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transformation.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) 2018, Thibaud Briand <[email protected]>
// Copyright (C) 2015, Javier Sánchez Pérez <[email protected]>
// All rights reserved.
#include "transformation.h"
#include <math.h>
/**
*
* Function to compute the Jacobian matrix
* These parametrizations of the Jacobian are taken from the book of Zselinski
* (chapter 6 and 9)
*
*/
void jacobian
(
double *J, //computed Jacobian
int nparams, //number of parameters
int nx, //number of columns of the image
int ny //number of rows of the image
)
{
switch(nparams)
{
default: case TRANSLATION_TRANSFORM: //p=(tx, ty)
for(int i=0; i<nx*ny; i++)
{
int c=2*i*nparams;
J[c] =1.0; J[c+1]=0.0;
J[c+2]=0.0; J[c+3]=1.0;
}
break;
case EUCLIDEAN_TRANSFORM: //p=(tx, ty, theta)
for(int i=0; i<ny; i++)
for(int j=0; j<nx; j++)
{
int c=2*(i*nx+j)*nparams;
J[c] =1.0; J[c+1]=0.0; J[c+2]=-i;
J[c+3]=0.0; J[c+4]=1.0; J[c+5]= j;
}
break;
case SIMILARITY_TRANSFORM: //p=(tx, ty, a, b)
for(int i=0; i<ny; i++)
for(int j=0; j<nx; j++)
{
int c=2*(i*nx+j)*nparams;
J[c] =1.0; J[c+1]=0.0; J[c+2]=j; J[c+3]=-i;
J[c+4]=0.0; J[c+5]=1.0; J[c+6]=i; J[c+7]= j;
}
break;
case AFFINITY_TRANSFORM: //p=(tx, ty, a00, a01, a10, a11)
for(int i=0; i<ny; i++)
for(int j=0; j<nx; j++)
{
int c=2*(i*nx+j)*nparams;
J[c] =1.0;J[c+1]=0.0;J[c+2]= j;J[c+3]= i;J[c+ 4]=0.0;J[c+ 5]=0.0;
J[c+6]=0.0;J[c+7]=1.0;J[c+8]=0.0;J[c+9]=0.0;J[c+10]= j;J[c+11]= i;
}
break;
case HOMOGRAPHY_TRANSFORM: //p=(h00, h01,..., h21)
for(int i=0; i<ny; i++)
for(int j=0; j<nx; j++)
{
int c=2*(i*nx+j)*nparams;
J[c] = j; J[c+1]= i; J[c+2]=1.0; J[c+3]=0.0;
J[c+4]=0.0; J[c+5]=0.0; J[c+6]=-j*j; J[c+7]=-j*i;
J[c+8]=0.0; J[c+9] =0.0; J[c+10]= 0.0; J[c+11]= j;
J[c+12]= i; J[c+13]=1.0; J[c+14]=-j*i; J[c+15]=-i*i;
}
break;
}
}
/**
*
* Function to update the current transform with the computed increment
* x'(x;p) = x'(x;p) o x'(x;dp)^-1
*
*/
void update_transform
(
double *p, //output accumulated transform
double *dp, //computed increment
int nparams //number of parameters
)
{
switch(nparams)
{
default: case TRANSLATION_TRANSFORM: //p=(tx, ty)+++
for(int i = 0; i < nparams; i++)
p[i]-=dp[i];
break;
case EUCLIDEAN_TRANSFORM: //p=(tx, ty, tita)
{
double a=cos(dp[2]);
double b=sin(dp[2]);
double c=dp[0];
double d=dp[1];
double ap=cos(p[2]);
double bp=sin(p[2]);
double cp=p[0];
double dp=p[1];
double cost=a*ap+b*bp;
double sint=a*bp-b*ap;
p[0]=cp-bp*(b*c-a*d)-ap*(a*c+b*d);
p[1]=dp-bp*(a*c+b*d)+ap*(b*c-a*d);
p[2]=atan2(sint,cost);
}
break;
case SIMILARITY_TRANSFORM: //p=(tx, ty, a, b)
{
double a=dp[2];
double b=dp[3];
double c=dp[0];
double d=dp[1];
double det=(2*a+a*a+b*b+1);
if(det*det>1E-10)
{
double ap=p[2];
double bp=p[3];
double cp=p[0];
double dp=p[1];
p[0]=cp-bp*(-d-a*d+b*c)/det+(ap+1)*(-c-a*c-b*d)/det;
p[1]=dp+bp*(-c-a*c-b*d)/det+(ap+1)*(-d-a*d+b*c)/det;
p[2]=b*bp/det+(a+1)*(ap+1)/det-1;
p[3]=-b*(ap+1)/det+bp*(a+1)/det ;
}
}
break;
case AFFINITY_TRANSFORM: //p=(tx, ty, a00, a01, a10, a11)
{
double a=dp[2];
double b=dp[3];
double c=dp[0];
double d=dp[4];
double e=dp[5];
double f=dp[1];
double det=(a-b*d+e+a*e+1);
if(det*det>1E-10)
{
double ap=p[2];
double bp=p[3];
double cp=p[0];
double dp=p[4];
double ep=p[5];
double fp=p[1];
p[0]=cp+(-f*bp-a*f*bp+c*d*bp)/det+(ap+1)*(-c+b*f-c*e)/det;
p[1]=fp+dp*(-c+b*f-c*e)/det+(-f+c*d-a*f-f*ep-a*f*ep+d*d*ep)/det;
p[2]=((1+ap)*(1+e)-d*bp)/det-1;
p[3]=(bp+a*bp-b-b*ap)/det;
p[4]=(dp*(1+e)-d-d*ep)/det;
p[5]=(a+ep+a*ep+1-b*dp)/det-1;
}
}
break;
case HOMOGRAPHY_TRANSFORM: //p=(h00, h01,..., h21)
{
double a=dp[0];
double b=dp[1];
double c=dp[2];
double d=dp[3];
double e=dp[4];
double f=dp[5];
double g=dp[6];
double h=dp[7];
double ap=p[0];
double bp=p[1];
double cp=p[2];
double dp=p[3];
double ep=p[4];
double fp=p[5];
double gp=p[6];
double hp=p[7];
double det=f*hp+a*f*hp-c*d*hp+gp*(c-b*f+c*e)-a+b*d-e-a*e-1;
if(det*det>1E-10)
{
p[0]=((d*bp-f*g*bp)+cp*(g-d*h+g*e)+(ap+1)*(f*h-e-1))/det-1;
p[1]=(h*cp+a*h*cp-b*g*cp-bp-a*bp+c*g*bp+b-c*h+b*ap-c*h*ap)/det;
p[2]=(f*bp+a*f*bp-c*d*bp+(ap+1)*(c-b*f+c*e)+cp*(-a+b*d-e-a*e-1))/det;
p[3]=(fp*(g-d*h+g*e)+d-f*g+d*ep-f*g*ep+dp*(f*h-e-1))/det;
p[4]=(b*dp-c*h*dp+h*fp+a*h*fp-b*g*fp-a+c*g-ep-a*ep+c*g*ep-1)/det-1;
p[5]=(dp*(c-b*f+c*e)+f+a*f-c*d+f*ep+a*f*ep-c*d*ep+fp*(-a+b*d-e-a*e-1))/det;
p[6]=(d*hp-f*g*hp+g-d*h+g*e+gp*(f*h-e-1))/det;
p[7]=(h+a*h-b*g+b*gp-c*h*gp-hp-a*hp+c*g*hp)/det;
}
}
break;
}
}
/**
*
* Function to transform a 2D point (x,y) through a parametric model
*
*/
void project
(
int x, //x component of the 2D point
int y, //y component of the 2D point
double *p, //parameters of the transformation
double &xp, //x component of the transformed point
double &yp, //y component of the transformed point
int nparams //number of parameters
)
{
switch(nparams) {
default: case TRANSLATION_TRANSFORM: //p=(tx, ty)
xp=x+p[0];
yp=y+p[1];
break;
case EUCLIDEAN_TRANSFORM: //p=(tx, ty, tita)
xp=cos(p[2])*x-sin(p[2])*y+p[0];
yp=sin(p[2])*x+cos(p[2])*y+p[1];
break;
case SIMILARITY_TRANSFORM: //p=(tx, ty, a, b)
xp=(1+p[2])*x-p[3]*y+p[0];
yp=p[3]*x+(1+p[2])*y+p[1];
break;
case AFFINITY_TRANSFORM: //p=(tx, ty, a00, a01, a10, a11)
xp=(1+p[2])*x+p[3]*y+p[0];
yp=p[4]*x+(1+p[5])*y+p[1];
break;
case HOMOGRAPHY_TRANSFORM: //p=(h00, h01,..., h21)
double d=p[6]*x+p[7]*y+1;
xp=((1+p[0])*x+p[1]*y+p[2])/d;
yp=(p[3]*x+(1+p[4])*y+p[5])/d;
break;
}
}
/**
*
* Function to convert a parametric model to its matrix representation
*
*/
void params2matrix
(
double *p, //input parametric model
double *matrix, //output matrix
int nparams //number of parameters
)
{
matrix[0]=matrix[4]=matrix[8]=1;
matrix[1]=matrix[2]=matrix[3]=0;
matrix[5]=matrix[6]=matrix[7]=0;
switch(nparams) {
default: case TRANSLATION_TRANSFORM: //p=(tx, ty)
matrix[2]=p[0];
matrix[5]=p[1];
break;
case EUCLIDEAN_TRANSFORM: //p=(tx, ty, tita)
matrix[0]=cos(p[2]);
matrix[1]=-sin(p[2]);
matrix[2]=p[0];
matrix[3]=sin(p[2]);
matrix[4]=cos(p[2]);
matrix[5]=p[1];
break;
case SIMILARITY_TRANSFORM: //p=(tx, ty, a, b)
matrix[0]=1+p[2];
matrix[1]=-p[3];
matrix[2]=p[0];
matrix[3]=-matrix[1];
matrix[4]=matrix[0];
matrix[5]=p[1];
break;
case AFFINITY_TRANSFORM: //p=(tx, ty, a00, a01, a10, a11)
matrix[0]=1+p[2];
matrix[1]=p[3];
matrix[2]=p[0];
matrix[3]=p[4];
matrix[4]=1+p[5];
matrix[5]=p[1];
break;
case HOMOGRAPHY_TRANSFORM: //p=(h00, h01,..., h21)
matrix[0]=1+p[0];
matrix[1]=p[1];
matrix[2]=p[2];
matrix[3]=p[3];
matrix[4]=1+p[4];
matrix[5]=p[5];
matrix[6]=p[6];
matrix[7]=p[7];
break;
}
}