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 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.

Besides the two fundamental operations of EROSION and DILATION, 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 subimage 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 available.

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 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).

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), vmdilate(1), lvmdilate(3)

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

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