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polyHaar Class Template Reference

This class implements the wavelet Lifting Scheme with polynomial interpolation. More...

#include <polyHaar.h>

Inheritance diagram for polyHaar::

List of all members.

Public Methods
	polyHaar ()
	polyHaar class constructor. More...
	~polyHaar ()
	polyHaar (const polyHaar &rhs)
void	forwardStep (T &vec, const int n)
	One step in the forward wavelet transform. More...
virtual void	inverseStep (T &vec, const int n)
	One inverse wavelet transform step. More...
Protected Methods
void	update (T &vec, int N, transDirection direction)
	The update step of the wavelet Lifting Scheme. More...
void	interp (T &vec, int N, transDirection direction)
	<. More...
void	predict (T &vec, int N, transDirection direction)
	Predict step of the wavelet Lifting Scheme. More...
Private Types
enum	bogus { numPts = 4 }
Private Methods
void	fill (T &vec, double d[], int N, int start)
	Copy four points or N (which ever is less) data points from vec into d These points are the "known" points used in the polynomial interpolation. More...
Private Attributes
polyinterp	fourPtInterp

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Detailed Description

template<class T> class polyHaar

This class implements the wavelet Lifting Scheme with polynomial interpolation.

This version of wavelets is based on Wim Sweldens' tutorial paper Building Your Own Wavelets at Home. This tutorial was presented at SIGGraph. The tutorial is available on the Web.

One of the attractive features of Lifting Scheme wavelets is that the transform and the inverse transform are exact mirrors of each other. To arrive at the inverse transform the order of the operations is reversed and subtraction and addition operations are exchanged. This allows a generic Lifting Scheme base class to be constructed, where the ordering is defined by the sub-classes.

Definition at line 59 of file polyHaar.h.

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Member Enumeration Documentation

template<class T> enum polyHaar<T>::bogus [private]

Enumeration values: numPts   Definition at line 71 of file polyHaar.h. { numPts = 4 } bogus;

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Constructor & Destructor Documentation

template<class T> polyHaar<T>::polyHaar<T> ( ) [inline]

polyHaar class constructor. Definition at line 65 of file polyHaar.h. {}

template<class T> polyHaar<T>::~polyHaar<T> ( ) [inline]

Definition at line 66 of file polyHaar.h. {}

template<class T> polyHaar<T>::polyHaar<T> ( const polyHaar<T> & rhs )

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Member Function Documentation

template<class T> void polyHaar<T>::fill ( T & vec, double d[], int N, int start ) [inline, private]

Copy four points or N (which ever is less) data points from vec into d These points are the "known" points used in the polynomial interpolation. Parameters: vec   [] the input data set on which the wavelet is calculated d   [] an array into which N data points, starting at start are copied. N   the number of polynomial interpolation points start   the index in vec from which copying starts Definition at line 85 of file polyHaar.h. Referenced by interp(). { int n = numPts; if (n > N) n = N; int end = start + n; int j = 0; for (int i = start; i < end; i++) { d[j] = vec[i]; j++; } } // fill

template<class T> void polyHaar<T>::forwardStep ( T & vec, const int n ) [inline, virtual]

One step in the forward wavelet transform. Reimplemented from liftbase. Definition at line 274 of file polyHaar.h. { split( vec, n ); predict( vec, n, forward ); update( vec, n, forward ); interp( vec, n, forward ); } // forwardStep

template<class T> void polyHaar<T>::interp ( T & vec, int N, transDirection direction ) [inline, protected]

<. p> Predict an odd point from the even points, using 4-point polynomial interpolation. The four points used in the polynomial interpolation are the even points. We pretend that these four points are located at the x-coordinates 0,1,2,3. The first odd point interpolated will be located between the first and second even point, at 0.5. The next N-3 points are located at 1.5 (in the middle of the four points). The last two points are located at 2.5 and 3.5. For complete documentation see http://www.bearcave.com/misl/misl_tech/wavelets/lifting/index.html The difference between the predicted (interpolated) value and the actual odd value replaces the odd value in the forward transform. As the recursive steps proceed, N will eventually be 4 and then 2. When N = 4, linear interpolation is used. When N = 2, Haar interpolation is used (the prediction for the odd value is that it is equal to the even value). Parameters: vec   the input data on which the forward or inverse transform is calculated. N   the area of vec over which the transform is calculated direction   forward or inverse transform Definition at line 175 of file polyHaar.h. Referenced by forwardStep(), and inverseStep(). { int half = N >> 1; double d[4]; for (int i = 0; i < half; i++) { double predictVal; if (i == 0) { if (half == 1) { // e.g., N == 2, and we use Haar interpolation predictVal = vec[0]; } else { fill( vec, d, N, 0 ); predictVal = fourPtInterp.interpPoint( 0.5, half, d ); } } else if (i == 1) { predictVal = fourPtInterp.interpPoint( 1.5, half, d ); } else if (i == half-2) { predictVal = fourPtInterp.interpPoint( 2.5, half, d ); } else if (i == half-1) { predictVal = fourPtInterp.interpPoint( 3.5, half, d ); } else { fill( vec, d, N, i-1); predictVal = fourPtInterp.interpPoint( 1.5, half, d ); } int j = i + half; if (direction == forward) { vec[j] = vec[j] - predictVal; } else if (direction == inverse) { vec[j] = vec[j] + predictVal; } else { printf("interp: bad direction value\n"); break; } } // for } // interp

template<class T> void polyHaar<T>::inverseStep ( T & vec, const int n ) [inline, virtual]

One inverse wavelet transform step. Reimplemented from liftbase. Definition at line 282 of file polyHaar.h. { interp( vec, n, inverse ); update( vec, n, inverse ); predict( vec, n, inverse ); merge( vec, n ); }

template<class T> void polyHaar<T>::predict ( T & vec, int N, transDirection direction ) [inline, protected, virtual]

Predict step of the wavelet Lifting Scheme. The term "predict" comes from Building Your Own Wavelets at Home. transform In the wavelet transform, calculate the difference between even and odd element pairs. This is a slightly modified version of the classic haar difference. If the even elements are labeled as a and the odd elements are labeled as b (where we start counting at zero) the difference is simply di = bi - ai Since an "in-place" algorithm is used, where we update the odd elements with the difference, we get bi = bi - ai inverse transform Reverse the transform predict step by adding the average (even element) to the difference (odd element). Reimplemented from liftbase. Definition at line 251 of file polyHaar.h. { int i; int half = N >> 1; int j = 0; for (i = half; i < N; i++) { if (direction == forward) { // forward transform stage vec[i] = vec[i] - vec[j]; } else if (direction == inverse ) { // inverse transform stage vec[i] = vec[i] + vec[j]; } else { printf("predict: bad direction\n"); break; } j++; } } // predict

template<class T> void polyHaar<T>::update ( T & vec, int N, transDirection direction ) [inline, protected, virtual]

The update step of the wavelet Lifting Scheme. transform In the Lifting Scheme transform the update step follows the predict step. After the predict step, the differences have been calculated in-place writing over the even (b) values. The update step calculates the Haar average using an even/odd pair. The average is placed in the even member of the pair. Reimplemented from liftbase. Definition at line 115 of file polyHaar.h. { int i; int half = N >> 1; int j = half; for (i = 0; i < half; i++) { if (direction == forward) { // forward transform stage vec[i] = vec[i] + (vec[j]/2.0); } else if (direction == inverse) { // inverse transform step vec[i] = vec[i] - (vec[j]/2.0); } else { printf("update: bad direction value\n"); break; } j++; } // for } // update

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Member Data Documentation

template<class T> polyinterp polyHaar<T>::fourPtInterp [private]

Definition at line 72 of file polyHaar.h.

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

• polyHaar.h

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