Multiscale median transform / hybrid median-wavelet transform. More...

#include <MultiscaleMedianTransform.h>

Inheritance diagram for pcl::MultiscaleMedianTransform:

Public Types
using	layer = RedundantMultiscaleTransform::layer

using	layer_state_set = RedundantMultiscaleTransform::layer_state_set

using	transform = RedundantMultiscaleTransform::transform

Public Types inherited from pcl::RedundantMultiscaleTransform
using	layer = Image

using	layer_state_set = GenericVector< bool >

using	transform = Array< layer >

Public Member Functions
	MultiscaleMedianTransform (const MultiscaleMedianTransform &)=default

	MultiscaleMedianTransform (int n=4, int d=0)

	MultiscaleMedianTransform (MultiscaleMedianTransform &&)=default

	~MultiscaleMedianTransform () override

void	DisableMultiwayStructures (bool disable=true)

void	EnableMultiwayStructures (bool enable=true)

bool	IsMedianWaveletTransform () const

float	MedianWaveletThreshold () const

MultiscaleMedianTransform &	operator= (const MultiscaleMedianTransform &)=default

MultiscaleMedianTransform &	operator= (MultiscaleMedianTransform &&)=default

void	SetMedianWaveletThreshold (float threshold)

void	SetMedianWaveletTransform (float threshold=5)

void	SetMultiscaleMedianTransform ()

bool	UsingMultiwayStructures () const

Public Member Functions inherited from pcl::RedundantMultiscaleTransform
	RedundantMultiscaleTransform (const RedundantMultiscaleTransform &x)

	RedundantMultiscaleTransform (int n=4, int d=0)

	RedundantMultiscaleTransform (RedundantMultiscaleTransform &&)=default

	~RedundantMultiscaleTransform () override

void	BiasLayer (int i, float k)

void	DeleteLayer (int i)

void	DisableLayer (int i, bool disable=true)

void	EnableLayer (int i, bool enable=true)

int	FilterSize (int j) const

bool	IsLayer (int i) const

bool	IsLayerEnabled (int i) const

layer &	Layer (int i)

const layer &	Layer (int i) const

int	NumberOfLayers () const

RedundantMultiscaleTransform &	operator= (const RedundantMultiscaleTransform &x)

RedundantMultiscaleTransform &	operator= (RedundantMultiscaleTransform &&)=default

layer &	operator[] (int i)

const layer &	operator[] (int i) const

virtual transform	ReleaseTransform ()

virtual void	Reset ()

int	ScalingSequence () const

void	SetDyadicScalingSequence ()

void	SetLinearScalingSequence (int d=1)

void	SetNumberOfLayers (int n)

void	SetScalingSequence (int d)

Public Member Functions inherited from pcl::BidirectionalImageTransformation
	BidirectionalImageTransformation ()=default

	BidirectionalImageTransformation (const BidirectionalImageTransformation &)=default

	~BidirectionalImageTransformation () override

template<class P >
const GenericImage< P > &	operator<< (const GenericImage< P > &image)

const ImageVariant &	operator<< (const ImageVariant &image)

Public Member Functions inherited from pcl::ImageTransformation
	ImageTransformation ()=default

	ImageTransformation (const ImageTransformation &)=default

virtual	~ImageTransformation ()

template<class P >
GenericImage< P > &	operator>> (GenericImage< P > &image) const

ImageVariant &	operator>> (ImageVariant &image) const

Public Member Functions inherited from pcl::ParallelProcess
	ParallelProcess ()=default

	ParallelProcess (const ParallelProcess &)=default

virtual	~ParallelProcess ()

void	DisableParallelProcessing (bool disable=true) noexcept

void	EnableParallelProcessing (bool enable=true, int maxProcessors=0) noexcept

bool	IsParallelProcessingEnabled () const noexcept

int	MaxProcessors () const noexcept

ParallelProcess &	operator= (const ParallelProcess &)=default

void	SetMaxProcessors (int maxProcessors) noexcept

void	Swap (ParallelProcess &process) noexcept

Additional Inherited Members
Protected Member Functions inherited from pcl::RedundantMultiscaleTransform
void	Apply (pcl::ComplexImage &) const override

void	Apply (pcl::DComplexImage &) const override

void	Apply (pcl::DImage &) const override

void	Apply (pcl::Image &) const override

void	Apply (pcl::UInt16Image &) const override

void	Apply (pcl::UInt32Image &) const override

void	Apply (pcl::UInt8Image &) const override

Detailed Description

The multiscale median transform algorithm produces a set {w1,w2,...,wN,cN}, where each wj is a set of coefficients at scale j, which we call detail layer, and cN is a large-scale smoothed residual, which we call residual layer. Each layer has the same dimensions as the input image, hence the generated multiscale transform is redundant.

The algorithm applies successive median filters with a structuring element of increasing size 2*s + 1, where s grows following a monotonically increasing sequence (the dyadic sequence 1, 2, 4, ... is used by default). Multiscale coefficients are the differences between each pair of successive median filtered images.

The hybrid median-wavelet transform merges the multiscale median and wavelet transforms in a single high-level operation. Wavelets are used to represent nonsignificant structures, such as noise and smooth regions, while median filtering is used to represent strong significant structures. This hybrid transform provides an optimal representation of the image by combining the strongest points of both techniques: wavelets are good to support smooth structures with weak variations, while the median transform is better at isolating significant, high-contrast structures.

The reconstruction algorithm consists of the sum of all wj multiscale layers for 1 <= j <= N, plus the residual layer cN.

References

Starck, J.-L., Murtagh, F. and J. Fadili, A. (2010), Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity, Cambridge University Press.

Barth, Timothy J., Chan, Tony, Haimes, Robert (Eds.) (2002), Multiscale and Multiresolution Methods: Theory and Applications, Springer. invited paper: Jean-Luc Starck, Nonlinear Multiscale Transforms, pp. 239-279.

In our implementation, each layer in a multiscale median transform is a floating-point image with the same dimensions as the transformed image. Layers are indexed from 0 to N. Layers at indexes from 0 to N-1 are detail layers, whose elements are actually median difference coefficients. Pixels in a multiscale layer can be negative, zero or positive real values.

The last layer, at index N, is the large-scale residual layer. Pixels in the residual layer image can only be positive or zero real values.

The original algorithm uses square structuring elements. Square structures lead to relatively simple and efficient implementations, but unfortunately they tend to generate objectionable artifacts around round shapes. In our implementation we use special multiway structures to minimize these artifacts and to improve the behavior of the algorithm to isolate isotropic image structures.

Definition at line 124 of file MultiscaleMedianTransform.h.

Member Typedef Documentation

◆ layer

using pcl::MultiscaleMedianTransform::layer = RedundantMultiscaleTransform::layer

Represents a multiscale transform layer.

Definition at line 131 of file MultiscaleMedianTransform.h.

◆ layer_state_set

using pcl::MultiscaleMedianTransform::layer_state_set = RedundantMultiscaleTransform::layer_state_set

Represents a set of layer enabled/disabled states.

Definition at line 141 of file MultiscaleMedianTransform.h.

◆ transform

using pcl::MultiscaleMedianTransform::transform = RedundantMultiscaleTransform::transform

Represents a set of multiscale transform layers, or multiscale transform.

Definition at line 136 of file MultiscaleMedianTransform.h.

Constructor & Destructor Documentation

◆ MultiscaleMedianTransform() [1/3]

pcl::MultiscaleMedianTransform::MultiscaleMedianTransform	(	int	n = `4`,
		int	d = `0`
	)

inline

Constructs a MultiscaleMedianTransform instance.

Parameters

n	Number of detail layers. The transform will consist of n detail layers plus a residual layer, that is n+1 total layers. The default value is 4.
d	Scaling sequence. If d <= 0, the transform will use the dyadic sequence: 1, 2, 4, ... 2^i. If d > 0, its value is the distance in pixels between two successive scales.

The default values for n and d are 4 and 0, respectively (four layers and the dyadic scaling sequence).

Successive layers are computed by applying median filters with structuring elements of size 2*s + 1. The scaling sequence parameter d is interpreted as follows:

If the specified sequence parameter d is zero 0, then the transform uses the dyadic sequence: s = 1, 2, 4, ..., 2^j for 0 <= j < n.
If d > 0, then d is the constant increment in pixels between two successive scales (linear scaling sequence): s = d*j for 1 <= j < n.

Definition at line 167 of file MultiscaleMedianTransform.h.

◆ MultiscaleMedianTransform() [2/3]

pcl::MultiscaleMedianTransform::MultiscaleMedianTransform ( const MultiscaleMedianTransform & )

default

Copy constructor.

◆ MultiscaleMedianTransform() [3/3]

pcl::MultiscaleMedianTransform::MultiscaleMedianTransform ( MultiscaleMedianTransform && )

default

Move constructor.

◆ ~MultiscaleMedianTransform()

pcl::MultiscaleMedianTransform::~MultiscaleMedianTransform ( )

inlineoverride

Destroys a MultiscaleMedianTransform object. All existing transform layers are destroyed and deallocated.

Definition at line 186 of file MultiscaleMedianTransform.h.

Member Function Documentation

◆ DisableMultiwayStructures()

void pcl::MultiscaleMedianTransform::DisableMultiwayStructures ( bool disable = true )

inline

Disables the use of multiway structuring elements. See UsingMultiwayStructures() for more information.

Note: Calling this member function implicitly deletes all existing transform layers.

Definition at line 231 of file MultiscaleMedianTransform.h.

◆ EnableMultiwayStructures()

void pcl::MultiscaleMedianTransform::EnableMultiwayStructures ( bool enable = true )

inline

Enables the use of multiway structuring elements. See UsingMultiwayStructures() for more information.

Note: Calling this member function implicitly deletes all existing transform layers.

Definition at line 218 of file MultiscaleMedianTransform.h.

◆ IsMedianWaveletTransform()

bool pcl::MultiscaleMedianTransform::IsMedianWaveletTransform ( ) const

inline

Returns true iff this object performs a hybrid median-wavelet transform. Returns false if this is a pure multiscale median transform.

Definition at line 240 of file MultiscaleMedianTransform.h.

◆ MedianWaveletThreshold()

float pcl::MultiscaleMedianTransform::MedianWaveletThreshold ( ) const

inline

Returns the current median-wavelet threshold in sigma units. See the documentation for SetMedianWaveletThreshold() for more information.

Definition at line 289 of file MultiscaleMedianTransform.h.

◆ operator=() [1/2]

MultiscaleMedianTransform& pcl::MultiscaleMedianTransform::operator= ( const MultiscaleMedianTransform & )

default

Copy assignment operator. Returns a reference to this object.

◆ operator=() [2/2]

MultiscaleMedianTransform& pcl::MultiscaleMedianTransform::operator= ( MultiscaleMedianTransform && )

default

Move assignment operator. Returns a reference to this object.

◆ SetMedianWaveletThreshold()

void pcl::MultiscaleMedianTransform::SetMedianWaveletThreshold ( float threshold )

inline

Sets a threshold in sigma units for per-layer suppression of significant median transform coefficients. Image structures represented by median coefficients with absolute values smaller than this threshold will be supported by wavelet transform coefficients. The larger this value, the more image structures will be supported by wavelet coefficients.

By default the median-wavelet threshold is 5 sigma. This is normally large enough to prevent inclusion of the noise in median transform coefficients.

Note: Calling this member function implicitly deletes all existing transform layers.

Definition at line 279 of file MultiscaleMedianTransform.h.

References pcl::Max().

◆ SetMedianWaveletTransform()

void pcl::MultiscaleMedianTransform::SetMedianWaveletTransform ( float threshold = 5 )

inline

Causes this object to perform a hybrid wavelet-median transform.

Parameters

threshold Threshold in sigma units for per-layer suppression of significant median transform coefficients. Image structures represented by median coefficients with absolute values smaller than this threshold will be supported by wavelet transform coefficients. The default value is 5 sigma.

Note: Calling this member function implicitly deletes all existing transform layers.

Definition at line 258 of file MultiscaleMedianTransform.h.

References pcl::Max().

◆ SetMultiscaleMedianTransform()

void pcl::MultiscaleMedianTransform::SetMultiscaleMedianTransform ( )

inline

Causes this object to perform a pure multiscale median transform.

Note: Calling this member function implicitly deletes all existing transform layers.

Definition at line 300 of file MultiscaleMedianTransform.h.

◆ UsingMultiwayStructures()

bool pcl::MultiscaleMedianTransform::UsingMultiwayStructures ( ) const

inline

Returns true if this transform applies special multiway structuring elements for improved isotropic behavior. Returns false if simple structures are used instead for improved execution speed, at the cost of some performance degradation in the isotropic behavior of the transform.

Definition at line 206 of file MultiscaleMedianTransform.h.

The documentation for this class was generated from the following file:

MultiscaleMedianTransform.h

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ layer

◆ layer_state_set

◆ transform

Constructor & Destructor Documentation

◆ MultiscaleMedianTransform() [1/3]

◆ MultiscaleMedianTransform() [2/3]

◆ MultiscaleMedianTransform() [3/3]

◆ ~MultiscaleMedianTransform()

Member Function Documentation

◆ DisableMultiwayStructures()

◆ EnableMultiwayStructures()

◆ IsMedianWaveletTransform()

◆ MedianWaveletThreshold()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ SetMedianWaveletThreshold()

◆ SetMedianWaveletTransform()

◆ SetMultiscaleMedianTransform()

◆ UsingMultiwayStructures()