Dilation

Dilate binary or intensity image by finding local maxima

• 

Libraries:
Computer Vision Toolbox / Morphological Operations

Description

The Dilation block performs morphological dilation on an intensity or binary image and outputs the dilated image.

To define the structuring element that the block applies to the image, use the Neighborhood or structuring element parameter.

This block uses two-dimensional flat structuring elements only.

Examples

Dilation of Binary Image

Increase the size of a binary image object and fill holes in it.

• Open Script

Ports

Input

I — Input image

matrix

Specify an input image as a matrix of intensity values. This port is unnamed unless you set the Neighborhood or structuring element source parameter to Input port.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | Boolean | fixed point

Nhood — Neighborhood values

vector | matrix

Specify neighborhood values representing a structuring element as a vector or matrix of 1s and 0s or by using the strel function.

Dependencies

To enable this port, set the Neighborhood or structuring element source parameter to Input port.

Data Types: Boolean

Output

Port_1 — Dilated image

matrix

The block returns the dilated image as a matrix of intensity values. The size and data type of the output image are the same as those of the input image.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | Boolean | fixed point

Parameters

Neighborhood or structuring element source — Source of neighborhood or structuring element

Specify via dialog (default) | Input port

Specify the source of the neighborhood or structuring element as one of these options:

• Specify via dialog — Use the Neighborhood or structuring element parameter to specify a neighborhood or structuring element.

• Input port — Use the Nhood input port to specify neighborhood values representing a structuring element.

Neighborhood or structuring element — Neighborhood or structuring element

[1 1; 1 1] (default) | vector | matrix

Specify a neighborhood or structuring element as a vector or matrix of 1s and 0s, a strel object, or an array of strel objects. When you specify an array of strel objects, the block applies each object to the entire image sequentially.

If the structuring element is decomposable into smaller elements, the block uses a more efficient algorithm that can execute more quickly.

Dependencies

To enable this parameter, set the Neighborhood or structuring element source parameter, to Specify via dialog.

Block Characteristics

Data Types	Boolean | double | fixed point | integer | single
Multidimensional Signals	no
Variable-Size Signals	yes

More About

Dilation and Structuring Element

Performing dilation on an image includes:

• Increasing the size of the object by expanding the image pixels and adding pixels to the boundary of the object.

• Filling small holes and broken areas

• Connecting areas separated by a space smaller than the structuring element

The direction and extent of the growth of an object in an image depends on the shape of the structuring element. Each structuring element has an origin.

• If the structuring element is symmetrical, the origin coincides with its centroid.

• If the structuring element is asymmetrical, the pixel in the structuring element that is close to its centroid and is in the top-left direction is considered as the origin.

The Dilation block rotates the structuring element about this origin and places the origin over each pixel of the image object. The block creates the dilated image from the local maxima values at each pixel.

Binary Dilation

The binary dilation of A by B, denoted as A ⨁ B, is defined as the set operation:

$$A\oplus B=\left\{z|{\left(\widehat{B}\right)}_z\cap A\ne \varnothing \right\},$$

where $$\widehat{B}$$ is the reflection of the structuring element B. Note that some applications use a definition of dilation in which the structuring element is not reflected.

Grayscale Dilation

In the general form of grayscale dilation, the structuring element has a specified height. The grayscale dilation of A(x, y) by B(x, y) is defined as:

$$\left(A\oplus B\right)\left(x,y\right)=\max \left\{A(x-x^{\prime },y-y^{\prime })+B(x^{\prime },y^{\prime })|\left(x^{\prime },y^{\prime }\right)\in D_B\right\},$$

where D_B is the domain of the structuring element B and A(x, y) is assumed to be –∞ outside the domain of the image. To create a structuring element with nonzero height values, use the syntax strel(nhood,height), where height specifies the height values and nhood corresponds to the structuring element domain D_B.

Grayscale dilation is often performed with a flat structuring element (B(x,y) = 0). Grayscale dilation using such a structuring element is equivalent to a local-maximum operator:

$$\left(A\oplus B\right)\left(x,y\right)=\max \{A(x-x^{\prime },y-y^{\prime })|(x^{\prime },y^{\prime })\in D_B\}.$$

All of the strel syntaxes except for strel(nhood,height), strel("arbitrary",nhood,height), and strel("ball",...) produce flat structuring elements.

References

[1] Soille, Pierre. Morphological Image Analysis. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. https://doi.org/10.1007/978-3-662-05088-0.

[2] Gonzalez, Rafael C., Richard E. Woods, and Steven L. Eddins. Digital Image Processing Using MATLAB. Third edition. Knoxville: Gatesmark Publishing, 2020.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a