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imhmin

H-minima transform

Description

example

J = imhmin(I,H) suppresses all minima in the grayscale image I whose depth is less than H. Regional minima are connected components of pixels with a constant intensity value, t, whose external boundary pixels all have a value greater than t.

J = imhmin(I,H,conn) computes the H-minima transform, where conn specifies the connectivity.

Examples

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Create a sample image with two regional minima.

a = 10*ones(10,10);
a(2:4,2:4) = 7;  
a(6:8,6:8) = 2
a = 10×10

    10    10    10    10    10    10    10    10    10    10
    10     7     7     7    10    10    10    10    10    10
    10     7     7     7    10    10    10    10    10    10
    10     7     7     7    10    10    10    10    10    10
    10    10    10    10    10    10    10    10    10    10
    10    10    10    10    10     2     2     2    10    10
    10    10    10    10    10     2     2     2    10    10
    10    10    10    10    10     2     2     2    10    10
    10    10    10    10    10    10    10    10    10    10
    10    10    10    10    10    10    10    10    10    10

Suppress all minima below a specified value. Note how the region with pixels valued 7 disappears in the transformed image because its depth is less than the specified h value.

b = imhmin(a,4)
b = 10×10

    10    10    10    10    10    10    10    10    10    10
    10    10    10    10    10    10    10    10    10    10
    10    10    10    10    10    10    10    10    10    10
    10    10    10    10    10    10    10    10    10    10
    10    10    10    10    10    10    10    10    10    10
    10    10    10    10    10     6     6     6    10    10
    10    10    10    10    10     6     6     6    10    10
    10    10    10    10    10     6     6     6    10    10
    10    10    10    10    10    10    10    10    10    10
    10    10    10    10    10    10    10    10    10    10

Input Arguments

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Input image, specified as a numeric array of any dimension.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

H-minima transform, specified as a nonnegative scalar.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Pixel connectivity, specified as one of the values in this table. The default connectivity is 8 for 2-D images, and 26 for 3-D images.

Value

Meaning

Two-Dimensional Connectivities

4

Pixels are connected if their edges touch. The neighborhood of a pixel are the adjacent pixels in the horizontal or vertical direction.

3-by-3 pixel neighborhood with four pixels connected to the center pixel

Current pixel is shown in gray.

8

Pixels are connected if their edges or corners touch. The neighborhood of a pixel are the adjacent pixels in the horizontal, vertical, or diagonal direction.

3-by-3 pixel neighborhood with 8 pixels connected to the center pixel

Current pixel is shown in gray.

Three-Dimensional Connectivities

6

Pixels are connected if their faces touch. The neighborhood of a pixel are the adjacent pixels in:

  • One of these directions: in, out, left, right, up, and down

3-by-3-by-3 pixel neighborhood with 6 pixels connected to the faces of the center pixel

Current pixel is shown in gray.

18

Pixels are connected if their faces or edges touch. The neighborhood of a pixel are the adjacent pixels in:

  • One of these directions: in, out, left, right, up, and down

  • A combination of two directions, such as right-down or in-up

3-by-3-by-3 pixel neighborhood with 6 pixels connected to the faces and 12 pixels connected to the edges of the center pixel

Current pixel is center of cube.

26

Pixels are connected if their faces, edges, or corners touch. The neighborhood of a pixel are the adjacent pixels in:

  • One of these directions: in, out, left, right, up, and down

  • A combination of two directions, such as right-down or in-up

  • A combination of three directions, such as in-right-up or in-left-down

3-by-3-by-3 pixel neighborhood with 6 pixels connected to the faces, 12 pixels connected to the edges, and 8 pixels connected to the corners of the center pixel

Current pixel is center of cube.

For higher dimensions, imhmin uses the default value conndef(ndims(I),'maximal').

Connectivity can also be defined in a more general way for any dimension by specifying a 3-by-3-by- ... -by-3 matrix of 0s and 1s. The 1-valued elements define neighborhood locations relative to the center element of conn. Note that conn must be symmetric about its center element. See Specifying Custom Connectivities for more information.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output Arguments

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Transformed image, returned as a numeric array of the same size and data type as I.

References

[1] Soille, P. Morphological Image Analysis: Principles and Applications. Springer-Verlag, 1999, pp. 170-171.

Extended Capabilities

Version History

Introduced before R2006a