
vmdilate(1)                  Khoros                   vmdilate(1)

PROGRAM
     vmdilate - Dilate a binary image by a structuring element.

SYNTAX
     vmdilate

     -i             input image

     -k             input kernel

     -o             output image

     [-V]           Gives the version for vmdilate

     [-U]           Gives the usage for vmdilate

     [-P]           Prompts for command line options

     [-A [file1]]   Creates the answer file called vmdilate.ans
                    or file1

     [-a [file1]]   Uses vmdilate.ans or file1 as the answer file

DESCRIPTION
     vmdilate computes the Dilation of a binary image by a struc-
     turing 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 predeter-
     mined geometric shape known as a structuring element. Essen-
     tially, the manner in which the structuring element fits
     into the image is studied.

     The morphological operations can be employed for many pur-
     poses, including edge detection, segmentation, and enhance-
     ment 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 mor-
     phological kernel) B are represented as sets in two dimen-
     sional Euclidean space.  Let Bx denote the translation of
     the kernel B by the vector so that its origin is located at
     x.

     The dilation of the image X by the kernel 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 inter-
               section 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 dila-
               tion of X' by B, whatever B.  Now if the structur-
               ing 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 of 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. There-
     fore, 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).

     These algorithms were obtained from :

          "Morphological Methods in Image and Signal Processing"

          Charles R. Giardina

          Edward R. Dougherty

          Prentice Hall, Englewood Cliffs, New Jersey 07632

REQUIRED ARGUMENTS
     -i     type: infile
            desc: input image

     -k     type: infile
            desc: input kernel

     -o     type: outfile
            desc: output image

OPTIONAL ARGUMENTS
     none

EXAMPLES
     vmdilate -i image1 -k kernel -o image2
     Computes the dilation of an image X (input -i ) by a struc-
     turing element B (input -k) and store the result in the out-
     put image ( -o)

SEE ALSO
     intro(1), verror(3), vgparms(3), vutils(3), lvmdilate(3)
     vmcustom(1), lvmcustom(3)

RESTRICTIONS
     vmdilate accepts only BYTE images, and it is strongly advis-
     able to use vthresh to binarize the image  before eroding
     it.  The structuring element  is an image form file,
     nevertheless, it should always be created by  vmcustom.

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

Khoros                    Release: 1.0                          1

