687 lines
27 KiB
C++
687 lines
27 KiB
C++
// ____ ______ __
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// / __ \ / ____// /
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// / /_/ // / / /
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// / ____// /___ / /___ PixInsight Class Library
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// /_/ \____//_____/ PCL 2.4.23
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// ----------------------------------------------------------------------------
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// pcl/ATrousWaveletTransform.h - Released 2022-03-12T18:59:29Z
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// ----------------------------------------------------------------------------
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// This file is part of the PixInsight Class Library (PCL).
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// PCL is a multiplatform C++ framework for development of PixInsight modules.
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//
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// Copyright (c) 2003-2022 Pleiades Astrophoto S.L. All Rights Reserved.
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//
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// Redistribution and use in both source and binary forms, with or without
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// modification, is permitted provided that the following conditions are met:
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//
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// 1. All redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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//
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// 2. All redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// 3. Neither the names "PixInsight" and "Pleiades Astrophoto", nor the names
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// of their contributors, may be used to endorse or promote products derived
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// from this software without specific prior written permission. For written
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// permission, please contact info@pixinsight.com.
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//
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// 4. All products derived from this software, in any form whatsoever, must
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// reproduce the following acknowledgment in the end-user documentation
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// and/or other materials provided with the product:
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//
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// "This product is based on software from the PixInsight project, developed
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// by Pleiades Astrophoto and its contributors (https://pixinsight.com/)."
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//
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// Alternatively, if that is where third-party acknowledgments normally
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// appear, this acknowledgment must be reproduced in the product itself.
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//
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// THIS SOFTWARE IS PROVIDED BY PLEIADES ASTROPHOTO AND ITS CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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// TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL PLEIADES ASTROPHOTO OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, BUSINESS
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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// ----------------------------------------------------------------------------
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#ifndef __PCL_ATrousWaveletTransform_h
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#define __PCL_ATrousWaveletTransform_h
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/// \file pcl/ATrousWaveletTransform.h
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#include <pcl/Defs.h>
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#include <pcl/Diagnostics.h>
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#include <pcl/AutoPointer.h>
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#include <pcl/KernelFilter.h>
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#include <pcl/RedundantMultiscaleTransform.h>
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#include <pcl/SeparableFilter.h>
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namespace pcl
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{
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// ----------------------------------------------------------------------------
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class InterlacedTransformation;
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/*!
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* \class ATrousWaveletTransform
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* \brief Discrete isotropic à trous wavelet transform.
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*
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* The Isotropic Undecimated Wavelet Transform, also known as starlet transform
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* or <em>à trous</em> (with holes) wavelet transform, produces a coefficient
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* set {w1,w2,...,wN,cN}, where each wj is a set of zero-mean coefficients at
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* scale j, which we call <em>detail layer</em>, and cN is a large-scale
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* smoothed residual, which we call <em>residual layer</em>. Each layer has the
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* same dimensions as the input image, hence the transform is redundant.
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*
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* The wavelet function in the à trous algorithm is the difference between the
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* values of a scaling function F at two successive scales. Using the dyadic
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* scaling sequence, the wavelet function can be represented as
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* (F(x) - F(x/2)). The scaling function F can be any positive low-pass filter.
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*
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* The reconstruction algorithm consists of the sum of all wj detail layers
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* for 1 <= j <= N, plus the residual layer cN.
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*
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* \b References
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*
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* \li Jean-Luc Starck, Fionn Murtagh, Mario Bertero, <em>Handbook of
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* Mathematical Methods in Imaging</em>, ch. 34, <em>Starlet Transform in
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* Astronomical Data Processing</em>, Springer, 2011, pp. 1489-1531.
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*
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* \li Starck, J.-L., Murtagh, F. and J. Fadili, A., <em>Sparse %Image and
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* Signal Processing: Wavelets, Curvelets, Morphological Diversity</em>,
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* Cambridge University Press, 2010.
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*
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* \li Starck, J.-L., Murtagh, F., <em>Astronomical %Image and Data
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* Analysis</em>, Springer, 2002.
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*
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* \li Jean-Luc Starck, Fionn Murtagh, Albert Bijaoui, <em>%Image processing
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* and Data Analysis: The Multiscale Approach</em>, Cambridge University Press,
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* 1998.
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*
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* \b Implementation
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*
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* In our implementation, each layer in a wavelet transform is a floating-point
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* image with the same dimensions as the transformed image. Layers are indexed
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* from 0 to N. Layers at indexes from 0 to N-1 are detail layers, whose
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* elements are actually wavelet difference coefficients. Pixels in a detail
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* layer can be negative, zero or positive real values.
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*
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* The last layer, at index N, is the large-scale residual layer. Pixels in the
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* residual layer image can only be positive or zero real values.
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*
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* \ingroup multiscale_transforms
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*
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* \note The StarletTransform class is an alias for %ATrousWaveletTransform.
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*/
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class PCL_CLASS ATrousWaveletTransform : public RedundantMultiscaleTransform
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{
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public:
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/*!
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* Represents a wavelet layer.
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*/
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typedef RedundantMultiscaleTransform::layer layer;
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/*!
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* Represents a set of wavelet layers, or wavelet transform.
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*/
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typedef RedundantMultiscaleTransform::transform transform;
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/*!
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* Represents a set of layer enabled/disabled states.
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*/
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typedef RedundantMultiscaleTransform::layer_state_set layer_state_set;
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/*!
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* \brief The scaling function of a wavelet transform.
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*
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* A wavelet scaling function can be either a non-separable kernel filter,
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* implemented as the KernelFilter class, or a separable filter implemented
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* as SeparableFilter.
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*
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* Separable filters should be better in terms of performance, since
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* separable convolution has O(N) complexity, as opposed to O(N^2) for
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* non-separable convolution. However, in current PCL versions separable
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* convolutions are only faster for relatively large filter sizes as a resut
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* of vectorization with SIMD processor instructions. See the
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* SeparableConvolution class and the \ref convolution_speed_limits "Helper
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* Functions for Selection of Convolution Algorithms" section for more
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* information.
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*
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* \sa KernelFilter, SeparableFilter
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*/
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struct WaveletScalingFunction
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{
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AutoPointer<KernelFilter> kernelFilter; //!< Non-separable kernel filter
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AutoPointer<SeparableFilter> separableFilter; //!< Separable filter
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/*!
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* Default constructor. Constructs an uninitialized instance.
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*/
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WaveletScalingFunction() = default;
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/*!
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* Non-separable filter constructor. The scaling function will own a
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* duplicate of the specified kernel filter.
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*/
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WaveletScalingFunction( const KernelFilter& f )
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{
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kernelFilter = f.Clone();
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PCL_CHECK( !kernelFilter.IsNull() )
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}
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/*!
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* Separable filter constructor. The scaling function will own a
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* duplicate of the specified separable filter.
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*/
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WaveletScalingFunction( const SeparableFilter& f )
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{
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separableFilter = f.Clone();
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PCL_CHECK( !separableFilter.IsNull() )
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}
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/*!
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* Copy constructor. The scaling function will own a duplicate of the
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* kernel or separable filter in the source object.
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*/
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WaveletScalingFunction( const WaveletScalingFunction& s )
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{
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if ( !s.kernelFilter.IsNull() )
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{
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kernelFilter = s.kernelFilter->Clone();
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PCL_CHECK( !kernelFilter.IsNull() )
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}
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if ( !s.separableFilter.IsNull() )
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{
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separableFilter = s.separableFilter->Clone();
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PCL_CHECK( !separableFilter.IsNull() )
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}
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}
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/*!
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* Move constructor.
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*/
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WaveletScalingFunction( WaveletScalingFunction&& s )
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: kernelFilter( s.kernelFilter )
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, separableFilter( s.separableFilter )
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{
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}
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/*!
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* Destroys this scaling function object. Destroys and deallocates the
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* existing kernel or separable filter in this object.
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*/
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virtual ~WaveletScalingFunction()
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{
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}
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/*!
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* Copy assignment operator. Returns a reference to this object.
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*/
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WaveletScalingFunction& operator =( const WaveletScalingFunction& s )
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{
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if ( s.kernelFilter.IsNull() )
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kernelFilter.Destroy();
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else
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{
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kernelFilter = s.kernelFilter->Clone();
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PCL_CHECK( !kernelFilter.IsNull() )
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}
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if ( s.separableFilter.IsNull() )
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separableFilter.Destroy();
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else
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{
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separableFilter = s.separableFilter->Clone();
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PCL_CHECK( !separableFilter.IsNull() )
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}
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return *this;
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}
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/*!
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* Move assignment operator. Returns a reference to this object.
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*/
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WaveletScalingFunction& operator =( WaveletScalingFunction&& ) = default;
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/*!
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* Returns true if this scaling function is a separable filter; false if
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* it is an invalid or non-separable kernel filter.
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*/
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bool IsSeparable() const
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{
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return !separableFilter.IsNull() && !separableFilter->IsEmpty();
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}
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/*!
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* Returns true if this scaling function is a non-separable kernel
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* filter; false if it is an invalid or separable filter.
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*/
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bool IsNonseparable() const
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{
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return !kernelFilter.IsNull() && !kernelFilter->IsEmpty();
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}
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/*!
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* Returns true iff this scaling function is valid, that is, if it owns a
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* nonempty filter.
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*/
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bool IsValid() const
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{
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return IsSeparable() || IsNonseparable();
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}
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/*!
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* Causes this scaling function to own a duplicate of the specified
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* non-separable kernel filter. A previously existing filter is destroyed
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* and deallocated.
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*/
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void Set( const KernelFilter& f )
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{
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separableFilter.Destroy();
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kernelFilter = f.Clone();
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PCL_CHECK( !kernelFilter.IsNull() )
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}
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/*!
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* Causes this scaling function to own a duplicate of the specified
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* separable filter. A previously existing filter is destroyed and
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* deallocated.
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*/
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void Set( const SeparableFilter& f )
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{
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kernelFilter.Destroy();
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separableFilter = f.Clone();
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PCL_CHECK( !separableFilter.IsNull() )
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}
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/*!
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* Destroys the kernel and/or separable filter(s) owned by this object,
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* yielding an invalid instance.
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*/
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void Clear()
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{
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kernelFilter.Destroy();
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separableFilter.Destroy();
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}
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/*!
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* Equality operator. Returns true only if this scaling function is equal
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* to another instance.
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*/
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bool operator ==( const WaveletScalingFunction& other ) const
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{
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if ( !kernelFilter.IsNull() )
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return !other.kernelFilter.IsNull() && *kernelFilter == *other.kernelFilter;
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if ( !separableFilter.IsNull() )
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return !other.separableFilter.IsNull() && *separableFilter == *other.separableFilter;
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return other.kernelFilter.IsNull() && other.separableFilter.IsNull();
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}
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};
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/*!
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* Default constructor.
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*
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* \note This constructor yields an uninitialized instance that cannot be
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* used prior to initializing it with a reference to a filter object
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* (either KernelFilter or SeparableFilter), which will be used as the
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* scaling function of the wavelet transform.
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*/
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ATrousWaveletTransform() = default;
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/*!
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* Constructs an %ATrousWaveletTransform instance using the specified
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* scaling function.
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*
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* \param f A wavelet scaling function that can be either a non-separable
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* filter (KernelFilter) or a separable filter (SeparableFilter).
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*
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* \param n Number of wavelet layers. The transform will consist of \a n
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* wavelet layers plus a residual layer, i.e. n+1 total layers.
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*
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* \param d Scaling sequence. If \a d <= 0, the transform will use the
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* dyadic sequence: 1, 2, 4, ... 2^i. If \a d > 0, its value is
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* the distance in pixels between two successive scales.
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*
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* The default values for \a n and \a d are 4 and 0, respectively (four
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* wavelet layers and the dyadic scaling sequence).
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*/
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ATrousWaveletTransform( const WaveletScalingFunction& f, int n = 4, int d = 0 )
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: RedundantMultiscaleTransform( n, d )
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, m_scalingFunction( f )
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{
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PCL_CHECK( m_scalingFunction.IsValid() )
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}
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/*!
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* Constructs an %ATrousWaveletTransform instance that uses a non-separable
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* kernel filter as a scaling function.
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*
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* \param f Non-separable filter that will be used as the scaling
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* function of the transform. Must be a positive, low-pass
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* filter function.
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*
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* \param n Number of wavelet layers. The transform will consist of \a n
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* wavelet layers plus a residual layer, i.e. n+1 total layers.
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*
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* \param d Scaling sequence. If \a d <= 0, the transform will use the
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* dyadic sequence: 1, 2, 4, ... 2^i. If \a d > 0, its value is
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* the distance in pixels between two successive scales.
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*
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* The default values for \a n and \a d are 4 and 0, respectively (four
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* wavelet layers and the dyadic scaling sequence).
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*/
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ATrousWaveletTransform( const KernelFilter& f, int n = 4, int d = 0 )
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: RedundantMultiscaleTransform( n, d )
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, m_scalingFunction( f )
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{
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PCL_CHECK( m_scalingFunction.IsValid() )
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}
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/*!
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* Constructs an %ATrousWaveletTransform instance that uses a separable
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* kernel filter as a scaling function.
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*
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* \param f Separable filter that will be used as the scaling function of
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* the transform. Must be a positive, low-pass filter function.
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*
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* \param n Number of wavelet layers. The transform will consist of \a n
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* wavelet layers plus a residual layer, i.e. n+1 total layers.
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*
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* \param d Scaling sequence. If \a d <= 0, the transform will use the
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* dyadic sequence: 1, 2, 4, ... 2^i. If \a d > 0, its value is
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* the distance in pixels between two successive scales.
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*
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* The default values for \a n and \a d are 4 and 0, respectively (four
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* wavelet layers and the dyadic scaling sequence).
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*/
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ATrousWaveletTransform( const SeparableFilter& f, int n = 4, int d = 0 )
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: RedundantMultiscaleTransform( n, d )
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, m_scalingFunction( f )
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{
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PCL_CHECK( m_scalingFunction.IsValid() )
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}
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/*!
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* Copy constructor.
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*/
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ATrousWaveletTransform( const ATrousWaveletTransform& ) = default;
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/*!
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* Move constructor.
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*/
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ATrousWaveletTransform( ATrousWaveletTransform&& ) = default;
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/*!
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* Destroys this %ATrousWaveletTransform object. All existing wavelet layers
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* and the internal scaling function filter object are destroyed and
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* deallocated.
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*/
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virtual ~ATrousWaveletTransform()
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{
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}
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/*!
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* Copy assignment operator. Returns a reference to this object.
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*/
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ATrousWaveletTransform& operator =( const ATrousWaveletTransform& ) = default;
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/*!
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* Move assignment operator. Returns a reference to this object.
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*/
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ATrousWaveletTransform& operator =( ATrousWaveletTransform&& ) = default;
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/*!
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* Returns a reference to the (immutable) scaling function used by this
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* wavelet transform.
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*/
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const WaveletScalingFunction& ScalingFunction() const
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{
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return m_scalingFunction;
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}
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/*!
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* Sets a new scaling function \a f for this wavelet transform.
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*
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* \note As a consequence of calling this member function, all existing
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* wavelet layers in this transform are destroyed.
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*/
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void SetScalingFunction( const WaveletScalingFunction& f )
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{
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DestroyLayers();
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m_scalingFunction = f;
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PCL_CHECK( m_scalingFunction.IsValid() )
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}
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/*!
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* Sets a non-separable kernel filter as the scaling function \a f used by
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* this wavelet transform.
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*
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* \note As a consequence of calling this member function, all existing
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* wavelet layers in this transform are destroyed.
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*/
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void SetScalingFunction( const KernelFilter& f )
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{
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DestroyLayers();
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m_scalingFunction.Set( f );
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PCL_CHECK( m_scalingFunction.IsValid() )
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}
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/*!
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* Sets a separable kernel filter as the scaling function \a f used by this
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* wavelet transform.
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*
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* \note As a consequence of calling this member function, all existing
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* wavelet layers in this transform are destroyed.
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*/
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void SetScalingFunction( const SeparableFilter& f )
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{
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DestroyLayers();
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m_scalingFunction.Set( f );
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PCL_CHECK( m_scalingFunction.IsValid() )
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}
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/*!
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* Estimation of the standard deviation of the noise, assuming a Gaussian
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* noise distribution. This routine implements the k-sigma clipping noise
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* estimation algorithm described by Starck et al. (see the references in
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* the detailed documentation for this class). The algorithm is described
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* for example in <em>Astronomical %Image and Data Analysis</em>, pp. 37-38.
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*
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* This routine can be used to provide an initial estimate to the more
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* accurate <em>multiresolution support noise estimation algorithm</em>,
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* implemented as the NoiseMRS() routine. When used with a relative error
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* bound (see the \a eps parameter), this routine can easily yield noise
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* estimates to within 1% accuracy.
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*
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* \param j Wavelet layer index (zero-based). The default index is 0.
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*
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* \param k Clipping multiplier in sigma units. The default value is 3.
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*
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* \param eps Fractional relative accuracy. If this parameter is greater
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* than zero, the algorithm will iterate until the difference
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* between two successive iterations is less than \a eps. The
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* default value is 0.01, so this routine iterates to achieve an
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* estimate to within 1% accuracy.
|
|
*
|
|
* \param n Maximum number of iterations. When \a eps is zero, this is
|
|
* the fixed number of iterations of the noise estimation
|
|
* algorithm. Three iterations usually give an estimate to
|
|
* within 5% accuracy. 5 or 6 iterations can provide 1% accuracy
|
|
* in most cases. When \a eps is greater than zero, this
|
|
* parameter works as a security limit to prevent too long
|
|
* execution times when convergence is slow (which shouldn't
|
|
* happen under normal conditions). The default value is 10.
|
|
*
|
|
* \param[out] N Pointer to a variable that will receive the total number
|
|
* of pixels tagged as noise during the noise evaluation
|
|
* process. This pointer can legally be \c nullptr, which is
|
|
* also the default value of this parameter.
|
|
*
|
|
* Returns the estimated standard deviation of the noise in the specified
|
|
* scale \a j of the wavelet transform after a relative \a eps accuracy has
|
|
* been reached or \a n sigma clipping iterations have been performed,
|
|
* whichever happens first.
|
|
*
|
|
* The returned value must be scaled by the standard deviation of the
|
|
* Gaussian noise at the specified wavelet scale. The scaling factor depends
|
|
* on the wavelet scaling function used to perform the wavelet decomposition
|
|
* and must be coherent with the transform performed by this object.
|
|
*
|
|
* If this %ATrousWaveletTransform object does not contain a valid wavelet
|
|
* transform, or if the specified wavelet layer has been deleted, this
|
|
* routine throws an Error exception.
|
|
*/
|
|
double NoiseKSigma( int j = 0, float k = 3,
|
|
float eps = 0.01, int n = 10, size_type* N = nullptr ) const;
|
|
|
|
/*!
|
|
* Estimation of the standard deviation of the noise, assuming a Gaussian
|
|
* noise distribution, for a specified range of pixel values.
|
|
*
|
|
* This routine implements essentially the same algorithm as its unbounded
|
|
* counterpart:
|
|
*
|
|
* NoiseKSigma( int j, float k, float eps, int n, size_type* N ).
|
|
*
|
|
* The difference is that this version allows you to specify a valid range
|
|
* of pixel values with the \a low, \a high and \a image parameters. The
|
|
* standard deviation of the noise will only be computed for those pixels
|
|
* whose values in the specified \a image pertain to the range
|
|
* (<em>low</em>,<em>high</em>), that is, for every pixel with value \a v in
|
|
* \a image such that the condition \a low < \e v < \a high is true.
|
|
*
|
|
* The specified \a image must be compatible with the wavelet transform. In
|
|
* particular, the dimensions of \a image must be identical to those of the
|
|
* wavelet layers in this transform; otherwise an Error exception will be
|
|
* thrown. For selection of pixels within the specified range, only the
|
|
* currently selected channel in \a image will be taken into account.
|
|
* Normally, the specified \a image must be the same image that was used to
|
|
* compute the current wavelet decomposition in this object.
|
|
*
|
|
* For detailed information on the rest of parameters, the implemented
|
|
* algorithm, and special usage conditions for this routine, refer to the
|
|
* documentation for the unbounded version of this member function.
|
|
*/
|
|
double NoiseKSigma( int j, const ImageVariant& image,
|
|
float low = 0.00002F, float high = 0.99998F,
|
|
float k = 3, float eps = 0.01, int n = 10, size_type* N = nullptr ) const;
|
|
|
|
/*!
|
|
* Estimation of the standard deviation of the Gaussian noise from the
|
|
* multiresolution support. This routine implements the iterative algorithm
|
|
* described by Jean-Luc Starck and Fionn Murtagh in their paper
|
|
* <em>Automatic Noise Estimation from the Multiresolution Support</em>
|
|
* (Publications of the Royal Astronomical Society of the Pacific, vol. 110,
|
|
* February 1998, pp. 193-199).
|
|
*
|
|
* \param image The original image. Normally this image should be the same
|
|
* image from which this wavelet transform has been
|
|
* calculated.
|
|
*
|
|
* \param sj Noise standard deviation at each wavelet scale for a
|
|
* Gaussian noise distribution with unit sigma. There must be
|
|
* at least NumberOfLayers() elements in the array pointed to
|
|
* by this parameter.
|
|
*
|
|
* \param sigma Initial estimate of the noise standard deviation in the
|
|
* image. The default value is zero. The best starting value
|
|
* is the result of the NoiseKSigma() routine. However, the
|
|
* noise estimate provided by NoiseKSigma() is relative to a
|
|
* particular wavelet layer, so it must be scaled as
|
|
* appropriate to make it coherent with the whole image.
|
|
*
|
|
* \param k Clipping multiplier in sigma units. The default value is 3.
|
|
*
|
|
* \param[out] N Pointer to a variable that will receive the total number
|
|
* of pixels tagged as noise during the noise evaluation
|
|
* process. This pointer can legally be \c nullptr, which is
|
|
* also the default value of this parameter.
|
|
*
|
|
* \param low Lower bound of the sampling range in the normalized [0,1]
|
|
* range. Pixel sample values less than or equal to \a low
|
|
* will be excluded from the noise evaluation process. The
|
|
* default value is 0.00002.
|
|
*
|
|
* \param high Upper bound of the sampling range in the normalized [0,1]
|
|
* range. Pixel sample values greater than or equal to
|
|
* \a high will be excluded from the noise evaluation
|
|
* process. The default value is 0.99998.
|
|
*
|
|
* Returns the estimated standard deviation of the noise from the
|
|
* multiresolution support, using all wavelet scales available. As long as
|
|
* successive noise estimates converge to a stable solution, this routine
|
|
* performs the necessary iterations until a relative fractional accuracy of
|
|
* 1e-4 is achieved. Normally this requires between 4 and 8 iterations,
|
|
* depending on the relation between the noise and significant structures in
|
|
* the image.
|
|
*
|
|
* If no convergence is achieved after a large number of iterations, this
|
|
* function returns zero and, if a nonzero N argument pointer is specified,
|
|
* sets *N = 0. This should never happen if this wavelet transform defines a
|
|
* reasonable number of wavelet layers (4 or 5 layers are recommended) and
|
|
* the passed parameters are valid and coherent with the wavelet transform.
|
|
*
|
|
* If this %ATrousWaveletTransform object does not contain a valid wavelet
|
|
* transform, if any wavelet layer has been deleted, or if the specified
|
|
* image doesn't have the same geometry as the wavelet layers in this
|
|
* transform, this routine throws an Error exception.
|
|
*/
|
|
double NoiseMRS( const ImageVariant& image, const float sj[],
|
|
double sigma = 0, float k = 3, size_type* N = nullptr,
|
|
float low = 0.00002F, float high = 0.99998F ) const;
|
|
|
|
private:
|
|
|
|
/*
|
|
* Wavelet scaling function.
|
|
*/
|
|
WaveletScalingFunction m_scalingFunction;
|
|
|
|
/*
|
|
* Transform (decomposition)
|
|
*/
|
|
void Transform( const pcl::Image& ) override;
|
|
void Transform( const pcl::DImage& ) override;
|
|
void Transform( const pcl::ComplexImage& ) override;
|
|
void Transform( const pcl::DComplexImage& ) override;
|
|
void Transform( const pcl::UInt8Image& ) override;
|
|
void Transform( const pcl::UInt16Image& ) override;
|
|
void Transform( const pcl::UInt32Image& ) override;
|
|
|
|
void ValidateScalingFunction() const;
|
|
|
|
friend class ATWTDecomposition;
|
|
};
|
|
|
|
// ----------------------------------------------------------------------------
|
|
|
|
/*!
|
|
* \class pcl::StarletTransform
|
|
* \brief Starlet wavelet transform, a synonym for ATrousWaveletTransform.
|
|
*
|
|
* The isotropic stationary wavelet transform known as <em>à trous wavelet
|
|
* transform</em> since the early publications of Mallat, Starck and Murtagh in
|
|
* the 90's, is now known "officially" as <em>starlet transform</em>, at least
|
|
* since 2010's <em>%Sparse %Image and %Signal %Processing</em> book.
|
|
*
|
|
* \ingroup multiscale_transforms
|
|
*/
|
|
typedef ATrousWaveletTransform StarletTransform;
|
|
|
|
// ----------------------------------------------------------------------------
|
|
|
|
} // pcl
|
|
|
|
#endif // __PCL_ATrousWaveletTransform_h
|
|
|
|
// ----------------------------------------------------------------------------
|
|
// EOF pcl/ATrousWaveletTransform.h - Released 2022-03-12T18:59:29Z
|