Contour stencil windowed interpolation. More...

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "basic.h"
#include "cwinterp.h"
#include "fitsten.h"
#include "invmat.h"
#include "nninterp.h"
#include "drawline.h"
#include "imageio.h"

Include dependency graph for cwinterp.c:

Go to the source code of this file.

Defines
#define	NUMSTENCILS 8
	The number of contour stencils, cardinality of $\Sigma$ .
#define	NEIGHRADIUS 1
	Cardinality of the neighborhood $\mathcal{N}$ .
#define	NEIGHDIAMETER (2*NEIGHRADIUS+1)
#define	NUMNEIGH (NEIGHDIAMETER*NEIGHDIAMETER)
#define	CORRECTION_IGNOREBITS 3
	`CWRefinementPass` residual tolerance.
#define	INPUT_FRACBITS 8
	Number of fractional bits in the input array.
#define	PSI_FRACBITS 12
	Number of fractional bits in the psi sample arrays.
#define	OUTPUT_FRACBITS (INPUT_FRACBITS + PSI_FRACBITS)
	Number of fractional bits in the output array.
#define	FIXED_ONE(N) (1 << (N))
	The number 1.0 in fixed-point with N fractional bits.
#define	FIXED_HALF(N) (1 << ((N) - 1))
	The number 0.5 in fixed-point with N fractional bits.
#define	PIXEL_STRIDE 3
	Number of elements between successive RGB fixed-point pixels.
#define	CLAMP(X, A, B) (((X) < (A)) ? (A) : (((X) > (B)) ? (B) : (X)))
	Clamp X to [A, B].
#define	ROUNDCLAMP(X, A, B) (((X) < (A)) ? (A) : (((X) > (B)) ? (B) : ROUND(X)))
	Round and clamp double X to integer.
#define	ROUNDCLAMP(X, A, B) (((X) < (A)) ? (A) : (((X) > (B)) ? (B) : ROUND(X)))
	Round and clamp double X to integer.
#define	XY_FRACBITS 15
#define	TRIG_FRACBITS 10
#define	PHITN_FRACBITS 9
#define	PHI_FRACBITS 10
#define	COEFF_FRACBITS 10
#define	WINDOW_FRACBITS 10
#define	UK_FRACBITS 10
#define	ROUND_FIXED(X, N) (((X) + FIXED_HALF(N)) >> (N))
#define	FLOAT_TO_FIXED(X, N) ((int32_t)ROUND((X) * FIXED_ONE(N)))
Functions
int32_t *	PreCWInterp (cwparams Param)
	Precomputations before windowed interpolation `CWInterp`.
int	CWInterp (uint32_t Output, const uint32_t Input, int InputWidth, int InputHeight, const int32_t *Psi, cwparams Param)
	Contour stencil windowed interpolation.
int	CWArbitraryInterp (uint32_t Output, int OutputWidth, int OutputHeight, const int32_t Input, int InputWidth, int InputHeight, const int Stencil, const double InverseA, cwparams Param)
	Arbitrary scale factor interpolation.
int	CWInterpEx (uint32_t Output, int OutputWidth, int OutputHeight, const uint32_t Input, int InputWidth, int InputHeight, const int32_t *Psi, cwparams Param)
	Contour stencil windowed interpolation for arbitrary scale factors.
int	DisplayContours (uint32_t Output, int OutputWidth, int OutputHeight, uint32_t Input, int InputWidth, int InputHeight, cwparams Param)
	Display the estimated contour orientations.

Detailed Description

Contour stencil windowed interpolation.

Author:: Pascal Getreuer <getreuer@gmail.com>

This file implements contour stencil windowed interpolation for integer scale factors. The interpolation model supposes that the input image $v$ was created by convolution followed by downsampling

$v = {\downarrow_r} (h * u)$

where $u$ is the underlying high resolution image, $h$ is the point- spread function (PSF), and $\downarrow_r$ denotes downsampling by factor $r$ . For simplicity, this code requires that $r$ is integer and $h$ is a Gaussian. The standard deviation $h$ is controlled by PsfSigma.

The image is interpolated by the following steps. First, contour stencils are applied to estimate the local contour orientations (in routine FitStencils). The image is then interpolated by the formula

$u(x) = \sum_{k\in\mathbb{Z}^2} w(x - k) \Bigl[ v_k + \sum_{n\in\mathcal{N}\backslash\{0\}} (v_{k+n} - v_k) \psi^n_{\mathcal{S}^\star(k)}(x - k) \Bigr]$

(routine CWFirstPass). This initial interpolation approximately satisfies the degradation model, $v \approx {\downarrow_r} (h * u)$ . To improve the accuracy, several correction passes are applied. In each pass, the residual is computed (routine CWResidual) and then applied to refine the interpolation (routine CWRefinementPass). Under typical settings, the degradation model is accurately satisfied after two or three correction passes.

The main computations CWFirstPass and CWRefinementPass are done in fixed-point integer arithmetic. The downsides of using fixed-point arithmetic compared to floating-point arithmetic are more involved code for multiplication and division (it is harder to read) and the range and precision of fixed-point integers must be explicitly managed for accurate results (need to be careful). The upside is that when it does work, fixed- point arithmetic is significantly faster. Fortunately, in this application, the only needed operations are fixed-point additions and fixed-point multiplies where both factors are in a predictable range of values. These conditions are good for fixed-point arithmetic.

The number of fractional bits used to represent $v$ and the residual is controlled by INPUT_FRACBITS. The number of fractional bits in representing $\psi$ is PSI_FRACBITS. Since $v$ and $\psi$ are multiplied, the output has OUTPUT_FRACBITS = (INPUT_FRACBITS + PSI_FRACBITS) fractional bits. These constants must be balanced between precision and avoiding overflow. Fortunately this balance is easy to find for this application (neither extreme range nor extreme precision are needed).

This program is free software: you can use, modify and/or redistribute it under the terms of the simplified BSD License. You should have received a copy of this license along this program. If not, see <http://www.opensource.org/licenses/bsd-license.html>.

Definition in file cwinterp.c.

Define Documentation

#define CLAMP	(	X,
		A,
		B
	)	(((X) < (A)) ? (A) : (((X) > (B)) ? (B) : (X)))

Clamp X to [A, B].

Definition at line 120 of file cwinterp.c.

#define COEFF_FRACBITS 10

Definition at line 962 of file cwinterp.c.

#define CORRECTION_IGNOREBITS 3

CWRefinementPass residual tolerance.

In the correction passes, pixels will be skipped if they have magnitude less than 2^(-INPUT_FRACBITS + CORRECTION_IGNOREBITS), which improves the speed. A larger value of CORRECTION_IGNOREBITS makes the correction passes faster, but less accurate.

Definition at line 89 of file cwinterp.c.

#define FIXED_HALF ( N ) (1 << ((N) - 1))

The number 0.5 in fixed-point with N fractional bits.

Definition at line 101 of file cwinterp.c.

#define FIXED_ONE ( N ) (1 << (N))

The number 1.0 in fixed-point with N fractional bits.

Definition at line 99 of file cwinterp.c.

#define FLOAT_TO_FIXED	(	X,
		N
	)	((int32_t)ROUND((X) * FIXED_ONE(N)))

Definition at line 967 of file cwinterp.c.

#define INPUT_FRACBITS 8

Number of fractional bits in the input array.

Definition at line 92 of file cwinterp.c.

#define NEIGHDIAMETER (2*NEIGHRADIUS+1)

Definition at line 78 of file cwinterp.c.

#define NEIGHRADIUS 1

Cardinality of the neighborhood $\mathcal{N}$ .

Definition at line 77 of file cwinterp.c.

#define NUMNEIGH (NEIGHDIAMETER*NEIGHDIAMETER)

Definition at line 79 of file cwinterp.c.

#define NUMSTENCILS 8

The number of contour stencils, cardinality of $\Sigma$ .

Definition at line 74 of file cwinterp.c.

#define OUTPUT_FRACBITS (INPUT_FRACBITS + PSI_FRACBITS)

Number of fractional bits in the output array.

Definition at line 96 of file cwinterp.c.

#define PHI_FRACBITS 10

Definition at line 961 of file cwinterp.c.

#define PHITN_FRACBITS 9

Definition at line 960 of file cwinterp.c.

#define PIXEL_STRIDE 3

Number of elements between successive RGB fixed-point pixels.

PIXEL_STRIDE is the number of elements between successive pixels in the RGB fixed-point representation used internally by the interpolation.

Note:: Unlike the other defines here, this one cannot be changed without also rewriting much of the code. Its purpose is more for clarity rather than working as a parameter.

Definition at line 114 of file cwinterp.c.

#define PSI_FRACBITS 12

Number of fractional bits in the psi sample arrays.

Definition at line 94 of file cwinterp.c.

#define ROUND_FIXED	(	X,
		N
	)	(((X) + FIXED_HALF(N)) >> (N))

Definition at line 966 of file cwinterp.c.

#define ROUNDCLAMP	(	X,
		A,
		B
	)	(((X) < (A)) ? (A) : (((X) > (B)) ? (B) : ROUND(X)))

Round and clamp double X to integer.

Definition at line 945 of file cwinterp.c.

#define ROUNDCLAMP	(	X,
		A,
		B
	)	(((X) < (A)) ? (A) : (((X) > (B)) ? (B) : ROUND(X)))

Round and clamp double X to integer.

Definition at line 945 of file cwinterp.c.

#define TRIG_FRACBITS 10

Definition at line 959 of file cwinterp.c.

#define UK_FRACBITS 10

Definition at line 964 of file cwinterp.c.

#define WINDOW_FRACBITS 10

Definition at line 963 of file cwinterp.c.

#define XY_FRACBITS 15

Definition at line 958 of file cwinterp.c.

Function Documentation

int CWArbitraryInterp	(	uint32_t *	Output,
		int	OutputWidth,
		int	OutputHeight,
		const int32_t *	Input,
		int	InputWidth,
		int	InputHeight,
		const int *	Stencil,
		const double *	InverseA,
		cwparams	Param
	)

Arbitrary scale factor interpolation.

Definition at line 970 of file cwinterp.c.

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int CWInterp	(	uint32_t *	Output,
		const uint32_t *	Input,
		int	InputWidth,
		int	InputHeight,
		const int32_t *	Psi,
		cwparams	Param
	)

Contour stencil windowed interpolation.

Parameters:

Output	pointer to memory for holding the interpolated image
Input	the input image
InputWidth,InputHeight	input image dimensions
Psi	$\psi$ samples computed by `PreCWInterp`
Param	cwparams struct of interpolation parameters

Definition at line 851 of file cwinterp.c.

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int CWInterpEx	(	uint32_t *	Output,
		int	OutputWidth,
		int	OutputHeight,
		const uint32_t *	Input,
		int	InputWidth,
		int	InputHeight,
		const int32_t *	Psi,
		cwparams	Param
	)

Contour stencil windowed interpolation for arbitrary scale factors.

Parameters:

Output	pointer to memory for holding the interpolated image
OutputWidth,OutputHeight	output image dimensions
Input	the input image
InputWidth,InputHeight	input image dimensions
Psi	$\psi$ samples computed by `PreCWInterp`
Param	cwparams struct of interpolation parameters

Definition at line 1274 of file cwinterp.c.

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int DisplayContours	(	uint32_t *	Output,
		int	OutputWidth,
		int	OutputHeight,
		uint32_t *	Input,
		int	InputWidth,
		int	InputHeight,
		cwparams	Param
	)

Display the estimated contour orientations.

Definition at line 1395 of file cwinterp.c.

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int32_t* PreCWInterp ( cwparams Param )

Precomputations before windowed interpolation CWInterp.

Parameters:

Param cwparams struct of interpolation parameters

Returns:: Pointer to $\psi$ samples array, or null on failure

PreCWInterp precomputes samples of the $\psi$ functions,

$\psi^n_\mathcal{S}(x) = \sum_{m\in\mathcal{N}} (A_\mathcal{S})^{-1}_{m,n} \varphi^m_\mathcal{S}(x - m).$

The routine allocates memory to store the samples and returns a pointer to this memory. It is the responsibility of the caller to call free on this pointer when done to release the memory.

A non-null pointer indicates success. On failure, the returned pointer is null.

Definition at line 323 of file cwinterp.c.

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cwinterp.c File Reference

Defines

Functions

Detailed Description

Define Documentation

Function Documentation