Contour stencil interpolation. More...

#include <string.h>
#include "invmat.h"
#include "sinterp.h"

Include dependency graph for sinterp.c:

Data Structures
struct	sinterpentry
	Data for interpolating with a contour stencil. More...

struct	sinterpstruct
	Data for interpolating with a contour stencil set. More...

Macros
#define	NEIGHRADIUS 1
	The size of the synthesis neighborhood $\mathcal{N}$ . More...

#define	QUAD_RES 8
	Quadrature resolution to use for integrals. More...

#define	TRIG_TABLE_SIZE 256
	Size of the trignometry tables used in RhoFast. More...

#define	EXP_TABLE_SIZE 1024
	Size of the exponential table used in RhoFast. More...

#define	WINDOWRADIUS (1 + NEIGHRADIUS)
	Support radius of the window function . More...

#define	NEIGHDIAMETER (1 + 2*NEIGHRADIUS)
	Diameter of the neighborhood. More...

#define	NEIGHCENTER (NEIGHRADIUS + NEIGHRADIUS*NEIGHDIAMETER)
	Index of the neighborhood center. More...

#define	NUMNEIGH (NEIGHDIAMETER*NEIGHDIAMETER)
	Number of neighbors in the neighborhood, $\|\mathcal{N}\|$ . More...

Typedefs
typedef struct sinterpstruct	sinterptype
	Data for interpolating with a contour stencil set. More...

Functions
int	InterpolateStencil (sinterp SInterp, int S, const double PsfSamples)
	Compute interpolation information for a stencil. More...

sinterp *	NewSInterp (const sset *StencilSet, float RhoSigmaTangent, float RhoSigmaNormal)
	Create a new sinterp object. More...

void	FreeSInterp (sinterp *SInterp)
	Free an sinterp object. More...

int	ArbitraryScale (float Output, int OutputWidth, int OutputHeight, const int Stencil, const sinterp SInterp, const float Input, int InputWidth, int InputHeight, float ScaleFactor, int CenteredGrid)
	Scale a color image by a possibly non-integer scale factor. More...

float *	ComputeRhoSamples (const sinterp *SInterp, int ScaleFactor, int CenteredGrid)
	Precompute samples of $\Tilde\rho$ for an integer scale factor. More...

void	IntegerScalePass (float Output, const int Stencil, const float RhoSamples, const float Input, int InputWidth, int InputHeight, int ScaleFactor, int CenteredGrid)
	Scale a color image by an integer factor. More...

int	Prefilter (float Filtered, const int Stencil, const float RhoSamples, const float Input, int InputWidth, int InputHeight, int ScaleFactor, int CenteredGrid, float PsfSigma, int NumPasses)
	Prefilter a color image to improve deconvolution accuracy. More...

float	DeconvResidual (float Residual, const float Coarse, int CoarseWidth, int CoarseHeight, const float *Interp, int InterpWidth, int InterpHeight, float ScaleFactor, int CenteredGrid, float PsfSigma)
	Compute deconvolution residual for prefiltering. More...

Detailed Description

Contour stencil interpolation.

Author: Pascal Getreuer getre.nosp@m.uer@.nosp@m.gmail.nosp@m..com

This file implements contour stencil interpolation for color images by integer and non-integer scale factors. The main routines are

NewSInterp() to compute data to use a stencil set for interpolation,
Prefilter() to perform iterative refinement,
IntegerScalePass() for interpolation by an integer scale factor,
ArbitraryScale() for interpolation by a non-integer scale factor.

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 sinterp.c.

Macro Definition Documentation

#define EXP_TABLE_SIZE 1024

Size of the exponential table used in RhoFast.

Definition at line 35 of file sinterp.c.

#define NEIGHCENTER (NEIGHRADIUS + NEIGHRADIUS*NEIGHDIAMETER)

Index of the neighborhood center.

Definition at line 43 of file sinterp.c.

#define NEIGHDIAMETER (1 + 2*NEIGHRADIUS)

Diameter of the neighborhood.

Definition at line 41 of file sinterp.c.

#define NEIGHRADIUS 1

The size of the synthesis neighborhood $\mathcal{N}$ .

Definition at line 29 of file sinterp.c.

#define NUMNEIGH (NEIGHDIAMETER*NEIGHDIAMETER)

Number of neighbors in the neighborhood, $|\mathcal{N}|$ .

Definition at line 45 of file sinterp.c.

#define QUAD_RES 8

Quadrature resolution to use for integrals.

Definition at line 31 of file sinterp.c.

#define TRIG_TABLE_SIZE 256

Size of the trignometry tables used in RhoFast.

Definition at line 33 of file sinterp.c.

#define WINDOWRADIUS (1 + NEIGHRADIUS)

Support radius of the window function $w(x)$ .

Definition at line 39 of file sinterp.c.

Typedef Documentation

typedef struct sinterpstruct sinterptype

Data for interpolating with a contour stencil set.

Function Documentation

int ArbitraryScale	(	float *	Output,
		int	OutputWidth,
		int	OutputHeight,
		const int *	Stencil,
		const sinterp *	SInterp,
		const float *	Input,
		int	InputWidth,
		int	InputHeight,
		float	ScaleFactor,
		int	CenteredGrid
	)

Scale a color image by a possibly non-integer scale factor.

Parameters

Output	the output image
OutputWidth,OutputHeight	dimensions of the output image
Stencil	the best-fitting stencils $\mathcal{S}^\star$
SInterp	stencil interpolation data
Input	the input image in row-major interleaved order
InputWidth,InputHeight	dimensions of the input image
ScaleFactor	scale factor between input and output images
CenteredGrid	use centered grid if nonzero or top-left otherwise

Returns: 1 on success, 0 on failure

This routine implements for a possibly non-integer scale factor the interpolation formula

$u(x) = \sum_{k \in \mathbb{Z}^2} w(x-k) \Bigl[ v_k + \sum_{m\in\mathcal{N}} c_m^k \, \rho_{\mathcal{S}^\star(k)}^m(x - m - k) \Bigr],$

where the coefficients $c_m^k$ are computed as

$c_m^k = \sum_{n\in\mathcal{N}} (A_{\mathcal{S}^\star(k)}^{-1})_{m,n} (v_{k+n} - v_k), \quad m \in \mathcal{N}.$

For more accurate deconvolution, Prefilter() should be called first to prefilter the input image.

In the code, the mathematical meanings of the variables are as follows:

Output:
Input:
Coeff[3*(NUMNEIGH + 1)*k + m]:
SInterp->StencilInterp[S].Matrix: $A_{\mathcal{S}}^{-1}$
WindowWeight:

For computational efficiency, RhoFast() is used to evaluate $\rho$ instead of Rho(), as $\rho$ needs to be evaluated here many times.

Definition at line 400 of file sinterp.c.

float* ComputeRhoSamples	(	const sinterp *	SInterp,
		int	ScaleFactor,
		int	CenteredGrid
	)

Precompute samples of $\Tilde\rho$ for an integer scale factor.

Parameters

SInterp	stencil interpolation data
ScaleFactor	the integer scale factor
CenteredGrid	use centered grid if nonzero or top-left otherwise

Returns: pointer to samples, or NULL on failure

This routine evaluates samples of

$\Tilde{\rho}_{\mathcal{S}}^n(x) = w(x) \sum_{m\in\mathcal{N}} (A_{\mathcal{S}}^{-1})_{m,n} \, \rho_{\mathcal{S}}^m(x-m).$

at locations on a fine grid with step size 1/ScaleFactor, where ScaleFactor is an integer. This precomputation significantly accelerates image scaling by an integer factor.

The samples are computed for every stencil $\mathcal{S}\in\Sigma$ for every neighbor $m\in\mathcal{N}$ over a square window of size SupportWidth by SupportWidth, where SupportWidth = 2*WINDOWRADIUS*ScaleFactor or this value minus 1, depending on the choice of grid and the oddness of ScaleFactor.

Definition at line 566 of file sinterp.c.

float DeconvResidual	(	float *	Residual,
		const float *	Coarse,
		int	CoarseWidth,
		int	CoarseHeight,
		const float *	Interp,
		int	InterpWidth,
		int	InterpHeight,
		float	ScaleFactor,
		int	CenteredGrid,
		float	PsfSigma
	)

Compute deconvolution residual for prefiltering.

Parameters

Residual	the residual image
Coarse	the coarse image
CoarseWidth,CoarseHeight	dimensions of the coarse image
Interp	the interpolated image
InterpWidth,InterpHeight	dimensions of the interpolated image
ScaleFactor	scale factor between coarse and interpolated images
CenteredGrid	use centered grid if nonzero or top-left otherwise
PsfSigma	Gaussian PSF standard deviation in units of input pixels

This routine computes the deconvolution residual

$r = v - \operatorname{sample}(h * u),$

where v is the coarse image and u is the interpolation. This residual is used in the iterative refinement procedure implemented in Prefilter().

Definition at line 880 of file sinterp.c.

void FreeSInterp ( sinterp * SInterp )

Free an sinterp object.

Parameters

SInterp the sinterp to free

Frees all memory associated with SInterp.

Definition at line 340 of file sinterp.c.

void IntegerScalePass	(	float *	Output,
		const int *	Stencil,
		const float *	RhoSamples,
		const float *	Input,
		int	InputWidth,
		int	InputHeight,
		int	ScaleFactor,
		int	CenteredGrid
	)

Scale a color image by an integer factor.

Parameters

Output	the output image
Stencil	the best-fitting stencils $\mathcal{S}^\star$
RhoSamples	precomputed samples of $\Tilde\rho$
Input	the input image in row-major interleaved order
InputWidth,InputHeight	dimensions of the input image
ScaleFactor	scale factor between input and output images
CenteredGrid	use centered grid if nonzero or top-left otherwise

This routine implements for a integer scale factor the interpolation formula

$u(x) = \sum_{k \in \mathbb{Z}^2} \biggl[ w(x-k) v_k + \sum_{n \in\mathcal{N}\backslash\{0\}} (v_{k+n} - v_k) \, \Tilde{\rho}_{\mathcal{S}^\star(k)}^n(x-k) \biggr].$

Definition at line 660 of file sinterp.c.

int InterpolateStencil	(	sinterp *	SInterp,
		int	S,
		const double *	PsfSamples
	)

Compute interpolation information for a stencil.

Parameters

SInterp	stencil set interpolation data
S	index of the stencil to interpolate
PsfSamples	precomputed samples of the PSF

Returns: 1 on success, 0 on failure

The orientation and anisotropy of the $\rho_\mathcal{S}^n$ synthesis functions are computed,

$\begin{aligned} \theta_\mathcal{S}^n &= \angle \int_{[-\frac{1}{2},+\frac{1}{2}]^2} \nabla\varphi_\mathcal{S}^\perp \bigl(x - n) \, dx, \\ \mu_\mathcal{S} &= \min_{n\in \mathcal{N}}\, \Bigl\lvert\int_{[-\frac{1}{2},+\frac{1}{2}]^2} \nabla\varphi_\mathcal{S} \bigl(x - n) \, dx\Bigr\rvert. \end{aligned}$

The interpolation matrix

$(A_\mathcal{S})_{m,n} = (h * \rho^n_\mathcal{S})(m - n), \quad m,n\in\mathcal{N}$

is computed and inverted with InvertMatrix().

Definition at line 170 of file sinterp.c.

sinterp* NewSInterp	(	const sset *	StencilSet,
		float	RhoSigmaTangent,
		float	RhoSigmaNormal
	)

Create a new sinterp object.

Parameters

StencilSet	stencil set $\Sigma$ to perform interpolation with
RhoSigmaTangent,RhoSigmaNormal	parameters for Rho

Returns: an sinterp*, or NULL on failure

Given a stencil set $\Sigma$ , this routine performs the necessary precomputations for interpolation and stores it in an sinterp data structure. Each stencil $\mathcal{S}\in\Sigma$ is processed with InterpolateStencil() to create an sinterpentry.

Definition at line 298 of file sinterp.c.

int Prefilter	(	float *	Filtered,
		const int *	Stencil,
		const float *	RhoSamples,
		const float *	Input,
		int	InputWidth,
		int	InputHeight,
		int	ScaleFactor,
		int	CenteredGrid,
		float	PsfSigma,
		int	NumPasses
	)

Prefilter a color image to improve deconvolution accuracy.

Parameters

Filtered	the prefiltered image
Stencil	the best-fitting stencils $\mathcal{S}^\star$
RhoSamples	precomputed samples of $\Tilde\rho$
Input	the input image in row-major interleaved order
InputWidth,InputHeight	dimensions of the input image
ScaleFactor	scale factor between input and output images
CenteredGrid	use centered grid if nonzero or top-left otherwise
PsfSigma	Gaussian PSF standard deviation in units of input pixels
NumPasses	number of passes of iterative refinement to perform

This routine performs the iterative refinement prefiltering

$v^0 = v, \quad v^{i+1} = v^i + \bigl(v - \operatorname{sample}(h*\mathcal{R}v^i)\bigr).$

Interpolation with a prefiltered image improves the resulting deconvolution accuracy. Interpolation is performed using the prefiltered image as input with either IntegerScalePass() for an integer scale factor or by ArbitraryScale() for a non-integer scale factor.

Prefiltering is implemented with IntegerScalePass() to perform the interpolations $\mathcal{R}v^i$ and DeconvResidual() to compute the deconvolution residuals $v - \operatorname{sample}(h*\mathcal{R}v^i)$ .

Definition at line 802 of file sinterp.c.

Data Structures

Macros

Typedefs

Functions

Detailed Description

Macro Definition Documentation

Typedef Documentation

Function Documentation