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opencv/modules/features2d/src/kaze/nldiffusion_functions.cpp

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//=============================================================================
//
// nldiffusion_functions.cpp
// Author: Pablo F. Alcantarilla
// Institution: University d'Auvergne
// Address: Clermont Ferrand, France
// Date: 27/12/2011
// Email: pablofdezalc@gmail.com
//
// KAZE Features Copyright 2012, Pablo F. Alcantarilla
// All Rights Reserved
// See LICENSE for the license information
//=============================================================================
/**
* @file nldiffusion_functions.cpp
* @brief Functions for non-linear diffusion applications:
* 2D Gaussian Derivatives
* Perona and Malik conductivity equations
* Perona and Malik evolution
* @date Dec 27, 2011
* @author Pablo F. Alcantarilla
*/
#include "../precomp.hpp"
#include "nldiffusion_functions.h"
#include <iostream>
// Namespaces
/* ************************************************************************* */
namespace cv
{
using namespace std;
/* ************************************************************************* */
/**
* @brief This function smoothes an image with a Gaussian kernel
* @param src Input image
* @param dst Output image
* @param ksize_x Kernel size in X-direction (horizontal)
* @param ksize_y Kernel size in Y-direction (vertical)
* @param sigma Kernel standard deviation
*/
void gaussian_2D_convolution(const cv::Mat& src, cv::Mat& dst, int ksize_x, int ksize_y, float sigma) {
int ksize_x_ = 0, ksize_y_ = 0;
// Compute an appropriate kernel size according to the specified sigma
if (sigma > ksize_x || sigma > ksize_y || ksize_x == 0 || ksize_y == 0) {
ksize_x_ = (int)ceil(2.0f*(1.0f + (sigma - 0.8f) / (0.3f)));
ksize_y_ = ksize_x_;
}
// The kernel size must be and odd number
if ((ksize_x_ % 2) == 0) {
ksize_x_ += 1;
}
if ((ksize_y_ % 2) == 0) {
ksize_y_ += 1;
}
// Perform the Gaussian Smoothing with border replication
GaussianBlur(src, dst, Size(ksize_x_, ksize_y_), sigma, sigma, BORDER_REPLICATE);
}
/* ************************************************************************* */
/**
* @brief This function computes image derivatives with Scharr kernel
* @param src Input image
* @param dst Output image
* @param xorder Derivative order in X-direction (horizontal)
* @param yorder Derivative order in Y-direction (vertical)
* @note Scharr operator approximates better rotation invariance than
* other stencils such as Sobel. See Weickert and Scharr,
* A Scheme for Coherence-Enhancing Diffusion Filtering with Optimized Rotation Invariance,
* Journal of Visual Communication and Image Representation 2002
*/
void image_derivatives_scharr(const cv::Mat& src, cv::Mat& dst, int xorder, int yorder) {
Scharr(src, dst, CV_32F, xorder, yorder, 1.0, 0, BORDER_DEFAULT);
}
/* ************************************************************************* */
/**
* @brief This function computes the Perona and Malik conductivity coefficient g1
* g1 = exp(-|dL|^2/k^2)
* @param Lx First order image derivative in X-direction (horizontal)
* @param Ly First order image derivative in Y-direction (vertical)
* @param dst Output image
* @param k Contrast factor parameter
*/
void pm_g1(const cv::Mat& Lx, const cv::Mat& Ly, cv::Mat& dst, float k) {
Size sz = Lx.size();
float inv_k = 1.0f / (k*k);
for (int y = 0; y < sz.height; y++) {
const float* Lx_row = Lx.ptr<float>(y);
const float* Ly_row = Ly.ptr<float>(y);
float* dst_row = dst.ptr<float>(y);
for (int x = 0; x < sz.width; x++) {
dst_row[x] = (-inv_k*(Lx_row[x]*Lx_row[x] + Ly_row[x]*Ly_row[x]));
}
}
exp(dst, dst);
}
/* ************************************************************************* */
/**
* @brief This function computes the Perona and Malik conductivity coefficient g2
* g2 = 1 / (1 + dL^2 / k^2)
* @param Lx First order image derivative in X-direction (horizontal)
* @param Ly First order image derivative in Y-direction (vertical)
* @param dst Output image
* @param k Contrast factor parameter
*/
void pm_g2(const cv::Mat &Lx, const cv::Mat& Ly, cv::Mat& dst, float k) {
Size sz = Lx.size();
dst.create(sz, Lx.type());
float k2inv = 1.0f / (k * k);
for(int y = 0; y < sz.height; y++) {
const float *Lx_row = Lx.ptr<float>(y);
const float *Ly_row = Ly.ptr<float>(y);
float* dst_row = dst.ptr<float>(y);
for(int x = 0; x < sz.width; x++) {
dst_row[x] = 1.0f / (1.0f + ((Lx_row[x] * Lx_row[x] + Ly_row[x] * Ly_row[x]) * k2inv));
}
}
}
/* ************************************************************************* */
/**
* @brief This function computes Weickert conductivity coefficient gw
* @param Lx First order image derivative in X-direction (horizontal)
* @param Ly First order image derivative in Y-direction (vertical)
* @param dst Output image
* @param k Contrast factor parameter
* @note For more information check the following paper: J. Weickert
* Applications of nonlinear diffusion in image processing and computer vision,
* Proceedings of Algorithmy 2000
*/
void weickert_diffusivity(const cv::Mat& Lx, const cv::Mat& Ly, cv::Mat& dst, float k) {
Size sz = Lx.size();
float inv_k = 1.0f / (k*k);
for (int y = 0; y < sz.height; y++) {
const float* Lx_row = Lx.ptr<float>(y);
const float* Ly_row = Ly.ptr<float>(y);
float* dst_row = dst.ptr<float>(y);
for (int x = 0; x < sz.width; x++) {
float dL = inv_k*(Lx_row[x]*Lx_row[x] + Ly_row[x]*Ly_row[x]);
dst_row[x] = -3.315f/(dL*dL*dL*dL);
}
}
exp(dst, dst);
dst = 1.0 - dst;
}
/* ************************************************************************* */
/**
* @brief This function computes Charbonnier conductivity coefficient gc
* gc = 1 / sqrt(1 + dL^2 / k^2)
* @param Lx First order image derivative in X-direction (horizontal)
* @param Ly First order image derivative in Y-direction (vertical)
* @param dst Output image
* @param k Contrast factor parameter
* @note For more information check the following paper: J. Weickert
* Applications of nonlinear diffusion in image processing and computer vision,
* Proceedings of Algorithmy 2000
*/
void charbonnier_diffusivity(const cv::Mat& Lx, const cv::Mat& Ly, cv::Mat& dst, float k) {
Size sz = Lx.size();
float inv_k = 1.0f / (k*k);
for (int y = 0; y < sz.height; y++) {
const float* Lx_row = Lx.ptr<float>(y);
const float* Ly_row = Ly.ptr<float>(y);
float* dst_row = dst.ptr<float>(y);
for (int x = 0; x < sz.width; x++) {
float den = sqrt(1.0f+inv_k*(Lx_row[x]*Lx_row[x] + Ly_row[x]*Ly_row[x]));
dst_row[x] = 1.0f / den;
}
}
}
/* ************************************************************************* */
/**
* @brief This function computes a good empirical value for the k contrast factor
* given an input image, the percentile (0-1), the gradient scale and the number of
* bins in the histogram
* @param img Input image
* @param perc Percentile of the image gradient histogram (0-1)
* @param gscale Scale for computing the image gradient histogram
* @param nbins Number of histogram bins
* @param ksize_x Kernel size in X-direction (horizontal) for the Gaussian smoothing kernel
* @param ksize_y Kernel size in Y-direction (vertical) for the Gaussian smoothing kernel
* @return k contrast factor
*/
float compute_k_percentile(const cv::Mat& img, float perc, float gscale, int nbins, int ksize_x, int ksize_y) {
int nbin = 0, nelements = 0, nthreshold = 0, k = 0;
float kperc = 0.0, modg = 0.0;
float npoints = 0.0;
float hmax = 0.0;
// Create the array for the histogram
std::vector<int> hist(nbins, 0);
// Create the matrices
Mat gaussian = Mat::zeros(img.rows, img.cols, CV_32F);
Mat Lx = Mat::zeros(img.rows, img.cols, CV_32F);
Mat Ly = Mat::zeros(img.rows, img.cols, CV_32F);
// Perform the Gaussian convolution
gaussian_2D_convolution(img, gaussian, ksize_x, ksize_y, gscale);
// Compute the Gaussian derivatives Lx and Ly
Scharr(gaussian, Lx, CV_32F, 1, 0, 1, 0, cv::BORDER_DEFAULT);
Scharr(gaussian, Ly, CV_32F, 0, 1, 1, 0, cv::BORDER_DEFAULT);
// Skip the borders for computing the histogram
for (int i = 1; i < gaussian.rows - 1; i++) {
const float *lx = Lx.ptr<float>(i);
const float *ly = Ly.ptr<float>(i);
for (int j = 1; j < gaussian.cols - 1; j++) {
modg = lx[j]*lx[j] + ly[j]*ly[j];
// Get the maximum
if (modg > hmax) {
hmax = modg;
}
}
}
hmax = sqrt(hmax);
// Skip the borders for computing the histogram
for (int i = 1; i < gaussian.rows - 1; i++) {
const float *lx = Lx.ptr<float>(i);
const float *ly = Ly.ptr<float>(i);
for (int j = 1; j < gaussian.cols - 1; j++) {
modg = lx[j]*lx[j] + ly[j]*ly[j];
// Find the correspondent bin
if (modg != 0.0) {
nbin = (int)floor(nbins*(sqrt(modg) / hmax));
if (nbin == nbins) {
nbin--;
}
hist[nbin]++;
npoints++;
}
}
}
// Now find the perc of the histogram percentile
nthreshold = (int)(npoints*perc);
for (k = 0; nelements < nthreshold && k < nbins; k++) {
nelements = nelements + hist[k];
}
if (nelements < nthreshold) {
kperc = 0.03f;
}
else {
kperc = hmax*((float)(k) / (float)nbins);
}
return kperc;
}
/* ************************************************************************* */
/**
* @brief This function computes Scharr image derivatives
* @param src Input image
* @param dst Output image
* @param xorder Derivative order in X-direction (horizontal)
* @param yorder Derivative order in Y-direction (vertical)
* @param scale Scale factor for the derivative size
*/
void compute_scharr_derivatives(const cv::Mat& src, cv::Mat& dst, int xorder, int yorder, int scale) {
Mat kx, ky;
compute_derivative_kernels(kx, ky, xorder, yorder, scale);
sepFilter2D(src, dst, CV_32F, kx, ky);
}
/* ************************************************************************* */
/**
* @brief Compute derivative kernels for sizes different than 3
* @param _kx Horizontal kernel ues
* @param _ky Vertical kernel values
* @param dx Derivative order in X-direction (horizontal)
* @param dy Derivative order in Y-direction (vertical)
* @param scale_ Scale factor or derivative size
*/
void compute_derivative_kernels(cv::OutputArray _kx, cv::OutputArray _ky, int dx, int dy, int scale) {
int ksize = 3 + 2 * (scale - 1);
// The standard Scharr kernel
if (scale == 1) {
getDerivKernels(_kx, _ky, dx, dy, 0, true, CV_32F);
return;
}
_kx.create(ksize, 1, CV_32F, -1, true);
_ky.create(ksize, 1, CV_32F, -1, true);
Mat kx = _kx.getMat();
Mat ky = _ky.getMat();
float w = 10.0f / 3.0f;
float norm = 1.0f / (2.0f*scale*(w + 2.0f));
for (int k = 0; k < 2; k++) {
Mat* kernel = k == 0 ? &kx : &ky;
int order = k == 0 ? dx : dy;
std::vector<float> kerI(ksize, 0.0f);
if (order == 0) {
kerI[0] = norm, kerI[ksize / 2] = w*norm, kerI[ksize - 1] = norm;
}
else if (order == 1) {
kerI[0] = -1, kerI[ksize / 2] = 0, kerI[ksize - 1] = 1;
}
Mat temp(kernel->rows, kernel->cols, CV_32F, &kerI[0]);
temp.copyTo(*kernel);
}
}
class Nld_Step_Scalar_Invoker : public cv::ParallelLoopBody
{
public:
Nld_Step_Scalar_Invoker(cv::Mat& Ld, const cv::Mat& c, cv::Mat& Lstep, float _stepsize)
: _Ld(&Ld)
, _c(&c)
, _Lstep(&Lstep)
, stepsize(_stepsize)
{
}
virtual ~Nld_Step_Scalar_Invoker()
{
}
void operator()(const cv::Range& range) const
{
cv::Mat& Ld = *_Ld;
const cv::Mat& c = *_c;
cv::Mat& Lstep = *_Lstep;
for (int i = range.start; i < range.end; i++)
{
const float *c_prev = c.ptr<float>(i - 1);
const float *c_curr = c.ptr<float>(i);
const float *c_next = c.ptr<float>(i + 1);
const float *ld_prev = Ld.ptr<float>(i - 1);
const float *ld_curr = Ld.ptr<float>(i);
const float *ld_next = Ld.ptr<float>(i + 1);
float *dst = Lstep.ptr<float>(i);
for (int j = 1; j < Lstep.cols - 1; j++)
{
float xpos = (c_curr[j] + c_curr[j+1])*(ld_curr[j+1] - ld_curr[j]);
float xneg = (c_curr[j-1] + c_curr[j]) *(ld_curr[j] - ld_curr[j-1]);
float ypos = (c_curr[j] + c_next[j]) *(ld_next[j] - ld_curr[j]);
float yneg = (c_prev[j] + c_curr[j]) *(ld_curr[j] - ld_prev[j]);
dst[j] = 0.5f*stepsize*(xpos - xneg + ypos - yneg);
}
}
}
private:
cv::Mat * _Ld;
const cv::Mat * _c;
cv::Mat * _Lstep;
float stepsize;
};
/* ************************************************************************* */
/**
* @brief This function performs a scalar non-linear diffusion step
* @param Ld2 Output image in the evolution
* @param c Conductivity image
* @param Lstep Previous image in the evolution
* @param stepsize The step size in time units
* @note Forward Euler Scheme 3x3 stencil
* The function c is a scalar value that depends on the gradient norm
* dL_by_ds = d(c dL_by_dx)_by_dx + d(c dL_by_dy)_by_dy
*/
void nld_step_scalar(cv::Mat& Ld, const cv::Mat& c, cv::Mat& Lstep, float stepsize) {
cv::parallel_for_(cv::Range(1, Lstep.rows - 1), Nld_Step_Scalar_Invoker(Ld, c, Lstep, stepsize), (double)Ld.total()/(1 << 16));
float xneg, xpos, yneg, ypos;
float* dst = Lstep.ptr<float>(0);
const float* cprv = NULL;
const float* ccur = c.ptr<float>(0);
const float* cnxt = c.ptr<float>(1);
const float* ldprv = NULL;
const float* ldcur = Ld.ptr<float>(0);
const float* ldnxt = Ld.ptr<float>(1);
for (int j = 1; j < Lstep.cols - 1; j++) {
xpos = (ccur[j] + ccur[j+1]) * (ldcur[j+1] - ldcur[j]);
xneg = (ccur[j-1] + ccur[j]) * (ldcur[j] - ldcur[j-1]);
ypos = (ccur[j] + cnxt[j]) * (ldnxt[j] - ldcur[j]);
dst[j] = 0.5f*stepsize*(xpos - xneg + ypos);
}
dst = Lstep.ptr<float>(Lstep.rows - 1);
ccur = c.ptr<float>(Lstep.rows - 1);
cprv = c.ptr<float>(Lstep.rows - 2);
ldcur = Ld.ptr<float>(Lstep.rows - 1);
ldprv = Ld.ptr<float>(Lstep.rows - 2);
for (int j = 1; j < Lstep.cols - 1; j++) {
xpos = (ccur[j] + ccur[j+1]) * (ldcur[j+1] - ldcur[j]);
xneg = (ccur[j-1] + ccur[j]) * (ldcur[j] - ldcur[j-1]);
yneg = (cprv[j] + ccur[j]) * (ldcur[j] - ldprv[j]);
dst[j] = 0.5f*stepsize*(xpos - xneg - yneg);
}
ccur = c.ptr<float>(1);
ldcur = Ld.ptr<float>(1);
cprv = c.ptr<float>(0);
ldprv = Ld.ptr<float>(0);
int r0 = Lstep.cols - 1;
int r1 = Lstep.cols - 2;
for (int i = 1; i < Lstep.rows - 1; i++) {
cnxt = c.ptr<float>(i + 1);
ldnxt = Ld.ptr<float>(i + 1);
dst = Lstep.ptr<float>(i);
xpos = (ccur[0] + ccur[1]) * (ldcur[1] - ldcur[0]);
ypos = (ccur[0] + cnxt[0]) * (ldnxt[0] - ldcur[0]);
yneg = (cprv[0] + ccur[0]) * (ldcur[0] - ldprv[0]);
dst[0] = 0.5f*stepsize*(xpos + ypos - yneg);
xneg = (ccur[r1] + ccur[r0]) * (ldcur[r0] - ldcur[r1]);
ypos = (ccur[r0] + cnxt[r0]) * (ldnxt[r0] - ldcur[r0]);
yneg = (cprv[r0] + ccur[r0]) * (ldcur[r0] - ldprv[r0]);
dst[r0] = 0.5f*stepsize*(-xneg + ypos - yneg);
cprv = ccur;
ccur = cnxt;
ldprv = ldcur;
ldcur = ldnxt;
}
Ld += Lstep;
}
/* ************************************************************************* */
/**
* @brief This function downsamples the input image using OpenCV resize
* @param img Input image to be downsampled
* @param dst Output image with half of the resolution of the input image
*/
void halfsample_image(const cv::Mat& src, cv::Mat& dst) {
// Make sure the destination image is of the right size
CV_Assert(src.cols / 2 == dst.cols);
CV_Assert(src.rows / 2 == dst.rows);
resize(src, dst, dst.size(), 0, 0, cv::INTER_AREA);
}
/* ************************************************************************* */
/**
* @brief This function checks if a given pixel is a maximum in a local neighbourhood
* @param img Input image where we will perform the maximum search
* @param dsize Half size of the neighbourhood
* @param value Response value at (x,y) position
* @param row Image row coordinate
* @param col Image column coordinate
* @param same_img Flag to indicate if the image value at (x,y) is in the input image
* @return 1->is maximum, 0->otherwise
*/
bool check_maximum_neighbourhood(const cv::Mat& img, int dsize, float value, int row, int col, bool same_img) {
bool response = true;
for (int i = row - dsize; i <= row + dsize; i++) {
for (int j = col - dsize; j <= col + dsize; j++) {
if (i >= 0 && i < img.rows && j >= 0 && j < img.cols) {
if (same_img == true) {
if (i != row || j != col) {
if ((*(img.ptr<float>(i)+j)) > value) {
response = false;
return response;
}
}
}
else {
if ((*(img.ptr<float>(i)+j)) > value) {
response = false;
return response;
}
}
}
}
}
return response;
}
}
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