ERODE Function

Implements the morphologic erosion operator for shape processing.

Usage

result = ERODE(image, structure [, x₀, y₀])

Input Parameters

image The array to be eroded.

structure The structuring element. May be a one- or two-dimensional array. Elements are interpreted as binary (values are either zero or nonzero), unless the Gray keyword is used.

x₀ (optional) The x-coordinates of structure's origin.

y₀ (optional) The y-coordinates of structure's origin.

Returned Value

The eroded image.

Keywords

Gray A flag which, if present, indicates that gray scale, rather than binary erosion, is to be used.

Values An array providing the values of the structuring element. Must have the same dimensions and number of elements as structure.

Discussion

If image is not of the byte type, PV-WAVE makes a temporary byte copy of image before using it for the processing.

The optional parameters x₀ and y₀ specify the row and column coordinates of the structuring element's origin. If omitted, the origin is set to the center, (N_x / 2 , N_y / 2 ), where N_x and N_y are the dimensions of the structuring element array. However, the origin need not be within the structuring element.

Nonzero elements of the structure parameter determine the shape of the structuring element (neighborhood).

If the Values keyword is not used, all elements of the structuring element are 0, yielding the neighborhood minimum operator.

You can choose whether you want to use gray scale or binary erosion:

If you select binary erosion type, the image is considered to be a binary image with all nonzero pixels considered as 1. (You will automatically select binary erosion if you don't use either the Gray or Values keyword.)
If you select gray scale erosion type, each pixel of the result is the minimum of the difference of the corresponding elements of Values overlaid with image. (You will automatically select gray scale erosion if you use either the Gray or Values keyword.)

Background Information

The ERODE function implements the morphologic erosion operator on binary and gray scale images and vectors. Mathematical morphology provides an approach to the processing of digital images on the basis of shape. This approach is summarized in the description of the DILATE function. Erosion is the complement (dual) of dilation; it does to the background what dilation does to the foreground.

Briefly, ERODE returns the erosion of image by the structuring element, structure. This operation is also commonly known as contracting or reducing. It can be used to remove islands smaller than the structuring element.

The result is an image that contains items that now contract away from each other. Features that either slightly touch or are connected by narrow areas may disconnect, becoming separate, smaller objects. Any holes or gaps in or between features become larger as the features in the image shrink away from each other. Sharp-edged items and harsh angles typically become dull as they are worn away; however, in some cases areas that were dull may become somewhat sharper as a feature erodes away.

TIP: Erosion can be used to change the morphological structure of objects or features in an image to see what would happen if they were to actually shrink over time.

Used with gray scale images, which are always converted to a byte type, the ERODE function is accomplished by taking the minimum of a set of differences. It may be conveniently used to implement the neighborhood minimum operator, with the shape of the neighborhood given by the structuring element.

Used with binary images, the origin of the structuring element is moved to each pixel of the image. If each nonzero element of the structuring element is contained in the image, the output pixel is set to one.

Letting A represent the erosion of an image A by structuring element B, erosion may be defined as:

where (A)_-b represents the translation of A by b. The structuring element B may be visualized as a probe which slides across the image A, testing the spatial nature of A at each point. Where B translated by i, j can be contained in A (by placing the origin of B at i, j), then A_{i, j} belongs to the erosion of A by B.

Example 1

In this example, the origin of the structuring element is at (0, 0):

Example 2

This example demonstrates what an aerial image looks like before and after applying the ERODE function three different times. For this example, the following parameters were used each time:

img = ERODE(aerial_img, struct, /Gray)

where struct has a value of [1 0 1].

Because the ERODE function was applied to the image three times, the "blurring" is more pronounced that it would have been with only one erosion.

Figure 2-33 The ERODE function has been used to "wear away" the visual elements of this 512-by-512 aerial image.

Figure 2-34 The ERODE function has been used to "wear away" the visual elements of this 512-by-512 aerial image.

See Also

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