regiongrowing_nregiongrowing_nRegiongrowingNregiongrowing_nRegiongrowingNRegiongrowingN (Operator)

Name

regiongrowing_nregiongrowing_nRegiongrowingNregiongrowing_nRegiongrowingNRegiongrowingN — Segment an image using regiongrowing for multi-channel images.

Signature

regiongrowing_n(MultiChannelImage : Regions : Metric, MinTolerance, MaxTolerance, MinSize : )

regiongrowing_nregiongrowing_nRegiongrowingNregiongrowing_nRegiongrowingNRegiongrowingN performs a multi-channel regiongrowing. The n channels give rise to an n-dimensional feature vector. Neighboring points are aggregated into the same region if the difference of their feature vectors with respect to the given metric lies in the interval [MinToleranceMinToleranceMinToleranceMinToleranceMinToleranceminTolerance, MaxToleranceMaxToleranceMaxToleranceMaxToleranceMaxTolerancemaxTolerance]. Only neighbors of the 4-neighborhood are examined. The following metrics can be used:

Let g_{A} denote the gray value in the feature vector A at point a of the image, and likewise be g_{B} the gray value in the feature vector B at point a neighboring point b. Let g(d) be the gray value with index d. Furthermore, let MinT denote MinToleranceMinToleranceMinToleranceMinToleranceMinToleranceminTolerance and MaxT denote MaxToleranceMaxToleranceMaxToleranceMaxToleranceMaxTolerancemaxTolerance.

'1-norm':

Sum of absolute values

                ----
            1   \
  MinT <=   - * /    |gA - gB|  <= MaxT
            n   ----

'2-norm':

Euclidian distance

             ---------------------
             |     ----
             | 1   \             2
  MinT <=  \ | - * /    (gA - gB)   <= MaxT
            \| n   ----

'3-norm':

p - Norm with p = 3

             ---------------------
             |     ----
           3 | 1   \             3
  MinT <=  \ | - * /    (gA - gB)   <= MaxT
            \| n   ----

'4-norm':

p - Norm with p = 4

             ---------------------
             |     ----
           4 | 1   \             4
  MinT <=  \ | - * /    (gA - gB)   <= MaxT
            \| n   ----

'n-norm':

Minkowski distance

             ---------------------
             |     ----
           n | 1   \             n
  MinT <=  \ | - * /    (gA - gB)   <= MaxT
            \| n   ----

'max-diff':

Supremum distance MinT <= max { |gA - gB| } <= MaxT

'min-diff':

Infimum distance MinT <= min { |gA - gB| } <= MaxT

'variance':

Variance of gray value differences

  X = gA - gB,
  MinT <= Var(X) <= MaxT

'dot-product':

Dot product

                 ------------------
                 |     ----
           1     | 1   \
  MinT <=  - * \ | - * /    gA * gB  <= MaxT
           n    \| n   ----

'correlation':

Correlation

             ----
         1   \
  SA   = - * /    gA ,
         n   ----

               -----------------
               | ----
         1     | \             2
  VarA = - * \ | /    (gA - SA)  ,
         n    \| ----

             ----
         1   \
  SB =   - * /    gB ,
         n   ----

               -----------------
               | ----
         1     | \             2
  VarB = - * \ | /    (gB - SB)  ,
         n    \| ----

           1    ----
           -- * \    (gA - SA)*(gB - SB)
  MinT <=   2   /    -------------------  <= MaxT
           n    ----     VarA * VarB

'mean-diff':

Difference of arithmetic means

  Difference of arithmetic means
          ----
      1   \
  a = - * /    gA ,
      n   ----

          ----
      1   \
  b = - * /    gB ,
      n   ----

  MinT <= |a - b| <= MaxT

'mean-ratio':

Ratio of arithmetic means

  Ratio of arithmetic means
          ----
      1   \
  a = - * /    gA ,
      n   ----

          ----
      1   \
  b = - * /    gB ,
      n   ----

  MinT <= min { a/b, b/a } <= MaxT

'length-diff':

Difference of the vector lengths

        ---------------
        |     ----
        | 1   \       2
  a = \ | - * /     gA  ,
       \| n   ----

        ---------------
        |     ----
        | 1   \       2
  b = \ | - * /     gB  ,
       \| n   ----

  MinT <= |a - b| <= MaxT

'length-ratio':

Ratio of the vector lengths

        ---------------
        |     ----
        | 1   \       2
  a = \ | - * /     gA  ,
       \| n   ----

        ---------------
        |     ----
        | 1   \       2
  b = \ | - * /     gB  ,
       \| n   ----

  MinT <= min { a/b, b/a } <= MaxT

'n-norm-ratio':

Ratio of the vector lengths w.r.t the p-norm with p = n

        ---------------
        |     ----
      n | 1   \       n
  a = \ | - * /     gA  ,
       \| n   ----

        ---------------
        |     ----
      n | 1   \       n
  b = \ | - * /     gB  ,
       \| n   ----

  MinT <= min { a/b, b/a } <= MaxT

'gray-max-diff':

Difference of the maximum gray values

  a = max { |gA| },
  b = max { |gB| },
  MinT <= |a - b| <= MaxT

'gray-max-ratio':

Ratio of the maximum gray values

  a = max { |gA| },
  b = max { |gB| },
  MinT <= min { a/b, b/a } <= MaxT

'gray-min-diff':

Difference of the minimum gray values

  a = min { |gA| },
  b = min { |gB| },
  MinT <= |a - b| <= MaxT

'gray-min-ratio':

Ratio of the minimum gray values

  a = min { |gA| },
  b = min { |gB| },
  MinT <= min { a/b, b/a } <= MaxT

'variance-diff':

Difference of the variances over all gray values (channels)

  MinT <= | Var(gA) - Var(gB) | <= MaxT

'variance-ratio':

Ratio of the variances over all gray values (channels)

  MinT <= Var(gB) / Var(gA) <= MaxT

'mean-abs-diff':

Difference of the sum of absolute values over all gray values (channels)

      ----
      \
  a = /    |gA(d) - gA(k)|
      ----
     d,k,k<d

      ----
      \
  b = /    |gB(d) - gB(k)|
      ----
     d,k,k<d

  MinT <= 1/z * |a - b| <= MaxT,  z = Anzahl der Summen

'mean-abs-ratio':

Ratio of the sum of absolute values over all gray values (channels)

      ----
      \
  a = /    |gA(d) - gA(k)|
      ----
     d,k,k<d

      ----
      \
  b = /    |gB(d) - gB(k)|
      ----
     d,k,k<d

  MinT <= min { a/b, b/a } <= MaxT

'max-abs-diff':

Difference of the maximum distance of the components

  a = max { gA(d), gA(k) },
  b = max { gB(d), gB(k) },
  MinT <= |a - b| <= MaxT

'max-abs-ratio':

Ratio of the maximum distance of the components

  a = max { gA(d), gA(k) },
  b = max { gB(d), gB(k) },
  MinT <= min { a/b, b/a } <= MaxT

'min-abs-diff':

Difference of the minimum distance of the components

  a = min { gA(d), gA(k) }, k < d
  b = min { gB(d), gB(k) }, k < d
  MinT <= |a - b| <= MaxT

'min-abs-ratio':

Ratio of the minimum distance of the components

  a = min { gA(d), gA(k) }, k < d
  b = min { gB(d), gB(k) }, k < d
  MinT <= min { a/b, b/a } <= MaxT

'plane':

The following has to hold for all d1, d2 in [1,n]:

  gA(d1) > gA(d2) ==> gB(d1) > gB(d2),
  gA(d1) < gA(d2) ==> gB(d1) < gB(d2)

Regions with an area less than MinSizeMinSizeMinSizeMinSizeMinSizeminSize are suppressed.

Parallelization

Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Automatically parallelized on tuple level.

Parameters

MultiChannelImageMultiChannelImageMultiChannelImageMultiChannelImageMultiChannelImagemultiChannelImage (input_object) (multichannel-)image(-array) → object (byte)

Input image.

RegionsRegionsRegionsRegionsRegionsregions (output_object) region-array → object

Segmented regions.

MetricMetricMetricMetricMetricmetric (input_control) string → (string)

Metric for the distance of the feature vectors.

Default value: '2-norm' "2-norm" "2-norm" "2-norm" "2-norm" "2-norm"

List of values: '1-norm'"1-norm""1-norm""1-norm""1-norm""1-norm", '2-norm'"2-norm""2-norm""2-norm""2-norm""2-norm", '3-norm'"3-norm""3-norm""3-norm""3-norm""3-norm", '4-norm'"4-norm""4-norm""4-norm""4-norm""4-norm", 'correlation'"correlation""correlation""correlation""correlation""correlation", 'dot-product'"dot-product""dot-product""dot-product""dot-product""dot-product", 'gray-max-diff'"gray-max-diff""gray-max-diff""gray-max-diff""gray-max-diff""gray-max-diff", 'gray-max-ratio'"gray-max-ratio""gray-max-ratio""gray-max-ratio""gray-max-ratio""gray-max-ratio", 'gray-min-diff'"gray-min-diff""gray-min-diff""gray-min-diff""gray-min-diff""gray-min-diff", 'gray-min-ratio'"gray-min-ratio""gray-min-ratio""gray-min-ratio""gray-min-ratio""gray-min-ratio", 'length-diff'"length-diff""length-diff""length-diff""length-diff""length-diff", 'length-ratio'"length-ratio""length-ratio""length-ratio""length-ratio""length-ratio", 'max-abs-diff'"max-abs-diff""max-abs-diff""max-abs-diff""max-abs-diff""max-abs-diff", 'max-abs-ratio'"max-abs-ratio""max-abs-ratio""max-abs-ratio""max-abs-ratio""max-abs-ratio", 'max-diff'"max-diff""max-diff""max-diff""max-diff""max-diff", 'mean-abs-diff'"mean-abs-diff""mean-abs-diff""mean-abs-diff""mean-abs-diff""mean-abs-diff", 'mean-abs-ratio'"mean-abs-ratio""mean-abs-ratio""mean-abs-ratio""mean-abs-ratio""mean-abs-ratio", 'mean-diff'"mean-diff""mean-diff""mean-diff""mean-diff""mean-diff", 'mean-ratio'"mean-ratio""mean-ratio""mean-ratio""mean-ratio""mean-ratio", 'min-abs-diff'"min-abs-diff""min-abs-diff""min-abs-diff""min-abs-diff""min-abs-diff", 'min-abs-ratio'"min-abs-ratio""min-abs-ratio""min-abs-ratio""min-abs-ratio""min-abs-ratio", 'min-diff'"min-diff""min-diff""min-diff""min-diff""min-diff", 'n-norm'"n-norm""n-norm""n-norm""n-norm""n-norm", 'n-norm-ratio'"n-norm-ratio""n-norm-ratio""n-norm-ratio""n-norm-ratio""n-norm-ratio", 'plane'"plane""plane""plane""plane""plane", 'variance'"variance""variance""variance""variance""variance", 'variance-diff'"variance-diff""variance-diff""variance-diff""variance-diff""variance-diff", 'variance-ratio'"variance-ratio""variance-ratio""variance-ratio""variance-ratio""variance-ratio"

MinToleranceMinToleranceMinToleranceMinToleranceMinToleranceminTolerance (input_control) number → (real / integer)

Lower threshold for the features' distance.

Default value: 0.0

Suggested values: 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0, 25.0, 30.0

MaxToleranceMaxToleranceMaxToleranceMaxToleranceMaxTolerancemaxTolerance (input_control) number → (real / integer)

Upper threshold for the features' distance.

Default value: 20.0

Suggested values: 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0, 25.0, 30.0

MinSizeMinSizeMinSizeMinSizeMinSizeminSize (input_control) integer → (integer)

Minimum size of the output regions.

Default value: 30

Suggested values: 1, 10, 25, 50, 100, 200, 500, 1000

Typical range of values: 1 ≤ MinSize MinSize MinSize MinSize MinSize minSize

Minimum increment: 1

Recommended increment: 5

Result

regiongrowing_nregiongrowing_nRegiongrowingNregiongrowing_nRegiongrowingNRegiongrowingN returns 2 (H_MSG_TRUE) if all parameters are correct. The behavior with respect to the input images and output regions can be determined by setting the values of the flags 'no_object_result'"no_object_result""no_object_result""no_object_result""no_object_result""no_object_result", 'empty_region_result'"empty_region_result""empty_region_result""empty_region_result""empty_region_result""empty_region_result", and 'store_empty_region'"store_empty_region""store_empty_region""store_empty_region""store_empty_region""store_empty_region" with set_systemset_systemSetSystemset_systemSetSystemSetSystem. If necessary, an exception is raised.

regiongrowing_nregiongrowing_nRegiongrowingNregiongrowing_nRegiongrowingNRegiongrowingN (Operator)

Name

Signature

Description

Parallelization

Parameters

Result

Possible Predecessors

Alternatives

See also

Module