DGtal::functions::dec Namespace Reference

Functions
template<typename Calculus , DGtal::Dimension dim, DGtal::Duality duality>
DGtal::LinearOperator< Calculus, dim, duality, dim, duality >	diagonal (const DGtal::KForm< Calculus, dim, duality > &kform)
template<typename Calculus , DGtal::Dimension dim, DGtal::Duality duality>
void	squares (DGtal::KForm< Calculus, dim, duality > &kform)
template<typename Calculus , DGtal::Dimension dim, DGtal::Duality duality>
DGtal::LinearOperator< Calculus, dim, duality, dim, duality >	squaredDiagonal (const DGtal::KForm< Calculus, dim, duality > &kform)
template<typename Image >
void	writePixel (Image &image, typename Image::Point pt, typename Image::Value val, int pixel_size=1)
template<typename Image >
void	writePrimalLinel (Image &image, typename Image::Point pt, typename Image::Value val, int pixel_size=1)
template<typename Image >
void	writeDualLinel (Image &image, typename Image::Point pt, typename Image::Value val, int pixel_size=1)
template<typename Calculus , typename AnyForm2 , typename Image , typename Function >
void	form2ToImage (const Calculus &calculus, const AnyForm2 &u, Image &image, const Function &functor, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename Form1 , typename Image , typename Function , typename Predicate >
void	form1ToImage (const Calculus &calculus, const Form1 &v, bool primal, Image &image, const Function &functor, const Predicate &predicate, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename Image , typename Function , typename Predicate >
void	dualForm1ToImage (const Calculus &calculus, const typename Calculus::DualForm1 &v, Image &image, const Function &functor, const Predicate &predicate, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename Image , typename Function , typename Predicate >
void	primalForm1ToImage (const Calculus &calculus, const typename Calculus::PrimalForm1 &v, Image &image, const Function &functor, const Predicate &predicate, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename AnyForm2 , typename Image , typename Function >
void	threeForms2ToImage (const Calculus &calculus, const AnyForm2 &u0, const AnyForm2 &u1, const AnyForm2 &u2, Image &image, const Function &functor, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename AnyForm2 , typename Image >
void	form2ToGreyLevelImage (const Calculus &calculus, const AnyForm2 &u, Image &image, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename Image >
void	primalForm1ToGreyLevelImage (const Calculus &calculus, const typename Calculus::PrimalForm1 &v, Image &image, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename Image >
void	dualForm1ToGreyLevelImage (const Calculus &calculus, const typename Calculus::DualForm1 &v, Image &image, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename Image >
void	primalForm1ToRGBColorImage (const Calculus &calculus, const typename Calculus::PrimalForm1 &v, Image &image, Color color, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename Image >
void	dualForm1ToRGBColorImage (const Calculus &calculus, const typename Calculus::DualForm1 &v, Image &image, Color color, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
template<typename Calculus , typename AnyForm2 , typename Image >
void	threeForms2ToRGBColorImage (const Calculus &calculus, const AnyForm2 &u0, const AnyForm2 &u1, const AnyForm2 &u2, Image &image, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)

Function Documentation

diagonal()

template<typename Calculus , DGtal::Dimension dim, DGtal::Duality duality>

DGtal::LinearOperator<Calculus, dim, duality, dim, duality> DGtal::functions::dec::diagonal

(

const DGtal::KForm< Calculus, dim, duality > &

kform

)

Builds a diagonal linear operator from a k-form. These operators arise naturally when differentiating with respect to another variable (e.g. d/dx (vx)^t (vx) = diag(v^2) x).

Parameters

[in]

kform

any kform w.

Returns

the corresponding linear operator diag(w)

Template Parameters

Calculus	any discrete exterior calculus.
dim	the dimension of the form.
duality	either PRIMAL for a primal form or DUAL for a dual form.

Definition at line 72 of file DECImageHelpers.h.

      { 
        typedef DGtal::LinearOperator<Calculus,dim, duality, dim, duality> Operator; 
        typedef typename Calculus::LinearAlgebraBackend::Triplet           Triplet; 
        typedef typename Calculus::Index                                   Index; 
        typedef std::vector<Triplet>                                       Triplets;
 
        Triplets triplets;
        for (Index index=0; index<kform.length(); index++) 
          triplets.push_back(Triplet(index, index, kform.myContainer(index)));
        
        Operator op( kform.myCalculus );
        op.myContainer.setFromTriplets( triplets.begin(), triplets.end() );
        return op;
      }

References DGtal::KForm< TCalculus, order, duality >::length(), DGtal::KForm< TCalculus, order, duality >::myCalculus, and DGtal::KForm< TCalculus, order, duality >::myContainer.

Referenced by squaredDiagonal().

dualForm1ToGreyLevelImage()

template<typename Calculus , typename Image >

void DGtal::functions::dec::dualForm1ToGreyLevelImage	(	const Calculus &	calculus,
		const typename Calculus::DualForm1 &	v,
		Image &	image,
		double	cut_low = 0.0,
		double	cut_up = 1.0,
		int	pixel_size = 1
	)

Standard method to output a dual 1-form into a grey-level image.

Displays the dual 1-form v in the given image. Scalar values of v are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. If this value is belows 0.25, it is written in the image as a "line" of size pixel_size x 1 or 1 x pixel_size, depending on position.

Parameters

	calculus	the discrete exterior calculus containing the 1-form v.
	v	any dual 1-form defined in calculus.
[in,out]	image	the image where v is written.
	cut_low	every value of u below is set to cut_low.
	cut_up	every value of u above is set to cut_up.
	pixel_size	every value of a 1-form is mapped into image as pixel_size x 1 pixels or 1 x pixel_size pixels.

Template Parameters

Calculus	any discrete exterior calculus type.
Image	any image type (see concepts::CImage).

Definition at line 577 of file DECImageHelpers.h.

      {
        BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
        // Threshold is 0.25 instead of 0.5 because an edge connecting
        // two vertices with v=0 and v=1 should not belong to the
        // discontinuity set.
        dualForm1ToImage( calculus, v, image,
                          [] ( double x ) { return (unsigned char) ( round( x * 255.0 ) ); },
                          [] ( double x ) { return x < 0.25; },
                          cut_low, cut_up, pixel_size );
      }

References dualForm1ToImage().

dualForm1ToImage()

template<typename Calculus , typename Image , typename Function , typename Predicate >

void DGtal::functions::dec::dualForm1ToImage	(	const Calculus &	calculus,
		const typename Calculus::DualForm1 &	v,
		Image &	image,
		const Function &	functor,
		const Predicate &	predicate,
		double	cut_low = 0.0,
		double	cut_up = 1.0,
		int	pixel_size = 1
	)

Displays the dual 1-form v in the given image. Scalar values of v are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. Then these values are transformed to image values with the function functor. They are written in the image as "lines" of size pixel_size x 1 or 1 x pixel_size, depending on position and duality.

Parameters

	calculus	the discrete exterior calculus containing the 1-form v.
	v	any dual 1-form defined in calculus.
[in,out]	image	the image where v is written.
	functor	the function transforming scalar values to image values.
	predicate	the predicate telling for a value if it must be displayed (returns true in this case).
	cut_low	every value of u below is set to cut_low.
	cut_up	every value of u above is set to cut_up.
	pixel_size	every value of a 1-form is mapped into image as pixel_size x 1 pixels or 1 x pixel_size pixels.

Template Parameters

Calculus	any discrete exterior calculus type.
Image	any image type (see concepts::CImage).
Function	any function type (double) -> typename Image::Value to convert form value to Image value.
Predicate	any function type (double) -> bool to select 1-forms to display.

Definition at line 359 of file DECImageHelpers.h.

      {
        BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
        form1ToImage( calculus, v, false, image, functor, predicate,
                      cut_low, cut_up, pixel_size );
      }

References form1ToImage().

Referenced by dualForm1ToGreyLevelImage(), and dualForm1ToRGBColorImage().

dualForm1ToRGBColorImage()

template<typename Calculus , typename Image >

void DGtal::functions::dec::dualForm1ToRGBColorImage	(	const Calculus &	calculus,
		const typename Calculus::DualForm1 &	v,
		Image &	image,
		Color	color,
		double	cut_low = 0.0,
		double	cut_up = 1.0,
		int	pixel_size = 1
	)

Standard method to output a dual 1-form into a color image.

Displays the dual 1-form v in the given image. Scalar values of v are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. If this value is belows 0.25, it is written in the image as a "line" of size pixel_size x 1 or 1 x pixel_size, depending on position, and of color color.

Parameters

	calculus	the discrete exterior calculus containing the 1-form v.
	v	any dual 1-form defined in calculus.
[in,out]	image	the image where v is written.
	color	the color for displaying 1-forms below 0.25.
	cut_low	every value of u below is set to cut_low.
	cut_up	every value of u above is set to cut_up.
	pixel_size	every value of a 1-form is mapped into image as pixel_size x 1 pixels or 1 x pixel_size pixels.

Template Parameters

Calculus	any discrete exterior calculus type.
Image	any image type (see concepts::CImage).

Definition at line 655 of file DECImageHelpers.h.

      {
        BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
        // Threshold is 0.25 instead of 0.5 because an edge connecting
        // two vertices with v=0 and v=1 should not belong to the
        // discontinuity set.
        dualForm1ToImage( calculus, v, image,
                          [color] ( double x ) { return color; },
                          [] ( double x ) { return x < 0.25; },
                          cut_low, cut_up, pixel_size );
      }

References dualForm1ToImage().

form1ToImage()

template<typename Calculus , typename Form1 , typename Image , typename Function , typename Predicate >

void DGtal::functions::dec::form1ToImage	(	const Calculus &	calculus,
		const Form1 &	v,
		bool	primal,
		Image &	image,
		const Function &	functor,
		const Predicate &	predicate,
		double	cut_low = 0.0,
		double	cut_up = 1.0,
		int	pixel_size = 1
	)

Displays the primal or dual 1-form v in the given image. Scalar values of v are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. Then these values are transformed to image values with the function functor. They are written in the image as "lines" of size pixel_size x 1 or 1 x pixel_size, depending on position and duality.

Parameters

	calculus	the discrete exterior calculus containing the 1-form v.
	v	any primal 1-form defined in calculus if primal is true, otherwise a dual 1-form.
	primal	tells if v is a primal 1-form (true), or a dual 1-form (false).
[in,out]	image	the image where v is written.
	functor	the function transforming scalar values to image values.
	predicate	the predicate telling for a value if it must be displayed (returns true in this case).
	cut_low	every value of u below is set to cut_low.
	cut_up	every value of u above is set to cut_up.
	pixel_size	every value of a 1-form is mapped into image as pixel_size x 1 pixels or 1 x pixel_size pixels.

Template Parameters

Calculus	any discrete exterior calculus type.
Form1	either a primal 1-form if primal is true, or dual 1-form is primal is false.
Image	any image type (see concepts::CImage).
Function	any function type (double) -> typename Image::Value to convert form value to Image value.
Predicate	any function type (double) -> bool to select 1-forms to display.

Definition at line 297 of file DECImageHelpers.h.

      {
        BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
        typedef typename Calculus::Index  Index;
        typedef typename Calculus::SCell  SCell;
        typedef typename Calculus::Scalar Scalar;
        typedef typename Calculus::KSpace KSpace;
        typedef typename KSpace::Point    Point;
        typedef typename KSpace::Integer  Integer;
        double min_v = NumberTraits<Scalar>::castToDouble( v.myContainer[ 0 ] );
        double max_v = min_v;
        for ( Index index = 0; index < v.myContainer.rows(); index++)
          {
            double w = NumberTraits<Scalar>::castToDouble( v.myContainer[ index ] );
            min_v = std::min( min_v, w );
            max_v = std::max( max_v, w );
          }
        if ( min_v < cut_low ) min_v = cut_low;
        if ( max_v > cut_up  ) max_v = cut_up;
        for ( Index index = 0; index < v.myContainer.rows(); index++)
          {
            SCell cell = v.getSCell( index );
            double u = NumberTraits<Scalar>::castToDouble( v.myContainer[ index ] );
            if ( ! predicate( u ) ) continue; 
            double w = std::min( cut_up, std::max( cut_low, u ) );
            if ( min_v != max_v ) w = ( w - min_v ) / ( max_v - min_v );
            Point kpt = calculus.myKSpace.sKCoords( cell );
            if ( primal ) writePrimalLinel( image, kpt, functor( w ), pixel_size );
            else          writeDualLinel  ( image, kpt, functor( w ), pixel_size );
          }
      }

References DGtal::NumberTraits< T >::castToDouble(), DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::myKSpace, DGtal::KhalimskySpaceND< dim, TInteger >::sKCoords(), writeDualLinel(), and writePrimalLinel().

Referenced by dualForm1ToImage(), and primalForm1ToImage().

form2ToGreyLevelImage()

template<typename Calculus , typename AnyForm2 , typename Image >

void DGtal::functions::dec::form2ToGreyLevelImage	(	const Calculus &	calculus,
		const AnyForm2 &	u,
		Image &	image,
		double	cut_low = 0.0,
		double	cut_up = 1.0,
		int	pixel_size = 1
	)

Standard method to output a 2-form into a grey-level image.

Displays the 2-form u in the given image. Scalar values of u are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. They are written in the image as grey-level "pixels" of size pixel_size x pixel_size.

Parameters

	calculus	the discrete exterior calculus containing the 2-form u.
	u	any primal or dual 2-form defined in calculus.
[in,out]	image	the image where u is written.
	cut_low	every value of u below is set to cut_low.
	cut_up	every value of u above is set to cut_up.
	pixel_size	every value of a 2-form is mapped into image as pixel_size x pixel_size pixels.

Template Parameters

Calculus	any discrete exterior calculus type.
AnyForm2	either a primal 2-form type or a dual 2-form type of the given Calculus.
Image	any image type (see concepts::CImage).

Definition at line 505 of file DECImageHelpers.h.

      {
        BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
        form2ToImage( calculus, u, image,
                      [] ( double x ) { return (unsigned char) ( round( x * 255.0 ) ); },
                      cut_low, cut_up, pixel_size );
      }

References form2ToImage().

form2ToImage()

template<typename Calculus , typename AnyForm2 , typename Image , typename Function >

void DGtal::functions::dec::form2ToImage	(	const Calculus &	calculus,
		const AnyForm2 &	u,
		Image &	image,
		const Function &	functor,
		double	cut_low = 0.0,
		double	cut_up = 1.0,
		int	pixel_size = 1
	)

Displays the 2-form u in the given image. Scalar values of u are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. Then these values are transformed to image values with the function functor. They are written in the image as "pixels" of size pixel_size x pixel_size.

Parameters

	calculus	the discrete exterior calculus containing the 2-form u.
	u	any primal or dual 2-form defined in calculus.
[in,out]	image	the image where u is written.
	functor	the function transforming scalar values to image values.
	cut_low	every value of u below is set to cut_low.
	cut_up	every value of u above is set to cut_up.
	pixel_size	every value of a 2-form is mapped into image as pixel_size x pixel_size pixels.

Template Parameters

Calculus	any discrete exterior calculus type.
AnyForm2	either a primal 2-form type or a dual 2-form type of the given Calculus.
Image	any image type (see concepts::CImage).
Function	any function type (double) -> typename Image::Value to convert form value to Image value.

Definition at line 237 of file DECImageHelpers.h.

      {
        BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
        typedef typename Calculus::Index  Index;
        typedef typename Calculus::SCell  SCell;
        typedef typename Calculus::Scalar Scalar;
        typedef typename Calculus::KSpace KSpace;
        typedef typename KSpace::Point    Point;
        typedef typename KSpace::Integer  Integer;
        double min_u = NumberTraits<Scalar>::castToDouble( u.myContainer[ 0 ] );
        double max_u = min_u;
        for ( Index index = 0; index < u.myContainer.rows(); index++)
          {
            double v = NumberTraits<Scalar>::castToDouble( u.myContainer[ index ] );
            min_u = std::min( min_u, v );
            max_u = std::max( max_u, v );
          }
        if ( min_u < cut_low ) min_u = cut_low;
        if ( max_u > cut_up  ) max_u = cut_up;
        for ( Index index = 0; index < u.myContainer.rows(); index++)
          {
            SCell cell = u.getSCell( index );
            double v = NumberTraits<Scalar>::castToDouble( u.myContainer[ index ] );
            double w = std::min( cut_up, std::max( cut_low, v ) );
            if ( min_u != max_u ) w = ( w - min_u ) / ( max_u - min_u );
            writePixel( image, calculus.myKSpace.sCoords( cell ), functor( w ), pixel_size );
          }
      }

References DGtal::NumberTraits< T >::castToDouble(), DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::myKSpace, DGtal::KhalimskySpaceND< dim, TInteger >::sCoords(), and writePixel().

Referenced by form2ToGreyLevelImage().

primalForm1ToGreyLevelImage()

template<typename Calculus , typename Image >

void DGtal::functions::dec::primalForm1ToGreyLevelImage	(	const Calculus &	calculus,
		const typename Calculus::PrimalForm1 &	v,
		Image &	image,
		double	cut_low = 0.0,
		double	cut_up = 1.0,
		int	pixel_size = 1
	)

Standard method to output a primal 1-form into a grey-level image.

Displays the primal 1-form v in the given image. Scalar values of v are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. If this value is belows 0.25, it is written in the image as a "line" of size pixel_size x 1 or 1 x pixel_size, depending on position.

Parameters

	calculus	the discrete exterior calculus containing the 1-form v.
	v	any primal 1-form defined in calculus.
[in,out]	image	the image where v is written.
	cut_low	every value of u below is set to cut_low.
	cut_up	every value of u above is set to cut_up.
	pixel_size	every value of a 1-form is mapped into image as pixel_size x 1 pixels or 1 x pixel_size pixels.

Template Parameters

Calculus	any discrete exterior calculus type.
Image	any image type (see concepts::CImage).

Definition at line 539 of file DECImageHelpers.h.

      {
        BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
        // Threshold is 0.25 instead of 0.5 because an edge connecting
        // two vertices with v=0 and v=1 should not belong to the
        // discontinuity set.
        primalForm1ToImage( calculus, v, image,
                            [] ( double x ) { return (unsigned char) ( round( x * 255.0 ) ); },
                            [] ( double x ) { return x < 0.25; },
                            cut_low, cut_up, pixel_size );
      }

References primalForm1ToImage().

primalForm1ToImage()

template<typename Calculus , typename Image , typename Function , typename Predicate >

void DGtal::functions::dec::primalForm1ToImage	(	const Calculus &	calculus,
		const typename Calculus::PrimalForm1 &	v,
		Image &	image,
		const Function &	functor,
		const Predicate &	predicate,
		double	cut_low = 0.0,
		double	cut_up = 1.0,
		int	pixel_size = 1
	)

Displays the primal 1-form v in the given image. Scalar values of v are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. Then these values are transformed to image values with the function functor. They are written in the image as "lines" of size pixel_size x 1 or 1 x pixel_size, depending on position and duality.

Parameters

	calculus	the discrete exterior calculus containing the 1-form v.
	v	any primal 1-form defined in calculus.
[in,out]	image	the image where v is written.
	functor	the function transforming scalar values to image values.
	predicate	the predicate telling for a value if it must be displayed (returns true in this case).
	cut_low	every value of u below is set to cut_low.
	cut_up	every value of u above is set to cut_up.
	pixel_size	every value of a 1-form is mapped into image as pixel_size x 1 pixels or 1 x pixel_size pixels.

Template Parameters

Calculus	any discrete exterior calculus type.
Image	any image type (see concepts::CImage).
Function	any function type (double) -> typename Image::Value to convert form value to Image value.
Predicate	any function type (double) -> bool to select 1-forms to display.

Definition at line 396 of file DECImageHelpers.h.

      {
        BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
        form1ToImage( calculus, v, true, image, functor, predicate,
                      cut_low, cut_up, pixel_size );
      }

References form1ToImage().

Referenced by primalForm1ToGreyLevelImage(), and primalForm1ToRGBColorImage().

primalForm1ToRGBColorImage()

template<typename Calculus , typename Image >

void DGtal::functions::dec::primalForm1ToRGBColorImage	(	const Calculus &	calculus,
		const typename Calculus::PrimalForm1 &	v,
		Image &	image,
		Color	color,
		double	cut_low = 0.0,
		double	cut_up = 1.0,
		int	pixel_size = 1
	)

Standard method to output a primal 1-form into a color image.

Displays the primal 1-form v in the given image. Scalar values of v are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. If this value is belows 0.25, it is written in the image as a "line" of size pixel_size x 1 or 1 x pixel_size, depending on position, and of color color.

Parameters

	calculus	the discrete exterior calculus containing the 1-form v.
	v	any primal 1-form defined in calculus.
[in,out]	image	the image where v is written.
	color	the color for displaying 1-forms below 0.25.
	cut_low	every value of u below is set to cut_low.
	cut_up	every value of u above is set to cut_up.
	pixel_size	every value of a 1-form is mapped into image as pixel_size x 1 pixels or 1 x pixel_size pixels.

Template Parameters

Calculus	any discrete exterior calculus type.
Image	any image type (see concepts::CImage).

Definition at line 616 of file DECImageHelpers.h.

      {
        BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
        // Threshold is 0.25 instead of 0.5 because an edge connecting
        // two vertices with v=0 and v=1 should not belong to the
        // discontinuity set.
        primalForm1ToImage( calculus, v, image,
                            [color] ( double x ) { return color; },
                            [] ( double x ) { return x < 0.25; },
                            cut_low, cut_up, pixel_size );
      }

References primalForm1ToImage().

squaredDiagonal()

template<typename Calculus , DGtal::Dimension dim, DGtal::Duality duality>

DGtal::LinearOperator<Calculus, dim, duality, dim, duality> DGtal::functions::dec::squaredDiagonal

(

const DGtal::KForm< Calculus, dim, duality > &

kform

)

Builds a diagonal linear operator from a k-form and squares it. These operators arise naturally when differentiating with respect to another variable (e.g. d/dx (vx)^t (vx) = diag(v^2) x).

Parameters

[in]

kform

any kform v

Returns

the corresponding linear operator diag(v^2)

Template Parameters

Calculus	any discrete exterior calculus.
dim	the dimension of the form.
duality	either PRIMAL for a primal form or DUAL for a dual form.

Definition at line 118 of file DECImageHelpers.h.

      {
        auto v2 = kform;
        squares( v2 );
        return diagonal( v2 );
      }

References diagonal(), and squares().

squares()

template<typename Calculus , DGtal::Dimension dim, DGtal::Duality duality>

void DGtal::functions::dec::squares

(

DGtal::KForm< Calculus, dim, duality > &

kform

)

Squares the given k-form.

Parameters

[in,out]

kform

any kform.

Template Parameters

Calculus	any discrete exterior calculus.
dim	the dimension of the form.
duality	either PRIMAL for a primal form or DUAL for a dual form.

Definition at line 99 of file DECImageHelpers.h.

      {
        kform.myContainer.array() = kform.myContainer.array().square();
      }

References DGtal::KForm< TCalculus, order, duality >::myContainer.

Referenced by squaredDiagonal().

threeForms2ToImage()

template<typename Calculus , typename AnyForm2 , typename Image , typename Function >

void DGtal::functions::dec::threeForms2ToImage	(	const Calculus &	calculus,
		const AnyForm2 &	u0,
		const AnyForm2 &	u1,
		const AnyForm2 &	u2,
		Image &	image,
		const Function &	functor,
		double	cut_low = 0.0,
		double	cut_up = 1.0,
		int	pixel_size = 1
	)

Displays the three 2-forms u0, u1, u2 in the given image. Scalar values of u0, u1, u2 are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. Then these values are transformed to image values with the function functor. They are written in the image as "pixels" of size pixel_size x pixel_size.

Parameters

	calculus	the discrete exterior calculus containing the 2-forms u0, u1, u2.
	u0	any primal or dual 2-form defined in calculus.
	u1	any primal or dual 2-form defined in calculus.
	u2	any primal or dual 2-form defined in calculus.
[in,out]	image	the image where u is written.
	functor	the function transforming three scalar values to image values.
	cut_low	every value of u0, u1, u2 below is set to cut_low.
	cut_up	every value of u0, u1, u2 above is set to cut_up.
	pixel_size	every value of 2-forms is mapped into image as pixel_size x pixel_size pixels.

Template Parameters

Calculus	any discrete exterior calculus type.
AnyForm2	either a primal 2-form type or a dual 2-form type of the given Calculus.
Image	any image type (see concepts::CImage).
Function	any function type (double,double,double) -> typename Image::Value to convert form value to Image value.

Definition at line 433 of file DECImageHelpers.h.

      {
        BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
        typedef typename Calculus::Index  Index;
        typedef typename Calculus::SCell  SCell;
        typedef typename Calculus::Scalar Scalar;
        double min_u = NumberTraits<Scalar>::castToDouble( u0.myContainer[ 0 ] );
        double max_u = min_u;
        for ( Index index = 0; index < u0.myContainer.rows(); index++)
          {
            double v = NumberTraits<Scalar>::castToDouble( u0.myContainer[ index ] );
            min_u = std::min( min_u, v );
            max_u = std::max( max_u, v );
          }
        for ( Index index = 0; index < u1.myContainer.rows(); index++)
          {
            double v = NumberTraits<Scalar>::castToDouble( u1.myContainer[ index ] );
            min_u = std::min( min_u, v );
            max_u = std::max( max_u, v );
          }
        for ( Index index = 0; index < u2.myContainer.rows(); index++)
          {
            double v = NumberTraits<Scalar>::castToDouble( u2.myContainer[ index ] );
            min_u = std::min( min_u, v );
            max_u = std::max( max_u, v );
          }
        if ( min_u < cut_low ) min_u = cut_low;
        if ( max_u > cut_up  ) max_u = cut_up;
        for ( Index index = 0; index < u0.myContainer.rows(); index++)
          {
            SCell cell = u0.getSCell( index );
            double v0 = NumberTraits<Scalar>::castToDouble( u0.myContainer[ index ] );
            double w0 = std::min( cut_up, std::max( cut_low, v0 ) );
            if ( min_u != max_u ) w0 = ( w0 - min_u ) / ( max_u - min_u );
            double v1 = NumberTraits<Scalar>::castToDouble( u1.myContainer[ index ] );
            double w1 = std::min( cut_up, std::max( cut_low, v1 ) );
            if ( min_u != max_u ) w1 = ( w1 - min_u ) / ( max_u - min_u );
            double v2 = NumberTraits<Scalar>::castToDouble( u2.myContainer[ index ] );
            double w2 = std::min( cut_up, std::max( cut_low, v2 ) );
            if ( min_u != max_u ) w2 = ( w2 - min_u ) / ( max_u - min_u );
            writePixel( image, calculus.myKSpace.sCoords( cell ), functor( w0, w1, w2 ), pixel_size );
          }
      }

References DGtal::NumberTraits< T >::castToDouble(), DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::myKSpace, DGtal::KhalimskySpaceND< dim, TInteger >::sCoords(), and writePixel().

Referenced by threeForms2ToRGBColorImage().

threeForms2ToRGBColorImage()

template<typename Calculus , typename AnyForm2 , typename Image >

void DGtal::functions::dec::threeForms2ToRGBColorImage	(	const Calculus &	calculus,
		const AnyForm2 &	u0,
		const AnyForm2 &	u1,
		const AnyForm2 &	u2,
		Image &	image,
		double	cut_low = 0.0,
		double	cut_up = 1.0,
		int	pixel_size = 1
	)

Standard method to output three 2-forms into a RGB Color image.

Displays the three 2-forms u0, u1, u2 in the given image as RGB colors. Scalar values of u0, u1, u2 are first cut up and low according to cut_low and cut_up, and then rescaled according to max and min value. Then these values are transformed to RGB color image values (u0 defines the intensity of the red channel, u1 the green channel, u2, the blue channel). They are written in the image as "pixels" of size pixel_size x pixel_size.

Parameters

	calculus	the discrete exterior calculus containing the 2-forms u0, u1, u2.
	u0	any primal or dual 2-form defined in calculus.
	u1	any primal or dual 2-form defined in calculus.
	u2	any primal or dual 2-form defined in calculus.
[in,out]	image	the image where u is written.
	cut_low	every value of u0, u1, u2 below is set to cut_low.
	cut_up	every value of u0, u1, u2 above is set to cut_up.
	pixel_size	every value of 2-forms is mapped into image as pixel_size x pixel_size pixels.

Template Parameters

Calculus	any discrete exterior calculus type.
AnyForm2	either a primal 2-form type or a dual 2-form type of the given Calculus.
Image	any image type (see concepts::CImage).

Definition at line 698 of file DECImageHelpers.h.

      {
        BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
        threeForms2ToImage
          ( calculus, u0, u1, u2, image,
            [] ( double r, double g, double b )
            { return Color( (unsigned char) ( round( r * 255.0 ) ),
                            (unsigned char) ( round( g * 255.0 ) ),
                            (unsigned char) ( round( b * 255.0 ) ) ); },
            cut_low, cut_up, pixel_size );
      }

References threeForms2ToImage().

writeDualLinel()

template<typename Image >

void DGtal::functions::dec::writeDualLinel	(	Image &	image,
		typename Image::Point	pt,
		typename Image::Value	val,
		int	pixel_size = 1
	)

Considers an image image to have pixels of size pixel_size x pixel_size, and writes the value val at the specified linel position pt.

Parameters

[in,out]	image	any image of sufficient size.
	pt	a linel Khalimsky coordinates.
	val	the value to write in pixel_size x 1 pixels (if horizontal) or 1 x pixel_size pixels (if vertical).
	pixel_size	the chosen pixel_size (when 1, this is the normal setValue of an image).

Template Parameters

Image

any image type (see concepts::CImage).

Definition at line 197 of file DECImageHelpers.h.

      {
        BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
        typedef typename Image::Point      Point;
        typedef typename Point::Coordinate Coordinate;
        int pixel_size_x = NumberTraits<Coordinate>::even( pt[ 0 ] ) ? 0 : pixel_size-1;
        int pixel_size_y = NumberTraits<Coordinate>::even( pt[ 1 ] ) ? 0 : pixel_size-1;
        pt /= 2;
        pt *= pixel_size;
        for ( int y = pixel_size_y; y < pixel_size; y++ )
          for ( int x = pixel_size_x; x < pixel_size; x++ )
            {
              Point q( (Coordinate) x, (Coordinate) y );
              image.setValue( pt + q, val );
            }
      }

References DGtal::NumberTraits< T >::even(), and DGtal::Image< class >::setValue().

Referenced by form1ToImage().

writePixel()

template<typename Image >

void DGtal::functions::dec::writePixel	(	Image &	image,
		typename Image::Point	pt,
		typename Image::Value	val,
		int	pixel_size = 1
	)

Considers an image image to have pixels of size pixel_size x pixel_size, and writes the value val at the specified pixel position pt.

Parameters

[in,out]	image	any image of sufficient size.
	pt	a pixel coordinate (which is multiplied by pixel_size within).
	val	the value to write in pixel_size x pixel_size pixels.
	pixel_size	the chosen pixel_size (when 1, this is the normal setValue of an image).

Template Parameters

Image

any image type (see concepts::CImage).

Definition at line 138 of file DECImageHelpers.h.

      {
        BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
        typedef typename Image::Point      Point;
        typedef typename Point::Coordinate Coordinate;
        pt *= pixel_size;
        for ( int y = 0; y < pixel_size; y++ )
          for ( int x = 0; x < pixel_size; x++ )
            {
              Point q( (Coordinate) x, (Coordinate) y );
              image.setValue( pt + q, val );
            }
      }

References DGtal::Image< class >::setValue().

Referenced by form2ToImage(), and threeForms2ToImage().

writePrimalLinel()

template<typename Image >

void DGtal::functions::dec::writePrimalLinel	(	Image &	image,
		typename Image::Point	pt,
		typename Image::Value	val,
		int	pixel_size = 1
	)

Considers an image image to have pixels of size pixel_size x pixel_size, and writes the value val at the specified linel position pt.

Parameters

[in,out]	image	any image of sufficient size.
	pt	a linel Khalimsky coordinates.
	val	the value to write in pixel_size x 1 pixels (if horizontal) or 1 x pixel_size pixels (if vertical).
	pixel_size	the chosen pixel_size (when 1, this is the normal setValue of an image).

Template Parameters

Image

any image type (see concepts::CImage).

Definition at line 166 of file DECImageHelpers.h.

      {
        BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
        typedef typename Image::Point      Point;
        typedef typename Point::Coordinate Coordinate;
        int pixel_size_x = NumberTraits<Coordinate>::even( pt[ 0 ] ) ? 1 : pixel_size;
        int pixel_size_y = NumberTraits<Coordinate>::even( pt[ 1 ] ) ? 1 : pixel_size;
        pt /= 2;
        pt *= pixel_size;
        for ( int y = 0; y < pixel_size_y; y++ )
          for ( int x = 0; x < pixel_size_x; x++ )
            {
              Point q( (Coordinate) x, (Coordinate) y );
              image.setValue( pt + q, val );
            }
      }

References DGtal::NumberTraits< T >::even(), and DGtal::Image< class >::setValue().

Referenced by form1ToImage().