
vmclose(1)                   Khoros                    vmclose(1)

PROGRAM
     vmclose - Computes the closing of image by a structuring
     element

SYNTAX
     vmclose

     -i             input image

     -k             input kernel

     -o             output image

     [-V]           Gives the version for vmclose

     [-U]           Gives the usage for vmclose

     [-P]           Prompts for command line options

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

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

DESCRIPTION
     vmclose computes the closing of an image by a structuring
     element B.

     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.

     Essentially, 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.

     Besides the two fundamental operations of EROSION and DILA-
     TION, two other operations play an important role in image
     analysis.

     These two secondary operations, called OPENING and CLOSING
     are only defined by a combination of erosion and dilation.

     Notation: erode(A,B) = E(A,B)
               dilate(A,B) = D(A,B)
               open(A,B) = O(A,B)
               close(A,B) = C(A,B)
               complement(A) = Ac    (complement of A)

     DEFINITION OF THE CLOSING
               C(A,B) = E(D(A,-B),-B) with
               -B=rotation(B,180 degrees) = vm180(B).
               For information O(A,B) = D(E(A,B),B)

     PROPERTIES of the CLOSING:

     1. duality between the opening & closing
               C(Ac,B) = O(A,B)
               C(Ac,B) = COMPLEMENT[ O(A,B) ]
               COMPLEMENT[ C(A,B) ] = O(Ac,B)
               C(A,B) = COMPLEMENT[ O(Ac,B) ]

     2. Extensivity
               A is a subimage of C(A,B)

     3. Increasing monotonicity
               If A1 is a subimage of A2, the C(A1,B) is a subim-
               age of C(A2,B)

     4. Idempotence
               C[C(A,B),B] = C(A,B)

     These properties play a role in the use of opening for the
     construction of morphological filters.

     The opening by a disk can have a smoothing effect (from the
     outside); it acts as a filter, with the exact result being
     dependent upon the shape of the structuring template.

     Set of morphological functions:

     vmclose is part of a set of morphological functions avail-
     able.

     vmcustom:   Customizes a structuring element.

     vm180:      180 degree rotation of a structuring element.

     vmerode:    dilation.

     vmdilate:   dilation.

     vmopen:     opening.

     vmoredge:   edge extractor.

     vmskeleton: skeleton extractor.

     ADVICE:

          For this binary closing function, all grey levels dif-
          ferent 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 func-
          tion.

     The structuring element must be a morphological kernel
     (created by vmcustom).
     This kernel is nothing but an image form file with two vari-
     ables, 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
     vmclose -i image1 -k kernel -o image2

     This will compute the opening of image1 by the structuring
     element (morphological kernel) kernel, and store the result
     in image2.

SEE ALSO
     intro(1), verror(3), vgparms(3), vutils(3), lvmclose(3)
     vmcustom(1), lvmcustom(3), vmerode(1), lvmerode(3), vmdi-
     late(1), lvmdilate(3)

RESTRICTIONS
     vmclose will only work on two valued BYTE images and on mor-
     phological kernels created with vmcustom.

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

Khoros                    Release: 1.0                          1

