public interface Morphology extends ArrayProcessorWithContextSwitching
Mathematical morphology over ndimensional matrices
with a random
ndimensional structuring element (shape), represented by Pattern
class.
It is supposed that the type of matrix elements is one of primitive Java types
(boolean, char, byte, short, int,
long, float, double) and, so, represents an integer or a real number,
according to comments to PFixedArray.getLong(long)
and PArray.getDouble(long)
methods.
In 2dimensional case, these operations can be used for processing grayscale digital images.
Please see
Basic operations, defined by this interface, are dilation
and erosion
. Other operations are combinations
of the basic ones and, probably, some arithmetic elementwise operations.
This package provides the following basic methods for creating objects, implementing this interface:
BasicMorphology.getInstance(ArrayContext)
;BasicMorphology.getInstance(ArrayContext, long)
;ContinuedMorphology.getInstance(Morphology, Matrix.ContinuationMode)
;and also the methods creating RankMorphology
objects — see comments to that interface.
The classes, implementing this interface, are immutable and threadsafe: there are no ways to modify settings of the created instance.
AlgART Laboratory 2007–2014
Modifier and Type  Interface and Description 

static class 
Morphology.SubtractionMode
Subtraction mode for some methods of
Morphology interface. 
Modifier and Type  Method and Description 

Matrix<? extends PArray> 
asDilation(Matrix<? extends PArray> src,
Pattern pattern)
Returns an immutable view of the passed source matrix,
such that any reading data from it calculates and returns the dilation
of the source matrix by the specified pattern.

Matrix<? extends PArray> 
asErosion(Matrix<? extends PArray> src,
Pattern pattern)
Returns an immutable view of the passed source matrix,
such that any reading data from it calculates and returns the erosion
of the source matrix by the specified pattern.

Matrix<? extends UpdatablePArray> 
beucherGradient(Matrix<? extends PArray> src,
Pattern pattern)

Matrix<? extends UpdatablePArray> 
closing(Matrix<? extends PArray> src,
Pattern pattern,
Morphology.SubtractionMode subtractionMode)
Returns a new updatable matrix, containing the closing
of the source matrix by the specified pattern.

Morphology 
context(ArrayContext newContext)
Switches the context: returns an instance, identical to this one excepting
that it uses the specified newContext for all operations.

Matrix<? extends UpdatablePArray> 
dilation(Matrix<? extends PArray> src,
Pattern pattern)
Returns a new updatable matrix, containing the dilation
of the source matrix by the specified pattern.

Matrix<? extends UpdatablePArray> 
dilation(Matrix<? extends PArray> src,
Pattern pattern,
Morphology.SubtractionMode subtractionMode)
Extended version of
dilation(Matrix, Pattern) method: if subtractionMode argument
is not Morphology.SubtractionMode.NONE ,
returns the difference between the dilation and the src matrix,
according the specified mode. 
void 
dilation(Matrix<? extends UpdatablePArray> dest,
Matrix<? extends PArray> src,
Pattern pattern)
Equivalent to
dilation(dest, src, pattern, false) . 
void 
dilation(Matrix<? extends UpdatablePArray> dest,
Matrix<? extends PArray> src,
Pattern pattern,
boolean disableMemoryAllocation)
Equivalent to
dilation(Matrix, Pattern) method, but the result matrix
will be placed in the dest argument. 
Matrix<? extends UpdatablePArray> 
dilationErosion(Matrix<? extends PArray> src,
Pattern dilationPattern,
Pattern erosionPattern,
Morphology.SubtractionMode subtractionMode)
Returns a new updatable matrix, containing the result of sequential
dilation(src, dilationPattern) and
erosion(src, erosionPattern)
of the source matrix by the specified patterns. 
Matrix<? extends UpdatablePArray> 
erosion(Matrix<? extends PArray> src,
Pattern pattern)
Returns a new updatable matrix, containing the erosion
of the source matrix by the specified pattern.

Matrix<? extends UpdatablePArray> 
erosion(Matrix<? extends PArray> src,
Pattern pattern,
Morphology.SubtractionMode subtractionMode)
Extended version of
erosion(Matrix, Pattern) method: if subtractionMode argument
is not Morphology.SubtractionMode.NONE ,
returns the difference between the erosion and the src matrix,
according the specified mode. 
void 
erosion(Matrix<? extends UpdatablePArray> dest,
Matrix<? extends PArray> src,
Pattern pattern)
Equivalent to
erosion(dest, src, pattern, false) . 
void 
erosion(Matrix<? extends UpdatablePArray> dest,
Matrix<? extends PArray> src,
Pattern pattern,
boolean disableMemoryAllocation)
Equivalent to
erosion(Matrix, Pattern) method, but the result matrix
will be placed in the dest argument. 
Matrix<? extends UpdatablePArray> 
erosionDilation(Matrix<? extends PArray> src,
Pattern erosionPattern,
Pattern dilationPattern,
Morphology.SubtractionMode subtractionMode)
Returns a new updatable matrix, containing the result of sequential
erosion(src, erosionPattern) and
dilation(src, dilationPattern)
of the source matrix by the specified patterns. 
boolean 
isPseudoCyclic()
Returns true, if this class works in the default
pseudocyclic continuation mode . 
Matrix<? extends UpdatablePArray> 
maskedDilationErosion(Matrix<? extends PArray> src,
Pattern dilationPattern,
Pattern erosionPattern)
Returns the elementwise minimum between the source matrix and the result of
dilationErosion (src, dilationPattern, erosionPattern, Morphology.SubtractionMode.NONE ) call. 
Matrix<? extends UpdatablePArray> 
maskedErosionDilation(Matrix<? extends PArray> src,
Pattern erosionPattern,
Pattern dilationPattern)
Returns the elementwise maximum between the source matrix and the result of
erosionDilation (src, erosionPattern, dilationPattern, Morphology.SubtractionMode.NONE ) call. 
Matrix<? extends UpdatablePArray> 
opening(Matrix<? extends PArray> src,
Pattern pattern,
Morphology.SubtractionMode subtractionMode)
Returns a new updatable matrix, containing the opening
of the source matrix by the specified pattern.

Matrix<? extends UpdatablePArray> 
weakDilation(Matrix<? extends PArray> src,
Pattern pattern)
Returns a new updatable matrix, containing the weak dilation
of the source matrix by the specified pattern.

Matrix<? extends UpdatablePArray> 
weakErosion(Matrix<? extends PArray> src,
Pattern pattern)
Returns a new updatable matrix, containing the weak erosion
of the source matrix by the specified pattern.

context
Morphology context(ArrayContext newContext)
ArrayProcessorWithContextSwitching
subtask
of the full task.context
in interface ArrayProcessorWithContextSwitching
newContext
 another context, used by the returned instance; may be null.boolean isPseudoCyclic()
pseudocyclic continuation mode
.
More precisely, it means that when the value in some element of the processed matrix,
returned by a method of this class, depends on elements of the source matrix, lying outside its bounds,
then it is supposed that the values outside the source matrix are calculated as described in
Matrix.ContinuationMode.PSEUDO_CYCLIC
. Exactly such behaviour is specified in
the comments to the basic dilation(Matrix, Pattern)
and erosion(Matrix, Pattern)
methods as the default definition of dilation and erosion.
This method returns true in BasicMorphology
and BasicRankMorphology
implementation.
However, it usually returns false in ContinuedMorphology
and
ContinuedRankMorphology
classes — excepting the only degenerated case when the used
continuation mode
is
PSEUDO_CYCLIC
.
Matrix<? extends PArray> asDilation(Matrix<? extends PArray> src, Pattern pattern)
dilation(Matrix, Pattern)
method about the "dilation" term.
The element type
of the created matrix is the same as the element type of the source one.
The result is usually "lazy", that means that this method finishes immediately and all
actual calculations are performed while getting elements of the returned matrix.
It is true for all implementations provided by this package.
However, some implementations may not support lazy dilation;
then this method will be equivalent to dilation(Matrix, Pattern)
.
Please note: this method does not require time (if the result is "lazy"),
but the resulting matrix can work slowly!
For example, reading all its content than work much slower than dilation(Matrix, Pattern)
method for complex patterns.
Usually you should use it only for very little patterns, or if you know that the implementation
of this interface does not provide better algorithm for non"lazy"
dilation(Matrix, Pattern)
method.
src
 the source matrix.pattern
 the pattern.java.lang.NullPointerException
 if one of the arguments is null.java.lang.IllegalArgumentException
 if the number of the pattern dimensions
pattern.dimCount()
is not equal
to src.dimCount()
.Matrix<? extends PArray> asErosion(Matrix<? extends PArray> src, Pattern pattern)
erosion(Matrix, Pattern)
method about the "erosion" term.
The element type
of the created matrix is the same as the element type of the source one.
The result is usually "lazy", that means that this method finishes immediately and all
actual calculations are performed while getting elements of the returned matrix.
It is true for all implementations provided by this package.
However, some implementations may not support lazy erosion;
then this method will be equivalent to erosion(Matrix, Pattern)
.
Please note: this method does not require time (if the result is "lazy"),
but the resulting matrix can work slowly!
For example, reading all its content than work much slower than dilation(Matrix, Pattern)
method for complex patterns.
Usually you should use it only for very little patterns, or if you know that the implementation
of this interface does not provide better algorithm for non"lazy"
erosion(Matrix, Pattern)
method.
src
 the source matrix.pattern
 the pattern.java.lang.NullPointerException
 if one of the arguments is null.java.lang.IllegalArgumentException
 if the number of the pattern dimensions
pattern.dimCount()
is not equal
to src.dimCount()
.Matrix<? extends UpdatablePArray> dilation(Matrix<? extends PArray> src, Pattern pattern)
Usually dilation means the elementwise maximum from the set of matrices,
obtained by pseudocyclic shifting the source matrix by the vectors,
equal to all pattern points.
More precisely, let m_{i}=Matrices.asShifted
(src,ip.coordinates()
),
where ip is the point #i from all points contained in the pattern.
Then the every element of the returned matrix is the maximum from all corresponding elements
of all m_{i} matrices. The element type
of the created matrix is the same as the element type of the source one.
The byte and short elements are considered to be unsigned.
In a case of bit elements, the maximum is equivalent to logical OR.
The basic morphology implementation BasicMorphology
strictly complies with this definition.
However, other implementations of this interface may use alternate definitions of the dilation term.
For example, some percentile (90% or 80%) may be used instead of strict maximum
(as in objects, returned by BasicRankMorphology.getInstance(ArrayContext, double, CustomRankPrecision)
method),
or elements outside the matrix may be supposed to be filled according some nontrivial rules
instead of pseudocyclic continuation
(as in ContinuedMorphology
objects),
or only some region of the matrix may be processed, etc.
Please see
src
 the source matrix.pattern
 the pattern.java.lang.NullPointerException
 if one of the arguments is null.java.lang.IllegalArgumentException
 if the number of the pattern dimensions
pattern.dimCount()
is not equal
to src.dimCount()
.asDilation(Matrix, Pattern)
,
dilation(Matrix, Matrix, Pattern, boolean)
,
dilation(Matrix, Pattern, Morphology.SubtractionMode)
Matrix<? extends UpdatablePArray> erosion(Matrix<? extends PArray> src, Pattern pattern)
Usually erosion means the elementwise minimum from the set of matrices,
obtained by pseudocyclic shifting the source matrix by the vectors,
symmetric to all pattern points relatively the origin of coordinates.
More precisely, let m_{i}=Matrices.asShifted
(src,ip.symmetric()
.coordinates()
),
where ip is the point #i from all points contained in the pattern.
Then the every element of the returned matrix is the minimum from all corresponding elements
of all m_{i} matrices. The element type
of the created matrix is the same as the element type of the source one.
The byte and short elements are considered to be unsigned.
In a case of bit elements, the minimum is equivalent to logical AND.
The basic morphology implementation BasicMorphology
strictly complies with this definition.
However, other implementations of this interface may use alternate definitions of the erosion term.
For example, some percentile (10% or 20%) may be used instead of strict minimum
(as in objects, returned by BasicRankMorphology.getInstance(ArrayContext, double, CustomRankPrecision)
method),
or elements outside the matrix may be supposed to be filled according some nontrivial rules
instead of pseudocyclic continuation
(as in ContinuedMorphology
objects),
or only some region of the matrix may be processed, etc.
Please see
src
 the source matrix.pattern
 the pattern.java.lang.NullPointerException
 if one of the arguments is null.java.lang.IllegalArgumentException
 if the number of the pattern dimensions
pattern.dimCount()
is not equal
to src.dimCount()
.asDilation(Matrix, Pattern)
,
erosion(Matrix, Matrix, Pattern, boolean)
,
erosion(Matrix, Pattern, Morphology.SubtractionMode)
Matrix<? extends UpdatablePArray> dilation(Matrix<? extends PArray> src, Pattern pattern, Morphology.SubtractionMode subtractionMode)
dilation(Matrix, Pattern)
method: if subtractionMode argument
is not Morphology.SubtractionMode.NONE
,
returns the difference between the dilation and the src matrix,
according the specified mode.
If subtractionMode==Morphology.SubtractionMode.NONE
, this method is strictly equivalent
to dilation(Matrix, Pattern)
.
The result of this operation with subtractionMode==Morphology.SubtractionMode.SUBTRACT_SRC_FROM_RESULT
is also called the external gradient of the source matrix.
src
 the source matrix.pattern
 the pattern.subtractionMode
 whether the difference of the dilation and the source matrix should be returned.java.lang.NullPointerException
 if one of the arguments is null.java.lang.IllegalArgumentException
 if the number of the pattern dimensions
pattern.dimCount()
is not equal
to src.dimCount()
.Matrix<? extends UpdatablePArray> erosion(Matrix<? extends PArray> src, Pattern pattern, Morphology.SubtractionMode subtractionMode)
erosion(Matrix, Pattern)
method: if subtractionMode argument
is not Morphology.SubtractionMode.NONE
,
returns the difference between the erosion and the src matrix,
according the specified mode.
If subtractionMode==Morphology.SubtractionMode.NONE
, this method is strictly equivalent
to erosion(Matrix, Pattern)
.
The result of this operation with subtractionMode==Morphology.SubtractionMode.SUBTRACT_RESULT_FROM_SRC
is also called the internal gradient of the source matrix.
src
 the source matrix.pattern
 the pattern.subtractionMode
 whether the difference of the erosion and the source matrix should be returned.java.lang.NullPointerException
 if one of the arguments is null.java.lang.IllegalArgumentException
 if the number of the pattern dimensions
pattern.dimCount()
is not equal
to src.dimCount()
.void dilation(Matrix<? extends UpdatablePArray> dest, Matrix<? extends PArray> src, Pattern pattern, boolean disableMemoryAllocation)
dilation(Matrix, Pattern)
method, but the result matrix
will be placed in the dest argument.
It allows to avoid extra memory allocation if you need to perform dilation many times
from one matrix to another.
Moreover, if disableMemoryAllocation argument is true, this method
guarantees that no any additional memory will be allocated, even if it can optimize the algorithm speed.
In this case, this method is always executed in one pass:
it is equivalent to creating new lazy matrix by asDilation(Matrix src, Pattern pattern)
method
and further copying it into dest by Matrices.copy(ArrayContext, Matrix, Matrix)
method.
It can be useful if you are sure that the pattern is small enough (usually 210 points),
and allocation additional work matrices can slow down the algorithm to greater extent
than using the simple onepass algorithm.
If the element type of the dest matrix is not the same as the source element type
(dest.elementType()
!=src.elementType()
),
the elements are automatically cast to the necessary type. More precisely, in this case
the dest matrix, before all further calculations, is replaced with
Matrices.asUpdatableFuncMatrix
(true,Func.UPDATABLE_IDENTITY
, src.updatableType(UpdatablePArray.class), dest)
We do not recommend to pass matrices with different element types: it can slow down calculations.
dest
 the target matrix.src
 the source matrix.pattern
 the pattern.disableMemoryAllocation
 if false, this method may allocate additional temporary matrices
for optimizing the algorithm speed;
if true, no any work memory will be allocated.java.lang.NullPointerException
 if one of the arguments is null.SizeMismatchException
 if the passed matrices have different dimensions.java.lang.IllegalArgumentException
 if the number of the pattern dimensions
pattern.dimCount()
is not equal
to src.dimCount()
.void erosion(Matrix<? extends UpdatablePArray> dest, Matrix<? extends PArray> src, Pattern pattern, boolean disableMemoryAllocation)
erosion(Matrix, Pattern)
method, but the result matrix
will be placed in the dest argument.
It allows to avoid extra memory allocation if you need to perform erosion many times
from one matrix to another.
Moreover, if disableMemoryAllocation argument is true, this method
guarantees that no any additional memory will be allocated, even if it can optimize the algorithm speed.
In this case, this method is always executed in one pass:
it is equivalent to creating new lazy matrix by asDilation(Matrix src, Pattern pattern)
method
and further copying it into dest by Matrices.copy(ArrayContext, Matrix, Matrix)
method.
It can be useful if you are sure that the pattern is small enough (usually 210 points),
and allocation additional work matrices can slow down the algorithm to greater extent
than using the simple onepass algorithm.
If the element type of the dest matrix is not the same as the source element type
(dest.elementType()
!=src.elementType()
),
the elements are automatically cast to the necessary type. More precisely, in this case
the dest matrix, before all further calculations, is replaced with
Matrices.asUpdatableFuncMatrix
(true,Func.UPDATABLE_IDENTITY
, src.updatableType(UpdatablePArray.class), dest)
We do not recommend to pass matrices with different element types: it can slow down calculations.
dest
 the target matrix.src
 the source matrix.pattern
 the pattern.disableMemoryAllocation
 if false, this method may allocate additional temporary matrices
for optimizing the algorithm speed;
if true, no any work memory will be allocated.java.lang.NullPointerException
 if one of the arguments is null.SizeMismatchException
 if the passed matrices have different dimensions.java.lang.IllegalArgumentException
 if the number of the pattern dimensions
pattern.dimCount()
is not equal
to src.dimCount()
.void dilation(Matrix<? extends UpdatablePArray> dest, Matrix<? extends PArray> src, Pattern pattern)
dilation(dest, src, pattern, false)
.dest
 the target matrix.src
 the source matrix.pattern
 the pattern.java.lang.NullPointerException
 if one of the arguments is null.SizeMismatchException
 if the passed matrices have different dimensions.java.lang.IllegalArgumentException
 if the number of the pattern dimensions
pattern.dimCount()
is not equal
to src.dimCount()
.void erosion(Matrix<? extends UpdatablePArray> dest, Matrix<? extends PArray> src, Pattern pattern)
erosion(dest, src, pattern, false)
.dest
 the target matrix.src
 the source matrix.pattern
 the pattern.java.lang.NullPointerException
 if one of the arguments is null.SizeMismatchException
 if the passed matrices have different dimensions.java.lang.IllegalArgumentException
 if the number of the pattern dimensions
pattern.dimCount()
is not equal
to src.dimCount()
.Matrix<? extends UpdatablePArray> dilationErosion(Matrix<? extends PArray> src, Pattern dilationPattern, Pattern erosionPattern, Morphology.SubtractionMode subtractionMode)
dilation(src, dilationPattern)
and
erosion(src, erosionPattern)
of the source matrix by the specified patterns.
If subtractionMode is not Morphology.SubtractionMode.NONE
,
the behaviour is little other: this method returns the difference between
the result of these two operation and the src matrix, according the specified mode.
When both patterns are equal, the result is the closing
of the matrix.
src
 the source matrix.dilationPattern
 the pattern for dilation.erosionPattern
 the pattern for erosion.subtractionMode
 whether the difference with the source matrix should be returned.java.lang.NullPointerException
 if one of the arguments is null.java.lang.IllegalArgumentException
 if dilationPattern.dimCount()
or
erosionPattern.dimCount()
is not equal
to src.dimCount()
.Matrix<? extends UpdatablePArray> erosionDilation(Matrix<? extends PArray> src, Pattern erosionPattern, Pattern dilationPattern, Morphology.SubtractionMode subtractionMode)
erosion(src, erosionPattern)
and
dilation(src, dilationPattern)
of the source matrix by the specified patterns.
If subtractionMode is not Morphology.SubtractionMode.NONE
,
the behaviour is little other: this method returns the difference between
the result of these two operation and the src matrix, according the specified mode.
When both patterns are equal, the result is the opening
of the matrix.
src
 the source matrix.erosionPattern
 the pattern for erosion.dilationPattern
 the pattern for dilation.subtractionMode
 whether the difference with the source matrix should be returned.java.lang.NullPointerException
 if one of the arguments is null.java.lang.IllegalArgumentException
 if dilationPattern.dimCount()
or
erosionPattern.dimCount()
is not equal
to src.dimCount()
.Matrix<? extends UpdatablePArray> closing(Matrix<? extends PArray> src, Pattern pattern, Morphology.SubtractionMode subtractionMode)
Closing means the result of sequential performing
dilation
and erosion
of the source matrix
with the same pattern.
If subtractionMode is not Morphology.SubtractionMode.NONE
,
the behaviour is little other: this method returns the difference between
the closing and the src matrix, according the specified mode.
For example, Morphology.SubtractionMode.SUBTRACT_SRC_FROM_RESULT
argument
with this method allows to remove "light" background from a grayscale image,
represented by src matrix.
This method is equivalent to dilationErosion(src, pattern, pattern, subtractionMode)
.
Please see
src
 the source matrix.pattern
 the pattern.subtractionMode
 whether the difference of the closing and the source matrix should be returned.java.lang.NullPointerException
 if one of the arguments is null.java.lang.IllegalArgumentException
 if the number of the pattern dimensions
pattern.dimCount()
is not equal
to src.dimCount()
.Matrix<? extends UpdatablePArray> opening(Matrix<? extends PArray> src, Pattern pattern, Morphology.SubtractionMode subtractionMode)
Opening means the result of sequential performing
erosion
and dilation
of the source matrix
with the same pattern.
If subtractionMode is not Morphology.SubtractionMode.NONE
,
the behaviour is little other: this method returns the difference between
the opening and the src matrix, according the specified mode.
For example, Morphology.SubtractionMode.SUBTRACT_RESULT_FROM_SRC
argument
with this method allows to remove "dark" background from a grayscale image,
represented by src matrix.
This method is equivalent to erosionDilation(src, pattern, pattern, subtractionMode)
.
Please see
src
 the source matrix.pattern
 the pattern.subtractionMode
 whether the difference of the opening and the source matrix should be returned.java.lang.NullPointerException
 if one of the arguments is null.java.lang.IllegalArgumentException
 if the number of the pattern dimensions
pattern.dimCount()
is not equal
to src.dimCount()
.Matrix<? extends UpdatablePArray> weakDilation(Matrix<? extends PArray> src, Pattern pattern)
Weak dilation of the matrix A is defined as an elementwise difference
B=dilation
(A)(closing
(A)A).
It is obvious that, for any elements, A<=B<=dilation
(A)
(because both differences
dilation
(A)closing
(A)
and closing
(A)A are nonnegative).
(In this method, the closing
is supposed
to be performed with the last argument Morphology.SubtractionMode.NONE
.)
src
 the source matrix.pattern
 the pattern.java.lang.NullPointerException
 if one of the arguments is null.java.lang.IllegalArgumentException
 if the number of the pattern dimensions
pattern.dimCount()
is not equal
to src.dimCount()
.Matrix<? extends UpdatablePArray> weakErosion(Matrix<? extends PArray> src, Pattern pattern)
Weak erosion of the matrix A is defined as an elementwise sum
B=erosion
(A)+(Aopening
(A)).
It is obvious that, for any elements, A>=B>=erosion
(A)
(because both differences
opening
(A)erosion
(A)
and Aopening
(A) are nonnegative).
(In this method, the opening
is supposed
to be performed with the last argument Morphology.SubtractionMode.NONE
.)
src
 the source matrix.pattern
 the pattern.java.lang.NullPointerException
 if one of the arguments is null.java.lang.IllegalArgumentException
 if the number of the pattern dimensions
pattern.dimCount()
is not equal
to src.dimCount()
.Matrix<? extends UpdatablePArray> maskedDilationErosion(Matrix<? extends PArray> src, Pattern dilationPattern, Pattern erosionPattern)
dilationErosion
(src, dilationPattern, erosionPattern, Morphology.SubtractionMode.NONE
) call.
Let B is the result of this method, A is the source matrix,
Q is dilationPattern, P is erosionPattern:
B=min(A,erosion
(dilation
(A,Q),P))
for any elements.
It is obvious that (for any elements) A>=B>=erosion
(A,P).
But if Q is a some "boundary" or "carcass" of the erosion pattern P,
then a stronger condition is true:
A>=B>=opening
(A,P).
More precisely, there is the following theorem.
If Q is a subset of P and the Minkowski sum P⊕Q is equal to
P⊕P (see Pattern.carcass()
method),
then B>=opening
(A,P).
Below is the proof for the binary case. (For other element types, it's enough to consider the system of binary matrices A>=threshold for all possible real values threshold.)
Let some point x∈
opening
(A,P). It means: there is such p_{1}∈P, that for all p∈P we have x+p_{1}p∈A (the statement A). We already know, that x∈A (the case p=p_{1}), and we also need to prove, that x∈erosion
(dilation
(A,Q),P).Let's suppose that it is not true. It means: there is such p_{2}∈P, that for all q∈Q we have x+p_{2}q∉A (the statement B)
Let x will be the origin of coordinates: x=0. Then, let P_{1}=P+p_{1}={p_{1}p, p∈P}. Note: the origin 0∈P_{1} (the case p=p_{1}). We have P_{1}⊂A (statement A), so, for all q∈Q we have p_{2}q∉P_{1} (because p_{2}q∉A, statement B). In other words, p_{2}∉P_{1}⊕Q (dilation of P by Q, or Minkowski sum of P and Q). On the other hand, it's obvious that p_{2}∈P_{1}⊕P, because 0∈P_{1} and, so, P⊂P⊕P_{1}=P_{1}⊕P.
There is a contradiction: according to the condition, there must be P_{1}⊕P=P_{1}⊕Q. The theorem is proved.
This fact allows to interpret this method, if dilationPattern
is a "boundary" of erosionPattern (usually UniformGridPattern.surface()
or a similar point set), as a "weak" analog of opening.
For binary images, it helps to remove small isolated objects, but (unlike usual opening)
to preserve thin structures.
src
 the source matrix.dilationPattern
 the pattern for dilation.erosionPattern
 the pattern for erosion.java.lang.NullPointerException
 if one of the arguments is null.java.lang.IllegalArgumentException
 if dilationPattern.dimCount()
or
erosionPattern.dimCount()
is not equal
to src.dimCount()
.Matrix<? extends UpdatablePArray> maskedErosionDilation(Matrix<? extends PArray> src, Pattern erosionPattern, Pattern dilationPattern)
erosionDilation
(src, erosionPattern, dilationPattern, Morphology.SubtractionMode.NONE
) call.
This is an inverse method for maskedDilationErosion(Matrix, Pattern, Pattern)
.
src
 the source matrix.erosionPattern
 the pattern for erosion.dilationPattern
 the pattern for dilation.java.lang.NullPointerException
 if one of the arguments is null.java.lang.IllegalArgumentException
 if dilationPattern.dimCount()
or
erosionPattern.dimCount()
is not equal
to src.dimCount()
.Matrix<? extends UpdatablePArray> beucherGradient(Matrix<? extends PArray> src, Pattern pattern)
dilation
and erosion
of the source matrix with the same pattern.
More precisely, the Beucher gradient of the matrix A is defined
as an elementwise positive difference
B=max(0,dilation
(A)erosion
(A)).
The element type
of the created matrix is the same as the element type of the source one.
The byte and short elements are considered to be unsigned.
src
 the source matrix.pattern
 the pattern.java.lang.NullPointerException
 if one of the arguments is null.java.lang.IllegalArgumentException
 if the number of the pattern dimensions
pattern.dimCount()
is not equal
to src.dimCount()
.
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