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mask.cpp
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mask.cpp
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// 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>.
//
// Copyright (C) 2017, Thibaud Briand <[email protected]>
// Copyright (C) 2015, Javier Sánchez Pérez <[email protected]>
// Copyright (C) 2014, Nelson Monzón López <[email protected]>
// All rights reserved.
#include "mask.h"
#include <math.h>
#include <stdio.h>
#include <assert.h>
/** Macro to get the number of elements in a static array */
#define NUMEL(x) (sizeof(x)/sizeof(*(x)))
/**
*
* Function to apply a 3x3 mask to an image
*
*/
void
mask3x3 (double *input, //input image
double *output, //output image
int nx, //image width
int ny, //image height
int nz, // number of color channels in the image
double *mask //mask to be applied
)
{
int nx_rgb = nx * nz;
for (int index_color = 0; index_color < nz; index_color++)
{
//apply the mask to the center body of the image
for (int i = 1; i < ny - 1; i++)
{
for (int j = 1; j < nx - 1; j++)
{
int k = (i * nx + j) * nz + index_color;
double sum = 0;
for (int l = 0; l < 3; l++)
{
for (int m = 0; m < 3; m++)
{
int p =
((i + l - 1) * nx + j + m - 1) * nz + index_color;
sum += input[p] * mask[l * 3 + m];
}
}
output[k] = sum;
}
}
//apply the mask to the first and last rows
for (int j = 1; j < nx - 1; j++)
{
int index = j * nz + index_color;
double sum = 0;
sum += input[index - nz] * (mask[0] + mask[3]);
sum += input[index] * (mask[1] + mask[4]);
sum += input[index + nz] * (mask[2] + mask[5]);
sum += input[nx_rgb + j - nz] * mask[6];
sum += input[nx_rgb + j] * mask[7];
sum += input[nx_rgb + j + nz] * mask[8];
output[j] = sum;
index = ((ny - 2) * nx + j) * nz + index_color;
sum = 0;
sum += input[index - nz] * mask[0];
sum += input[index] * mask[1];
sum += input[index + nz] * mask[2];
index = ((ny - 1) * nx + j) * nz + index_color;
sum += input[index - nz] * (mask[6] + mask[3]);
sum += input[index] * (mask[7] + mask[4]);
sum += input[index + 1] * (mask[8] + mask[5]);
output[index] = sum;
}
//apply the mask to the first and last columns
for (int i = 1; i < ny - 1; i++)
{
int index = i * nx_rgb + index_color;
double sum = 0;
int index_row = (i - 1) * nx_rgb + index_color;
sum += input[index_row] * (mask[0] + mask[1]);
sum += input[index_row + nz] * mask[2];
sum += input[index] * (mask[3] + mask[4]);
sum += input[index + nz] * mask[5];
index_row = (i + 1) * nx_rgb + index_color;
sum += input[index_row] * (mask[6] + mask[7]);
sum += input[index_row + nz] * mask[8];
output[index] = sum;
sum = 0;
sum += input[index - 2 * nz] * mask[0];
sum += input[index - nz] * (mask[1] + mask[2]);
index_row = (i + 1) * nx_rgb + index_color;
sum += input[index_row - 2 * nz] * mask[3];
sum += input[index_row - nz] * (mask[4] + mask[5]);
index_row = (i + 2) * nx_rgb + index_color;
sum += input[index_row - 2 * nz] * mask[6];
sum += input[index_row - nz] * (mask[7] + mask[8]);
output[(i * nx + nx - 1) * nz + index_color] = sum;
}
//apply the mask to the four corners
output[index_color] =
input[index_color] * (mask[0] + mask[1] + mask[3] + mask[4]) +
input[index_color + nz] * (mask[2] + mask[5]) +
input[nx_rgb + index_color] * (mask[6] + mask[7]) +
input[nx_rgb + index_color + nz] * mask[8];
output[nx_rgb - nz + index_color] =
input[(nx - 2) * nz + index_color] * (mask[0] + mask[3]) +
input[(nx - 1) * nz + index_color] * (mask[1] + mask[2] + mask[4] +
mask[5]) + input[(2 * nx -
2) * nz +
index_color] *
mask[6] + input[(2 * nx - 1) * nz + index_color] * (mask[7] +
mask[8]);
output[(ny - 1) * nx_rgb + index_color] =
input[(ny - 2) * nx_rgb + index_color] * (mask[0] + mask[1]) +
input[((ny - 2) * nx + 1) * nz + index_color] * mask[2] +
input[(ny - 1) * nx_rgb + index_color] * (mask[3] + mask[4] +
mask[6] + mask[7]) +
input[((ny - 1) * nx + 1) * nz + index_color] * (mask[5] + mask[8]);
output[(ny * nx - 1) * nz + index_color] =
input[((ny - 1) * nx - 2) * nz + index_color] * mask[0] +
input[((ny - 1) * nx - 1) * nz + index_color] * (mask[1] + mask[2]) +
input[(ny * nx - 2) * nz + index_color] * (mask[3] + mask[6]) +
input[(ny * nx - 1) * nz + index_color] * (mask[4] + mask[5] +
mask[7] + mask[8]);
}// end loop for channels information
}// end mask3x3
/**
*
* Compute the gradient with central differences
*
*/
void
gradient (double *input, //input image
double *dx, //computed x derivative
double *dy, //computed y derivative
int nx, //image width
int ny, //image height
int nz //number of color channels in the image
)
{
int nx_rgb = nx * nz;
for (int index_color = 0; index_color < nz; index_color++)
{
//gradient in the center body of the image
for (int i = 1; i < ny - 1; i++)
{
for (int j = 1; j < nx - 1; j++)
{
int k = (i * nx + j) * nz + index_color;
dx[k] = 0.5 * (input[k + nz] - input[k - nz]);
dy[k] = 0.5 * (input[k + nx_rgb] - input[k - nx_rgb]);
}
}
//gradient in the first and last rows
for (int j = 1; j < nx - 1; j++)
{
int index = j * nz + index_color;
dx[index] = 0.5 * (input[index + nz] - input[index - nz]);
dy[index] = 0.5 * (input[index + nx_rgb] - input[index]);
int k = ((ny - 1) * nx + j) * nz + index_color;
dx[k] = 0.5 * (input[k + nz] - input[k - nz]);
dy[k] = 0.5 * (input[k] - input[k - nx_rgb]);
}
//gradient in the first and last columns
for (int i = 1; i < ny - 1; i++)
{
int p = (i * nx_rgb) + index_color;
dx[p] = 0.5 * (input[p + nz] - input[p]);
dy[p] = 0.5 * (input[p + nx_rgb] - input[p - nx_rgb]);
int k = ((i + 1) * nx - 1) * nz + index_color;
dx[k] = 0.5 * (input[k] - input[k - nz]);
dy[k] = 0.5 * (input[k + nx_rgb] - input[k - nx_rgb]);
}
//calculate the gradient in the corners
dx[index_color] = 0.5 * (input[index_color + nz] - input[index_color]);
dy[index_color] =
0.5 * (input[nx_rgb + index_color] - input[index_color]);
int corner_up_right = (nx - 1) * nz + index_color;
dx[corner_up_right] =
0.5 * (input[corner_up_right] - input[corner_up_right - nz]);
dy[corner_up_right] =
0.5 * (input[(2 * nx_rgb) + index_color - nz] -
input[corner_up_right]);
int corner_down_left = ((ny - 1) * nx) * nz + index_color;
dx[corner_down_left] =
0.5 * (input[corner_down_left + nz] - input[corner_down_left]);
dy[corner_down_left] =
0.5 * (input[corner_down_left] -
input[(ny - 2) * nx_rgb + index_color]);
int corner_down_right = ny * nx_rgb - nz + index_color;
dx[corner_down_right] =
0.5 * (input[corner_down_right] - input[corner_down_right - nz]);
dy[corner_down_right] =
0.5 * (input[corner_down_right] -
input[(ny - 1) * nx_rgb - nz + index_color]);
}
}
/**
*
* Convolution with a Gaussian
*
*/
void
gaussian (
double *I, //input/output image
int xdim, //image width
int ydim, //image height
int zdim, //number of color channels in the image
double sigma, //Gaussian sigma
int bc, //boundary condition
int precision //defines the size of the window
)
{
int i, j, k;
double den = 2 * sigma * sigma;
int size = (int) (precision * sigma) + 1;
int bdx = xdim + size;
int bdy = ydim + size;
if (bc && size > xdim){
printf("GaussianSmooth: sigma too large for this bc\n");
throw 1;
}
//compute the coefficients of the 1D convolution kernel
double *B = new double[size];
for (int i = 0; i < size; i++)
B[i] = 1 / (sigma * sqrt (2.0 * 3.1415926)) * exp (-i * i / den);
double norm = 0;
//normalize the 1D convolution kernel
for (int i = 0; i < size; i++)
norm += B[i];
norm *= 2;
norm -= B[0];
for (int i = 0; i < size; i++)
B[i] /= norm;
double *R = new double[size + xdim + size];
double *T = new double[size + ydim + size];
//Loop for every channel
for(int index_color = 0; index_color < zdim; index_color++){
//convolution of each line of the input image
for (k = 0; k < ydim; k++)
{
for (i = size; i < bdx; i++)
R[i] = I[(k * xdim + i - size) * zdim + index_color];
switch (bc)
{
case 0: //Dirichlet boundary conditions
for (i = 0, j = bdx; i < size; i++, j++)
R[i] = R[j] = 0;
break;
case 1: //Reflecting boundary conditions
for (i = 0, j = bdx; i < size; i++, j++)
{
R[i] = I[(k * xdim + size - i ) * zdim + index_color];
R[j] = I[(k * xdim + xdim - i - 1) * zdim + index_color ];
}
break;
case 2: //Periodic boundary conditions
for (i = 0, j = bdx; i < size; i++, j++)
{
R[i] = I[(k * xdim + xdim - size + i) * zdim + index_color];
R[j] = I[(k * xdim + i) * zdim + index_color];
}
break;
}
for (i = size; i < bdx; i++)
{
double sum = B[0] * R[i];
for (int j = 1; j < size; j++)
sum += B[j] * (R[i - j] + R[i + j]);
I[(k * xdim + i - size) * zdim + index_color] = sum;
}
}
//convolution of each column of the input image
for (k = 0; k < xdim; k++)
{
for (i = size; i < bdy; i++)
T[i] = I[((i - size) * xdim + k) * zdim + index_color];
switch (bc)
{
case 0: // Dirichlet boundary conditions
for (i = 0, j = bdy; i < size; i++, j++)
T[i] = T[j] = 0;
break;
case 1: // Reflecting boundary conditions
for (i = 0, j = bdy; i < size; i++, j++)
{
T[i] = I[((size - i) * xdim + k) * zdim + index_color];
T[j] = I[((ydim - i - 1) * xdim + k) * zdim + index_color];
}
break;
case 2: // Periodic boundary conditions
for (i = 0, j = bdx; i < size; i++, j++)
{
T[i] = I[((ydim - size + i) * xdim + k) * zdim + index_color];
T[j] = I[(i * xdim + k) * zdim + index_color];
}
break;
}
for (i = size; i < bdy; i++)
{
double sum = B[0] * T[i];
for (j = 1; j < size; j++)
sum += B[j] * (T[i - j] + T[i + j]);
I[((i - size) * xdim + k) * zdim + index_color] = sum;
}
}
}
delete[]B;
delete[]R;
delete[]T;
}
/**
*
* Convolution of the rows of an image with a kernel
*
*/
static void
convolution_rows (
double *I, //input/output image
int xdim, //image width
int ydim, //image height
int zdim, //number of color channels in the image
double *kernel, //kernel
int kdim, //kernel length
int bc //boundary condition
)
{
int i, j, k;
// kernel is of the form [ lpadding values, center, rpadding values ]
int kcenter = (kdim - 1)/2;
int lpadding = kcenter;
int rpadding = kdim/2;
// buffer taking into account the boundary condition
int Bdim = lpadding + xdim + rpadding;
double *B = new double[Bdim];
// position of the boundaries in the buffer
int bdx = xdim + lpadding;
//Loop for every channel
for(int index_color = 0; index_color < zdim; index_color++){
//convolution of each line of the input image
for (k = 0; k < ydim; k++) {
// construct buffer for the line k
for (i = lpadding; i < bdx; i++)
B[i] = I[(k * xdim + i - lpadding) * zdim + index_color];
switch (bc)
{
case 0: //Dirichlet boundary conditions
for (i = 0; i < lpadding; i++)
B[i] = 0;
for (j = bdx; j < Bdim; j++)
B[j] = 0;
break;
case 1: //Reflecting boundary conditions (wsym)
for (i = 0; i < lpadding; i++)
B[i] = I[(k * xdim + lpadding - i ) * zdim + index_color];
for (j = bdx; j < Bdim; j++)
B[j] = I[(k * xdim + xdim + bdx - j - 2) * zdim + index_color ];
break;
case 2: //Periodic boundary conditions
for (i = 0; i < lpadding; i++)
B[i] = I[(k * xdim + xdim - lpadding + i) * zdim + index_color];
for (j = bdx; j < Bdim; j++)
B[j] = I[(k * xdim + j - bdx) * zdim + index_color];
break;
}
// convolution of the line k
for (i = lpadding; i < bdx; i++) {
double sum = 0;
for (int j = 0; j < kdim; j++)
sum += B[i-lpadding+j]*kernel[j];
// update I
I[(k * xdim + i - lpadding) * zdim + index_color] = sum;
}
}
}
delete[]B;
}
/**
*
* Convolution of the columns of an image with a kernel
*
*/
static void
convolution_columns (
double *I, //input/output image
int xdim, //image width
int ydim, //image height
int zdim, //number of color channels in the image
double *kernel, //kernel
int kdim, //kernel length
int bc //boundary condition
)
{
int i, j, k;
// kernel is of the form [ lpadding values, center, rpadding values ]
int kcenter = (kdim - 1)/2;
int lpadding = kcenter;
int rpadding = kdim/2;
// buffer taking into account the boundary condition
int Bdim = lpadding + ydim + rpadding;
double *B = new double[Bdim];
// position of the boundaries in the buffer
int bdy = ydim + lpadding;
//Loop for every channel
for(int index_color = 0; index_color < zdim; index_color++){
//convolution of each column of the input image
for (k = 0; k < xdim; k++) {
// construct buffer for the column k
for (i = lpadding; i < bdy; i++)
B[i] = I[((i - lpadding) * xdim + k) * zdim + index_color];
switch (bc)
{
case 0: //Dirichlet boundary conditions
for (i = 0; i < lpadding; i++)
B[i] = 0;
for (j = bdy; j < Bdim; j++)
B[j] = 0;
break;
case 1: //Reflecting boundary conditions
for (i = 0; i < lpadding; i++)
B[i] = I[((lpadding - i) * xdim + k ) * zdim + index_color];
for (j = bdy; j < Bdim; j++)
B[j] = I[((bdy + ydim - j - 2) * xdim + k) * zdim + index_color ];
break;
case 2: //Periodic boundary conditions
for (i = 0; i < lpadding; i++)
B[i] = I[((ydim - lpadding + i) * xdim + k) * zdim + index_color];
for (j = bdy; j < Bdim; j++)
B[j] = I[((j - bdy) * xdim + k) * zdim + index_color];
break;
}
// convolution of the line k
for (i = lpadding; i < bdy; i++) {
double sum = 0;
for (int j = 0; j < kdim; j++)
sum += B[i-lpadding+j]*kernel[j];
// update I
I[((i - lpadding) * xdim + k) * zdim + index_color] = sum;
}
}
}
delete[]B;
}
/* Definition of the gradient estimators */
//Central
static double kCentral[3] = {0.0, 1.0, 0.0};
static double dCentral[3] = {-0.5, 0.0, 0.5};
//Hypomode
static double kHypomode[2] = {0.5, 0.5};
static double dHypomode[2] = {-1 , 1};
//Farid 3x3
static double kFarid3[3] = {0.229879, 0.540242, 0.229879};
static double dFarid3[3] = {-0.455271, 0.0, 0.455271};
//Farid 5x5
static double kFarid5[5] = {0.037659, 0.249153, 0.426375, 0.249153, 0.037659};
static double dFarid5[5] = {-0.109604, -0.276691, 0, 0.276691, 0.109604};
//Gaussian sigma = 0.3
static double kGaussian3[3] = {0.003865, 0.999990, 0.003865};
static double dGaussian3[3] = {-0.707110, 0.0, 0.707110};
//Gaussian sigma = 0.6
static double kGaussian5[5] = {0.003645, 0.235160, 0.943070, 0.235160, 0.003645};
static double dGaussian5[5] = {-0.021915,-0.706770, 0, 0.706770, 0.021915};
//Store the gradient in a table
static gradientStruct gradientTable[] = {
{kCentral, dCentral, 3},
{kHypomode, dHypomode, 2},
{kFarid3, dFarid3, 3},
{kFarid5, dFarid5, 5},
{kGaussian3, dGaussian3, 3},
{kGaussian5, dGaussian5, 5}
};
/**
*
* Compute the gradient estimator
* dx = d * k^t * I
* dy = k * d^t * I
* where * denotes the convolution operator
*
*/
void
gradient_robust (double *input, //input image
double *dx, //computed x derivative
double *dy, //computed y derivative
int nx, //image width
int ny, //image height
int nz, //number of color channels in the image
int gradientType //type of gradient
)
{
//kernel definition
assert(gradientType < (int) NUMEL(gradientTable));
double *kernel = gradientTable[gradientType].k;
double *differentiator = gradientTable[gradientType].d;
int nkernel = gradientTable[gradientType].size;
int bc = 1;
//initialization
for(int i = 0; i < nx*ny*nz; i++)
dx[i] = dy[i] = input[i];
//x derivative computation
//convolution of each column (k^t * I)
convolution_columns(dx, nx, ny , nz, kernel, nkernel, bc);
//convolution of each line (d * (k^t * I))
convolution_rows(dx, nx, ny , nz, differentiator, nkernel, bc);
//y derivative computation
//convolution of each column (d^t * I)
convolution_columns(dy, nx, ny , nz, differentiator, nkernel, bc);
//convolution of each line (k * (d^t * dx))
convolution_rows(dy, nx, ny , nz, kernel, nkernel, bc);
}
/**
*
* Prefiltering of an image
*
*/
void
prefiltering_robust (
double *I, //input/output image
int nx, //image width
int ny, //image height
int nz, //number of color channels in the image
int gradientType //type of gradient
)
{
// kernel definition
assert(gradientType < (int) NUMEL(gradientTable));
double *kernel = gradientTable[gradientType].k;
int nkernel = gradientTable[gradientType].size;
int bc = 1;
//convolution of each line of the input image
convolution_rows(I, nx, ny , nz, kernel, nkernel, bc);
//convolution of each column of the input image
convolution_columns(I, nx, ny , nz, kernel, nkernel, bc);
}