 0 0 0 0 0 0
cube_center(:,:,2) =
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 1 1 1 0 0 0
0 0 0 1 1 1 0 0 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 0 0 0 0 0 0
cube_center(:,:,3) =
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 1 1 1 0 0 0
0 0 0 1 1 1 0 0 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 0 0 0 0 0 0
Turning Pixels Off with the Remove Operation
Set the center voxel of the inner cube to 0 using the 'remove' operation. This operation sets the value of any 'on' voxel completely surrounded by 'on' voxels to 'off'.
remove_center = bwmorph3(cube_center,'remove')remove_center = 9x9x3 logical array
remove_center(:,:,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 1 1 1 0 0 0
0 0 0 1 1 1 0 0 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 0 0 0 0 0 0
remove_center(:,:,2) =
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 1 1 1 0 0 0
0 0 0 1 0 1 0 0 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 0 0 0 0 0 0
remove_center(:,:,3) =
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 1 1 1 0 0 0
0 0 0 1 1 1 0 0 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 0 0 0 0 0 0
Setting Pixels to On with the Fill Operation
Set the center voxel of the inner cube to 1 using the 'fill' operation. This operation sets the value of any 'off' voxel completely surrounded by 'on' voxels to 'on'.
fill_center = bwmorph3(remove_center,'fill')fill_center = 9x9x3 logical array
fill_center(:,:,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 1 1 1 0 0 0
0 0 0 1 1 1 0 0 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 0 0 0 0 0 0
fill_center(:,:,2) =
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 1 1 1 0 0 0
0 0 0 1 1 1 0 0 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 0 0 0 0 0 0
fill_center(:,:,3) =
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 1 1 1 0 0 0
0 0 0 1 1 1 0 0 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 0 0 0 0 0 0
Removing Unconnected Pixels with the Clean Operation
Use the 'clean' operation to remove any stray voxels that are set to 1 but are not connected to a component in the volume. The example creates a stray voxel by setting a random voxel on the second plane to 1 and then uses the 'clean' operation to remove it.
cube_center(2,2,2) = 1
cube_center =
cube_center(:,:,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 1 1 1 0 0 0
0 0 0 1 1 1 0 0 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 0 0 0 0 0 0
cube_center(:,:,2) =
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 1 1 1 0 0 0
0 0 0 1 1 1 0 0 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 0 0 0 0 0 0
cube_center(:,:,3) =
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 1 1 1 0 0 0
0 0 0 1 1 1 0 0 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 0 0 0 0 0 0
cube_cleaned = bwmorph3(cube_center,'clean')cube_cleaned = 9x9x3 logical array
cube_cleaned(:,:,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 1 1 1 0 0 0
0 0 0 1 1 1 0 0 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 0 0 0 0 0 0
cube_cleaned(:,:,2) =
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 1 1 1 0 0 0
0 0 0 1 1 1 0 0 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 0 0 0 0 0 0
cube_cleaned(:,:,3) =
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 1 1 1 0 0 0
0 0 0 1 1 1 0 0 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 0 0 0 0 0 0
Finding the Majority
Find the majority of the cube_center using the 'majority' operation. This operation retains a voxel only if more than half (the majority) of the voxels in the 26-connected neighborhood around the voxel are set to 1.
cube_major = bwmorph3(cube_center,'majority')cube_major = 9x9x3 logical array
cube_major(:,:,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 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 0 0 0 0 0 0 0 0
cube_major(:,:,2) =
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 1 0 0 0 0
0 0 0 1 1 1 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
cube_major(:,:,3) =
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 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 0 0 0 0 0 0 0 0
Creating a Shape Similar to a Skeleton
To illustrate the branch points and end points options, create another small matrix, this time with a linear shape, like a skeleton.
x1 = eye(5); x2 = zeros(5); x2(3,3) = 1; x3 = x2; shape = cat(3,x1,x2,x3)
shape =
shape(:,:,1) =
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
shape(:,:,2) =
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
shape(:,:,3) =
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
Finding End Points
Find the end points of the shape using the 'endpoints' operation. The shape has three end points, one at each end of the diagonal in the first plane and one at the end of the line through the center, on the third plane.
shape_endpts = bwmorph3(shape,'endpoints')shape_endpts = 5x5x3 logical array
shape_endpts(:,:,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 1
shape_endpts(:,:,2) =
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
shape_endpts(:,:,3) =
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
Finding Branch Points
Find the branch points of the shape using the 'branchpoints' operation. The shape has a single branch point, where the diagonal line and the horizontal line meet.
shape_brpts = bwmorph3(shape,'branchpoints')shape_brpts = 5x5x3 logical array
shape_brpts(:,:,1) =
0 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 0
shape_brpts(:,:,2) =
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
shape_brpts(:,:,3) =
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
Input Arguments
V — Input volume
numeric array | logical array
Input volume, specified as a numeric or logical array.
bwmorph3 accepts 1-D, 2-D, or 3-D arrays. If you
specify 1-D or 2-D input arrays, then bwmorph3 performs
the morphological operation as defined for a 3-D volume. If you want 2-D
behavior, use bwmorph instead.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical
operation — Morphological operation to perform
character vector | string scalar
Morphological operation to perform, specified as one of the following character vectors or string scalar. For examples of these operations, see Illustrations of Morphological Operations.
Operation | Description | Illustration |
|---|---|---|
| Find branch points of skeleton. Branch points are the voxels at the junction where multiple branches meet. To find branch points, the image must
be skeletonized. To create a skeletonized image, use
|
|
| Remove isolated voxels, setting them to 0. An
isolated voxel is an individual, 26-connected voxel that
is set to |
|
| Find end points of skeleton. End points are voxels at the ends of branches. Note: To find end
points, the image must be skeletonized. To create a
skeletonized image, use |
|
| Fill isolated interior voxels, setting them to
|
|
| Keep a voxel set to | See Illustrations of Morphological Operations. |
| Remove interior voxels, setting it to
|
|
Data Types: char | string
Output Arguments
Tips
To perform the morphological operations erosion or dilation on 3-D volumes, use the
imerodeorimdilatefunctions, specifying the structuring elementones(3,3,3).To perform morphological closing, opening, top-hat filtering, or bottom-hat filtering on 3-D volumes, use the
imclose,imopen,imtophat, orimbothatfunctions, specifying the structuring elementones(3,3,3).
Extended Capabilities
Version History
Introduced in R2018a
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