Source code for random phase noise texture synthesis. The front end functions for texture synthesis are rpn_color_different_size and rpn_color_same_size. More...

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <fftw3.h>
#include "mt.h"

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Defines
#define	M_PI 3.14159265358979323846
Functions
static float	mean (float *data_in, size_t N)
	Compute the mean of a 2D array of float type.
static fftwf_complex *	pointwise_complexfloat_multiplication (fftwf_complex comp_in, float float_in, size_t N)
	Pointwise multiplication of a complex array by a float array. The complex input is modified.
static fftwf_complex *	pointwise_complex_multiplication (fftwf_complex comp_in1, fftwf_complex comp_in2, size_t N)
	Pointwise multiplication of a complex array by another complex array. The first complex input is modified.
static float *	discrete_laplacian (float data_out, float data_in, size_t nx, size_t ny)
	Compute the discrete Laplacian of a 2D array, differences with "outside of the array" are 0.
static float *	poisson_complex_filter (float *data_out, size_t nx, size_t ny)
	Computation of the real factor which arrizes in the FFT-based discrete Poisson solver.
static float **	periodic_component_color (float **data_in_rgb, size_t nx, size_t ny)
	Computation of the periodic component of a color image.
static fftwf_complex *	random_phase (fftwf_complex *data_out, size_t nx, size_t ny)
	Draw an array of complex numbers on the unit disc having a random phase.
static float **	phase_randomization (float *data_in_rgb, fftwf_complex rp, size_t nx, size_t ny)
	Phase randomization of an RGB 2D float array.
static float *	compute_transition (float *transition, size_t nxin, size_t nyin, float alpha)
	Compute the transition function used to smooth the inner boundary of the extended spot.
static float **	spot_extension_color (float data_out_rgb, float data_in_rgb, size_t nxout, size_t nyout, size_t nxin, size_t nyin, float alpha)
	Extension of a color spot into a larger "equivalent spot".
float **	rpn_color_different_size (float data_out_rgb, float data_in_rgb, size_t nxout, size_t nyout, size_t nxin, size_t nyin, float alpha)
	Random Phase Noise computation when the sizes of the input and the output are different.
static fftwf_complex *	random_phase_with_poisson_complex_filter (fftwf_complex *data_out, size_t nx, size_t ny)
	Draw an array of complex numbers on the unit disc having a random phase, and multiply it by the Poisson complex filter.
float **	rpn_color_same_size (float **data_in_rgb, size_t nx, size_t ny)
	Fast Random Phase Noise when the sizes of the input and the output are the same.

Detailed Description

Source code for random phase noise texture synthesis. The front end functions for texture synthesis are rpn_color_different_size and rpn_color_same_size.

Version:: 1.2

Author:: Bruno Galerne ; <bruno.galerne@cmla.ens-cachan.fr> ; <http://www.cmla.ens-cachan.fr/~galerne>

Definition in file random_phase_noise_lib.c.

Define Documentation

#define M_PI 3.14159265358979323846

macro definition for Pi

Definition at line 36 of file random_phase_noise_lib.c.

Function Documentation

static float* compute_transition	(	float *	transition,
		size_t	nxin,
		size_t	nyin,
		float	alpha
	)			`[static]`

Compute the transition function used to smooth the inner boundary of the extended spot.

Compute the transition function used to smooth the inner boundary of the extended spot. This transition function is the convolution between a characteristic function and the standard separable molifier. More precisely the molifier is the product of an x and y function of the form:

$\varphi(t) = \exp\left(\frac{-1}{1-t^2}\right)$

if $ |t|<1 $ and 0 otherwise.

The resulting function equals 0 on the boundary and 1 on the centered inner frame of size (1-2alpha)*nxin x (1-2alpha)*nyin. It is illustrated below:

Cross section and gray-level

representation of the smooth transition function"

Parameters:

	transition	an already allocated array of size nxin x nyin
	nxin,nyin	input size
	alpha	parameter in [0, 0.5) for the smoothing function (ratio for the width of the smoothing zone)

Returns:: transition, or NULL if an error occured

Definition at line 603 of file random_phase_noise_lib.c.

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static float* discrete_laplacian	(	float *	data_out,
		float *	data_in,
		size_t	nx,
		size_t	ny
	)			`[static]`

Compute the discrete Laplacian of a 2D array, differences with "outside of the array" are 0.

This function computes the discrete laplacian, ie $(F_{i - 1, j} - F_{i + 1, j}) + (F_{i + 1, j} - F_{i, j}) + (F_{i, j - 1} - F_{i, j}) + (F_{i, j + 1} - F_{i, j})$ . On the border, differences with "outside of the array" are 0.

This is a slightly modified version of a function written by Nicolas Limare <nicolas.limare@cmla.ens-cachan.fr> .

Parameters:

	data_out	output array
	data_in	input array
	nx,ny	array size

Returns:: data_out, or NULL if an error occured

Definition at line 170 of file random_phase_noise_lib.c.

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static float mean	(	float *	data_in,
		size_t	N
	)			`[static]`

Compute the mean of a 2D array of float type.

Parameters:

	data_in	input array
	N	size of the array

Returns:: mean of data_in

Definition at line 56 of file random_phase_noise_lib.c.

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static float** periodic_component_color	(	float **	data_in_rgb,
		size_t	nx,
		size_t	ny
	)			`[static]`

Computation of the periodic component of a color image.

This function computes Lionel Moisan's periodic component of an RGB color image in solving a Poisson equation with forward and backward FFT for the three channels.

Reference: L. Moisan, "Periodic plus Smooth Image Decomposition", preprint MAP5, Université Paris Descartes, 2009, available at <http://www.math-info.univ-paris5.fr/~moisan/p+s/>.

For each color channel:

a discrete Laplacian is computed;
the discrete Laplacian is transformed by forward DFT;
the obtained DFT is modified by
$\hat{u}(i, j) = \hat{F}(i, j) / (4 - 2 \cos(\frac{2 i \pi}{n_x}) - 2 \cos(\frac{2 j \pi}{n_y})),$
and $\hat{u}(0, 0)$ is set to be the sum of the input channel;
this data is transformed by backward DFT.

Below is an illustration of a color image and its periodic component.

Input image (left) and its periodic

component (right)"

Parameters:

	data_in_rgb	input rgb float array. This input is lost.
	nx,ny	array size

Returns:: data_in_rgb or NULL if an error occured

Warning:: The input data_in_rgb is replaced by its periodic component, and therefore is lost.

Definition at line 332 of file random_phase_noise_lib.c.

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static float** phase_randomization	(	float **	data_in_rgb,
		fftwf_complex *	rp,
		size_t	nx,
		size_t	ny
	)			`[static]`

Phase randomization of an RGB 2D float array.

A random phase is added to the phase of each color channel.

Parameters:

	data_in_rgb	input float array
	rp	input complex random phase
	nx,ny	array size

Returns:: data_in_rgb or NULL if there is a problem

Warning:: The input data_in_rgb is lost

Definition at line 518 of file random_phase_noise_lib.c.

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static fftwf_complex* pointwise_complex_multiplication	(	fftwf_complex *	comp_in1,
		fftwf_complex *	comp_in2,
		size_t	N
	)			`[static]`

Pointwise multiplication of a complex array by another complex array. The first complex input is modified.

Parameters:

	comp_in1	input complex array
	comp_in2	input complex array
	N	common size of both arrays

Returns:: comp_in1 the multiplied complex array, or NULL if an error occured

Warning:: The first complex array is modified !

Definition at line 121 of file random_phase_noise_lib.c.

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static fftwf_complex* pointwise_complexfloat_multiplication	(	fftwf_complex *	comp_in,
		float *	float_in,
		size_t	N
	)			`[static]`

Pointwise multiplication of a complex array by a float array. The complex input is modified.

Parameters:

	comp_in	input complex array
	float_in	input float array
	N	common size of both arrays

Returns:: comp_in the multiplied complex array, or NULL if an error occured

Warning:: The complex array is modified !

Definition at line 88 of file random_phase_noise_lib.c.

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static float* poisson_complex_filter	(	float *	data_out,
		size_t	nx,
		size_t	ny
	)			`[static]`

Computation of the real factor which arrizes in the FFT-based discrete Poisson solver.

We have :

$out(\xi_1,\xi_2) = \frac{1}{N}\frac{1}{2\cos\left( \frac{2 \xi_1 \pi}{M} \right) + 2\cos\left( \frac{2 \xi_2 \pi}{N} \right) - 4}$

if $(\xi_1,\xi_2) \neq (0,0)$ and $ out(0,0) = 1 $ . Each coefficient is the inverse of an eigenvalue of the periodic Laplacian.

The factor $ 1/N $ is added to normalize the Fourier transform before the inversion (note that FFTW does NOT normalize the transforms).

Parameters:

	data_out	output float array
	nx,ny	input size

Returns:: data_out, or NULL if an error occured

Warning:: The ouput array data_out has size (nx/2+1)*ny to be compatible with the R2C FFT (which takes advantage of the symmetry of the DFT of real data).

Definition at line 242 of file random_phase_noise_lib.c.

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static fftwf_complex* random_phase	(	fftwf_complex *	data_out,
		size_t	nx,
		size_t	ny
	)			`[static]`

Draw an array of complex numbers on the unit disc having a random phase.

Draw a complex array having a random phase, that is a uniform white noise on the unit disc which is constained to be odd. The complex 2D array is only defined on the half 2D plane for compatibility with FFTW r2c and c2r transforms. This unit arrays are divided by 1/(nx*ny) for FFT normalization.

Parameters:

	data_out	output random phase
	nx,ny,:	size of the corresponding image

Returns:: the random phase data_out or NULL if there is a problem

Definition at line 433 of file random_phase_noise_lib.c.

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static fftwf_complex* random_phase_with_poisson_complex_filter	(	fftwf_complex *	data_out,
		size_t	nx,
		size_t	ny
	)			`[static]`

Draw an array of complex numbers on the unit disc having a random phase, and multiply it by the Poisson complex filter.

Values are divided by 1/(nx*ny) for FFT normalization.

Parameters:

	data_out	complex output having random phase
	nx,ny,:	size of the corresponding image

Returns:: data_out or NULL if there is a problem

Definition at line 904 of file random_phase_noise_lib.c.

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float** rpn_color_different_size	(	float **	data_out_rgb,
		float **	data_in_rgb,
		size_t	nxout,
		size_t	nyout,
		size_t	nxin,
		size_t	nyin,
		float	alpha
	)

Random Phase Noise computation when the sizes of the input and the output are different.

The algorithm consists of the following three steps:

Compute the periodic component of the input image (see the function periodic_component_color) .
Extend the periodic component in a larger equivalent spot (see the function spot_extension_color).
Randomize the phase of the extended spot (see the function phase_randomization).

Below is an illustration of the result:

Random Phase Noise with size

extension: original image (left) and output RPN texture (right)"

Parameters:

	data_out_rgb	output rgb float array
	data_in_rgb	input rgb float array
	nxout,nyout	output size
	nxin,nyin	input size
	alpha	parameter for the spot extension

Returns:: data_out_rgb or NULL if an error occured

Definition at line 850 of file random_phase_noise_lib.c.

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float** rpn_color_same_size	(	float **	data_in_rgb,
		size_t	nx,
		size_t	ny
	)

Fast Random Phase Noise when the sizes of the input and the output are the same.

When the sizes of the input and the output are the same, the computation of the perdiodic component and the phase randomization can be done simultaneously in the Fourier domain. As a consequence, the algorithm makes only two calls to the FFT algorithms (instead of four for the function rpn_color_different_size).

Here is an illustration of this function :

Random Phase Noise: input image

(left) and output RPN texture (right)"

Parameters:

	data_in_rgb	input rgb float array. The input is replaced by the RPN output.
	nx,ny	array size

Returns:: data_in_rgb or NULL if an error occured

Definition at line 1013 of file random_phase_noise_lib.c.

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static float** spot_extension_color	(	float **	data_out_rgb,
		float **	data_in_rgb,
		size_t	nxout,
		size_t	nyout,
		size_t	nxin,
		size_t	nyin,
		float	alpha
	)			`[static]`

Extension of a color spot into a larger "equivalent spot".

Extend a color spot in pasting an original variance-normalized copy of the original spot and in smoothing it arround the inner frame.

Spot extension technique: the

original spot (left) is extended into a larger equivalent spot (right) by copying its periodic component in the center, normalizing its variance, and smoothing the transition at the border of the inner frame" The smoothing is done using a smooth transition function (see the function compute_transition).

Parameters:

	data_out_rgb	output rgb float array
	data_in_rgb	input rgb float array
	nxout,nyout	output size
	nxin,nyin	input size
	alpha	parameter in [0,0.5] for the smoothing function (ratio for the width of the smoothing zone)

Returns:: data_out_rgb or NULL if an error occured

Definition at line 729 of file random_phase_noise_lib.c.

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random_phase_noise_lib.c File Reference

Defines

Functions

Detailed Description

Define Documentation

Function Documentation