lvmdilate(3)

LIBRARY ROUTINE
lvmdilate - Dilate a binary image by a structuring element.

LIBRARY CALL
#include "vinclude.h"
int
lvmdilate(image,kernel)
struct xvimage *image, *kernel;

INPUT

    img1 -- xvimage structure
    ker -- xvimage structure (morphological kernel)

OUTPUT

    img1 -- holds the result of the dilation by the kernel

MODIFICATIONS
Ghost Conversion by Pascal Adam (Thu May 24 14:14:55 MDT 1990)

DESCRIPTION
vmdilate computes the Dilation of an binary image by a structuring element.

From a general scientific perspective, the word MORPHOLOGY refers to the study of form and structure.

The morphological approach is generally based upon the analysis of a two valued image in terms of some predetermined geometric shape known as a structuring element.

Essentially, the manner in which the structuring element fits into the image is studied.

The morphological operations can be employed for many purposes, including edge detection, segmentation, and enhancement of images.

BASIC OPERATIONS:

Most morphological operations can be defined in terms of two basic operations, the EROSION and the DILATION.

Suppose the object X and the structuring element (or morphological kernel) B are represented as sets in two dimensional Euclidean space. Let Bx denote the translation of B so that its origin is located at x.

The dilation of X by B is defined as the set of all points x such that Bx intersects X, that is they have nonempty intersection:

DILATION(X,B) = { x : Intersection(Bx,X) is nonempty }

Dilating an image by a structuring element B has the effect of "expanding" the image in a manner determined by B.

It is obvious that the dilation of an object is accompanied by reduction or erosion of the background.

PROPERTIES:

The dilation has the following properties.

1. Translation Invariant
    that is, a translation of the object causes the same shift in the result. (the size of the image is a limitation of this property)

2. It is not the inverse of erosion

3. Distributivity
    DILATION does not distribute over the intersection from both the left and the right, but it does over the union.

4. Local knowledge
    The dilation of the intersection of two sets X and Z by a structuring element B, equals to the intersection of the dilation of X by B and Z by B.

5. Iteration
    Dilate(Dilate(X,B),B) = Dilate(X,Dilate(B,B).

6. Increasing
    if the set X is included in the set X', then the dilation of X by B is also included in the dilation of X' by B, whatever B. Now if the structuring element B is included in B', for a set X, we cannot say that the dilation of X by B is included in the dilation of X by B'.

7. Duality
    Erosion and dilation are dual with respect to the complement operation. In other words, eroding a set by a kernel is equivalent to dilating the background (or complement of the set).

Set of morphological functions:

vmdilate is one the morphological functions available.

vmcustom
    Customizes a structuring element vm180 180 degree rotation of a structuring element.

vmerode
    dilation.

vmopen
    opening.

vmclose
    closing.

vmoredge
    edge extractor.

vmskeleton
    skeleton extractor.

ADVICE:

For this binary dilation function, all grey levels different from 0 are considered "white" or equivalent to 255. Therefore, the image is not required to be binary, however, it is strongly advisable to use vthresh on grey level images before using any morphological function.

The structuring element must be a morphological kernel (created by vmcustom). This kernel is nothing but an image form file with two variables ispare1 and ispare2 that define the origin of the structuring element (refer to vmcustom and lvmcustom).

This algorithm was obtained from :

    "Morphological Methods in Image and Signal Processing"

    Charles R. Giardina

    Edward R. Dougherty

    Prentice Hall, Englewood Cliffs, New Jersey 07632

SEE ALSO
vmdilate(1), intro(3), vipl(3), verror(3), vutils(3) vmdilate(1)

RESTRICTIONS
vmdilate will only operate on BYTE data storage types.

AUTHOR
Pascal ADAM

COPYRIGHT
Copyright 1991, University of New Mexico. All rights reserved.