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posest.c
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posest.c
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/////////////////////////////////////////////////////////////////////////////////
//
// Non-linear calibrated camera pose estimation from 3D - 2D correspondences
// Copyright (C) 2011-13 Manolis Lourakis (lourakis **at** ics.forth.gr)
// Institute of Computer Science, Foundation for Research & Technology - Hellas
// Heraklion, Crete, Greece.
//
/////////////////////////////////////////////////////////////////////////////////
#include <stdio.h>
#include <stdlib.h>
#include <malloc.h>
#include <string.h>
#include <math.h>
#include <float.h>
#include "sam.h"
#include "compiler.h"
#include "util.h"
#include "posest.h"
#include "p3p.h"
#include "planep4p.h"
//#include "epnp.h"
#include "p4pf.h"
#include "poseproj.h"
#include "lqs.h"
#include "ransac.h"
#include "prosac.h"
#include "./levmar/levmar.h"
#include "./levmar/mestimators.h"
#include "./mlsl/mlsl.h"
#define USE_ROBUST_LM 1// enable robustified L-M?
#define USE_INPLACE_REFN 1 // enable in-place parameterization for refinement
#define USE_LQS_FIT 0 // use LQS (LMedS) if 1
#define USE_RANSAC_FIT 1 // use RANSAC if 1
#define USE_MLESAC_FIT 0 // use MLESAC if 1
#define USE_PROSAC_FIT 0 // use PROSAC if 1; ensure that sorting of matches is on in matchSIFT.c
#if USE_LQS_FIT + USE_RANSAC_FIT + USE_MLESAC_FIT + USE_PROSAC_FIT != 1
#error Exactly one of the USE_XXX_FIT macros should be defined as 1!
#endif
#define RANSAC_OUTL_THRESH 4.0 // relevant to RANSAC/PROSAC only
//#define USE_BUCKETS // CHECKME
/* minimal number of 2D-3D matches, selects the PNP algorithm to be used */
//#define NUM_PNPMATCHES 3 // P3P
#define NUM_PNPMATCHES 4 // P4P, 4th point used for verification of P3P results
//#define NUM_PNPMATCHES 6 // EPnP
/* minimal number of 2D-3D matches for the P4Pf algorithm */
#define NUM_P4PFMATCHES 4
#define MIN_TRIANG_AREA 200.0 // min allowable area for image points in P3P (pixels)
#define SQR(x) ((x)*(x))
/***** robust nonlinear estimation of rotation and translation, intrinsics assumed known *****/
/* variables used by various estimation routines */
struct RTdata {
double *K; // intrinsics
struct p3p_calib_params cal; // intrinsics as required by p3p
double (*pts2D)[2], (*pts3D)[3];
int *inliersidx, numInliers;
};
/* compute the rotation vector corresponding to a rotation matrix; see A8 in Horn's paper
* Similar to sam_rotmat2vec() with the addition of a return code.
*
* returns 0 if successful, 1 otherwise
*/
#define _CLAMP(a, b, x) ( ((x)<=(a))? (a) : (((x)<=(b))? (x) : (b)) )
static int rotmat2rodr(double R[9], double rv[3])
{
register int i;
int maxpos=-1; /* -Wall */
double q[4], tmp[4], mag, s, th;
/* convert to quaternion */
/* find the maximum of the 4 quantities */
tmp[0]=1.0 + R[0] + R[4] + R[8];
tmp[1]=1.0 + R[0] - R[4] - R[8];
tmp[2]=1.0 - R[0] + R[4] - R[8];
tmp[3]=1.0 - R[0] - R[4] + R[8];
for(i=0, mag=-1.0; i<4; i++)
if(tmp[i]>mag){
mag=tmp[i];
maxpos=i;
}
switch(maxpos){
case 0:
q[0]=sqrt(tmp[0])*0.5;
q[1]=(R[7] - R[5])/(4.0*q[0]);
q[2]=(R[2] - R[6])/(4.0*q[0]);
q[3]=(R[3] - R[1])/(4.0*q[0]);
break;
case 1:
q[1]=sqrt(tmp[1])*0.5;
q[0]=(R[7] - R[5])/(4.0*q[1]);
q[2]=(R[3] + R[1])/(4.0*q[1]);
q[3]=(R[2] + R[6])/(4.0*q[1]);
break;
case 2:
q[2]=sqrt(tmp[2])*0.5;
q[0]=(R[2] - R[6])/(4.0*q[2]);
q[1]=(R[3] + R[1])/(4.0*q[2]);
q[3]=(R[7] + R[5])/(4.0*q[2]);
break;
case 3:
q[3]=sqrt(tmp[3])*0.5;
q[0]=(R[3] - R[1])/(4.0*q[3]);
q[1]=(R[2] + R[6])/(4.0*q[3]);
q[2]=(R[7] + R[5])/(4.0*q[3]);
break;
default: /* should not happen */
fprintf(stderr, "Internal error in rotmat2rodr()\nR:\n");
fprintf(stderr, "%g %g %g\n", R[0], R[1], R[2]);
fprintf(stderr, "%g %g %g\n", R[3], R[4], R[5]);
fprintf(stderr, "%g %g %g\n", R[6], R[7], R[8]);
return 1;
//exit(1);
}
/* enforce unit length */
mag=q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3];
if(mag!=1.0){
mag=1.0/sqrt(mag);
q[0]*=mag; q[1]*=mag; q[2]*=mag; q[3]*=mag;
}
th=acos(_CLAMP(-1.0, 1.0, q[0]));
s=sin(th);
th=2.0*th;
if(fabs(s)>1E-08){
th/=s;
rv[0]=q[1]*th;
rv[1]=q[2]*th;
rv[2]=q[3]*th;
}
else{ // s close to zero, axis direction unimportant
rv[0]=th;
rv[1]=rv[2]=0.0;
}
return 0;
}
#undef _CLAMP
/* compute the rotation matrix corresponding to a rotation vector.
* Code generated by maple's codegen package and minimal editing (rodrigues.mpl)
*/
static void rvec2rotmat(double r[3], double R[9])
{
double t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t14, t16, t17, t18, t20, t22, t24, t27, t31, t33;
t1 = r[0]*r[0];
t2 = r[1]*r[1];
t3 = r[2]*r[2];
t4 = t1+t2+t3;
if(t4<=1E-14){ // zero, R=I
R[0]=R[4]=R[8]=1.0;
R[1]=R[2]=R[3]=R[5]=R[6]=R[7]=0.0;
return;
}
t5 = sqrt(t4);
#ifdef _MSC_VER
__asm {
fld QWORD PTR [t5]
fsincos
fstp QWORD PTR [t6] ; cosine
fstp QWORD PTR [t14] ; sine
}
#else
SINCOS(t5, &t14, &t6);
//t6 = cos(t5);
//t14 = sin(t5);
#endif
t7 = 1.0-t6;
t8 = 1/t4;
t9 = t8*t3;
t10 = t8*t2;
t16 = t14/t5;
t17 = t16*r[2];
t18 = t7*t8;
t20 = t18*r[1]*r[0];
t22 = t16*r[1];
t24 = t18*r[2]*r[0];
t27 = t8*t1;
t31 = t16*r[0];
t33 = t18*r[2]*r[1];
R[0] = 1.0+t7*(-t9-t10);
R[1] = -t17+t20;
R[2] = t22+t24;
R[3] = t17+t20;
R[4] = 1.0+t7*(-t9-t27);
R[5] = -t31+t33;
R[6] = -t22+t24;
R[7] = t31+t33;
R[8] = 1.0+t7*(-t10-t27);
}
/* P = K [R t] */
void posest_PfromKRt(double P[NUM_PPARAMS], double K[9], double rt[NUM_RTPARAMS])
{
register int j;
double R[9], *t=rt+3;
rvec2rotmat(rt, R);
/* compute the j-th row of K*[R t] */
for(j=0; j<3; ++j){
P[j]=K[0]*R[j] + K[1]*R[3+j] + K[2]*R[6+j];
P[3]=K[0]*t[0] + K[1]*t[1] + K[2]*t[2];
/* K[3] assumed zero */
P[4+j]=K[4]*R[3+j] + K[5]*R[6+j];
P[7]= K[4]*t[1] + K[5]*t[2];
/* K[6], K[7] assumed zero */
P[8+j]=K[8]*R[6+j];
P[11]= K[8]*t[2];
}
}
/* triangle area, see http://mathworld.wolfram.com/TriangleArea.html */
#define _TRIANGLE_AREA(pt1, pt2, pt3)\
fabs(0.5*(-(pt2)[0]*(pt1)[1] + (pt3)[0]*(pt1)[1] +\
(pt1)[0]*(pt2)[1] - (pt3)[0]*(pt2)[1] -\
(pt1)[0]*(pt3)[1] + (pt2)[0]*(pt3)[1]))
#define _CROSSPROD(v, x, y){ (v)[0]=(x)[1]*(y)[2] - (x)[2]*(y)[1]; (v)[1]=(x)[2]*(y)[0] - (x)[0]*(y)[2]; (v)[2]=(x)[0]*(y)[1] - (x)[1]*(y)[0]; }
#define _SAME_POINT(p1, p2) ( ( (p1)[0]==(p2)[0] ) && ( (p1)[1]==(p2)[1] ) )
/* estimate "point" pose P=K[R t] s.t. m=P*M, with m, M specified by ptsidx */
static int estP3PPose(double *rt, int npts, int *ptsidx, void *adata)
{
int nposes;
struct RTdata *dat=(struct RTdata *)adata;
double (*pts2D)[2]=dat->pts2D, (*pts3D)[3]=dat->pts3D;
double *m0, *m1, *m2, *M0, *M1, *M2;
double m[NUM_PNPMATCHES][2], M[NUM_PNPMATCHES][3];
//if(npts<NUM_PNPMATCHES) return 0; // not enough points
m0=pts2D[ptsidx[0]]; M0=pts3D[ptsidx[0]];
m1=pts2D[ptsidx[1]]; M1=pts3D[ptsidx[1]];
m2=pts2D[ptsidx[2]]; M2=pts3D[ptsidx[2]];
/* area check; note that this also enforces non-collinearity */
#if NUM_PNPMATCHES<=4
if(_TRIANGLE_AREA(m0, m1, m2)<MIN_TRIANG_AREA) return 0; // points not sufficiently far apart
#endif
#if 0 // next check only applies to non 1-1 matches
if(_SAME_POINT(m0, m1) || _SAME_POINT(m0, m2) || _SAME_POINT(m1, m2)) return 0; // not unique points
#endif
m[0][0]=m0[0]; m[0][1]=m0[1];
m[1][0]=m1[0]; m[1][1]=m1[1];
m[2][0]=m2[0]; m[2][1]=m2[1];
M[0][0]=M0[0]; M[0][1]=M0[1]; M[0][2]=M0[2];
M[1][0]=M1[0]; M[1][1]=M1[1]; M[1][2]=M1[2];
M[2][0]=M2[0]; M[2][1]=M2[1]; M[2][2]=M2[2];
#if NUM_PNPMATCHES==3 // up to 4 solutions
{
double R[4][3][3], t[4][3], *prt;
register int i, j;
/* solve P3P */
/* only the first 3 lines of m, M used in the following */
nposes=p3p_solve3(&(dat->cal), m, M, R, t); // Grunert's solution
//nposes=p3p_Kneip(&(dat->cal), m, M, R, t); // Kneip's solution
for(i=j=0; i<nposes; ++i){
prt=rt+j*NUM_RTPARAMS;
if(!rotmat2rodr((double *)R[i], prt)){
prt[3]=t[i][0];
prt[4]=t[i][1];
prt[5]=t[i][2];
++j;
}
}
nposes=j;
}
#elif NUM_PNPMATCHES==4 // P4P, single solution
{
double *rv, *t, R[3][3];
double *m3, *M3;
int ra, rb;
double u[3], v[3], plnorm[3];
u[0]=M1[0]-M0[0]; u[1]=M1[1]-M0[1]; u[2]=M1[2]-M0[2]; // M1-M0
v[0]=M2[0]-M0[0]; v[1]=M2[1]-M0[1]; v[2]=M2[2]-M0[2]; // M2-M0
_CROSSPROD(plnorm, u, v); // normal to the plane of M0, M1, M2
rv=rt; t=rt+3;
m3=pts2D[ptsidx[3]]; M3=pts3D[ptsidx[3]];
/* 4th line of m, M */
m[3][0]=m3[0]; m[3][1]=m3[1];
M[3][0]=M3[0]; M[3][1]=M3[1]; M[3][2]=M3[2];
/* solve P4P */
# if 1
ra=p3p_solve4_2Derr(&(dat->cal), m, M, R, t);
rb=p3p_solve4_3Derr(&(dat->cal), m, M, plnorm, R, t);
nposes=(ra && ra==rb);
/*
// solve with Ansar & Daniilidis
for(i=0; i<4; ++i){
m[i][0] = dat->cal.inv_fx * m[i][0] - dat->cal.s_fxfy * m[i][1] + dat->cal.scy_cxfy_fxfy;
m[i][1] = dat->cal.inv_fy * m[i][1] - dat->cal.cy_fy;
}
ra=ad_estPose(m, M, 4, R[0], t);
nposes=(ra==0);
*/
# else // differentiate between coplanar/non-coplanar point quadruples
{
double mag1, th;
const double tol=(7.0/180.0)*M_PI; // tolerance for an angle to be considered right
/* normalize plane normal and M3-M0 */
mag1=plnorm[0]*plnorm[0] + plnorm[1]*plnorm[1] + plnorm[2]*plnorm[2];
if(mag1< 1E-15) return 0; // points are collinear
mag1=1.0/sqrt(mag1);
plnorm[0]*=mag1; plnorm[1]*=mag1; plnorm[2]*=mag1;
u[0]=M3[0]-M0[0]; u[1]=M3[1]-M0[1]; u[2]=M3[2]-M0[2];
mag1=1.0/sqrt(u[0]*u[0] + u[1]*u[1] + u[2]*u[2]);
u[0]*=mag1; u[1]*=mag1; u[2]*=mag1;
/* angle between plane normal and u */
th=acos(plnorm[0]*u[0] + plnorm[1]*u[1] + plnorm[2]*u[2]);
if(fabs(M_PI_2-th)<=tol){ // th close to 90 degrees
//nposes=coplanarP4P_FB(&(dat->cal), m, M, R, t);
nposes=coplanarP4P_Zhang(&(dat->cal), m, M, R, t);
}else{
ra=p3p_solve4_2Derr(&(dat->cal), m, M, R, t);
rb=p3p_solve4_3Derr(&(dat->cal), m, M, plnorm, R, t);
nposes=(ra && ra==rb);
}
}
# endif
if(nposes)
nposes=!(rotmat2rodr((double *)R, rv));
}
#else // NUM_PNPMATCHES>4, single solution with EPnP
{
double *rv, *t, R[9];
register int i;
rv=rt; t=rt+3;
for(i=0; i<NUM_PNPMATCHES; ++i){
m0=pts2D[ptsidx[i]]; M0=pts3D[ptsidx[i]];
/* i-th line of m, M */
m[i][0]=m0[0]; m[i][1]=m0[1];
M[i][0]=M0[0]; M[i][1]=M0[1]; M[i][2]=M0[2];
/* remove effect of intrinsics */
m[i][0] = dat->cal.inv_fx * m[i][0] - dat->cal.s_fxfy * m[i][1] + dat->cal.scy_cxfy_fxfy;
m[i][1] = dat->cal.inv_fy * m[i][1] - dat->cal.cy_fy;
}
i=epnp_solve(m, M, NUM_PNPMATCHES, R, t);
nposes=(i==0);
if(nposes)
nposes=!(rotmat2rodr((double *)R, rv));
}
#endif
return nposes;
}
/* compute the geometric residuals corresponding to pose as the (squared) distance between actual and predicted point */
static void poseRTResidualsGeom(double rt[NUM_RTPARAMS], int numres, void *adata, double *resid)
{
register int i;
double P[NUM_PPARAMS], X, Y, Z, s, ppt[2];
struct RTdata *dat=(struct RTdata *)adata;
double (*pts2D)[2]=dat->pts2D, (*pts3D)[3]=dat->pts3D;
/* P=K[R t] */
posest_PfromKRt(P, dat->K, rt);
for(i=0; i<numres; ++i){
/* project 3D point */
X=pts3D[i][0]; Y=pts3D[i][1]; Z=pts3D[i][2];
s=1.0/(P[8]*X + P[9]*Y + P[10]*Z + P[11]);
ppt[0]=(P[0]*X + P[1]*Y + P[2]*Z + P[3])*s;
ppt[1]=(P[4]*X + P[5]*Y + P[6]*Z + P[7])*s;
ppt[0]-=pts2D[i][0]; ppt[1]-=pts2D[i][1];
resid[i]=(SQR(ppt[0]) + SQR(ppt[1]));
}
}
/* reprojection error and Jacobian */
static void ptsProjRT(double *rt, double *x, int m, int n, void *adata)
{
struct RTdata *dat=(struct RTdata *)adata;
int ninl=dat->numInliers, *inlidx=dat->inliersidx;
double *K=dat->K, (*pts3D)[3]=dat->pts3D;
register int i;
#if 1 /* fast version based on computing and reusing P */
double P[NUM_PPARAMS], X, Y, Z, s, *ppt;
int j;
/* P=K[R t] */
posest_PfromKRt(P, K, rt);
for(i=0; i<ninl; ++i){
j=inlidx[i];
ppt=x+(i<<1); // 2*i
X=pts3D[j][0]; Y=pts3D[j][1]; Z=pts3D[j][2];
// parentheses below break dependency chains
s=1.0/((P[8]*X + P[9]*Y) + (P[10]*Z + P[11]));
ppt[0]=((P[0]*X + P[1]*Y) + (P[2]*Z + P[3]))*s;
ppt[1]=((P[4]*X + P[5]*Y) + (P[6]*Z + P[7]))*s;
}
#else
for(i=0; i<ninl; ++i){
calc_poseProjRT(K, rt, pts3D[inlidx[i]], x+i*2);
}
#endif
}
static void ptsProjRTJac(double *rt, double *jac, int m, int n, void *adata)
{
register int i;
struct RTdata *dat=(struct RTdata *)adata;
int ninl=dat->numInliers, *inlidx=dat->inliersidx;
double *K=dat->K, (*pts3D)[3]=dat->pts3D;
register double *jacrow;
//memset(jac, 0, m*n*sizeof(double));
#if 1 /* fast version based on computing and reusing P with the chain rule */
{
double P[NUM_PPARAMS];
double gradP[2*12], gradrt[12*6];
register int j;
posest_PfromKRt(P, K, rt);
calc_posePRTJac(K, rt, (double (*)[6])gradrt); // d P / d rt
#if 0 // zero pattern
for(i=0; i<12; ++i){
for(j=0; j<6; ++j)
if(gradrt[i*6+j]) printf("x ");
else printf("0 ");
printf("\n");
}
printf("\n\n\n");
#endif
for(i=0, jacrow=jac; i<ninl; ++i, jacrow+=2*6){
calc_poseProjPJac(P, pts3D[inlidx[i]], (double (*)[12])gradP); // d m / d P
/* d m / d rt = d m / d P * d P / d rt
* unrolled multiplication jacrow=gradP*gradrt; parentheses are used to break dependency chains
*
* gradP is sparse: [x x x x 0 0 0 0 x x x x; 0 0 0 0 x x x x x x x x], hence we can exploit this
* to avoid a few multiplications
*/
//for(j=0; j<6; ++j)
for(j=6; j-->0; ){
jacrow[0*6+j]=
((gradP[0*12+0]*gradrt[0*6+j] + gradP[0*12+1]*gradrt[1*6+j]) + (gradP[0*12+2] *gradrt[2*6+j] + gradP[0*12+3] *gradrt[3*6+j])) +
//((gradP[0*12+4]*gradrt[4*6+j] + gradP[0*12+5]*gradrt[5*6+j]) + (gradP[0*12+6] *gradrt[6*6+j] + gradP[0*12+7] *gradrt[7*6+j])) +
((gradP[0*12+8]*gradrt[8*6+j] + gradP[0*12+9]*gradrt[9*6+j]) + (gradP[0*12+10]*gradrt[10*6+j] + gradP[0*12+11]*gradrt[11*6+j]));
jacrow[1*6+j]=
//((gradP[1*12+0]*gradrt[0*6+j] + gradP[1*12+1]*gradrt[1*6+j]) + (gradP[1*12+2] *gradrt[2*6+j] + gradP[1*12+3] *gradrt[3*6+j])) +
((gradP[1*12+4]*gradrt[4*6+j] + gradP[1*12+5]*gradrt[5*6+j]) + (gradP[1*12+6] *gradrt[6*6+j] + gradP[1*12+7] *gradrt[7*6+j])) +
((gradP[1*12+8]*gradrt[8*6+j] + gradP[1*12+9]*gradrt[9*6+j]) + (gradP[1*12+10]*gradrt[10*6+j] + gradP[1*12+11]*gradrt[11*6+j]));
}
}
}
#else
for(i=0, jacrow=jac; i<ninl; ++i, jacrow+=2*m){
calc_poseProjRTJac(K, rt, pts3D[inlidx[i]], jacrow, jacrow+m);
}
#endif
#if 0
printf("\n\n================================\n");
printf("\n%g %g %g %g %g %g\n", jacrow[0], jacrow[1], jacrow[2], jacrow[3], jacrow[4], jacrow[5]);
printf("%g %g %g %g %g %g\n\n", jacrow[6], jacrow[7], jacrow[8], jacrow[9], jacrow[10], jacrow[11]);
#endif
}
/* nonlinear refinement of camera pose; based on minimizing reprojection error
*
* doMLSL is 1 if the MLSL scheme schould be emplooyed, 0 otherwise
* inpl is 1 if function is called by refinePoseRT_inplace(), 0 otherwise
*/
static int refinePoseRT(double *p, struct RTdata *data, int doMLSL, int inpl, int verbose)
{
register int i, j;
double opts[LM_OPTS_SZ], info[LM_INFO_SZ], *x;
int m, n; // # unknowns & # constraints
int ninl=data->numInliers;
void (*err)(double *p, double *hx, int m, int n, void *adata);
void (*jacerr)(double *p, double *j, int m, int n, void *adata);
int ret;
opts[0]=LM_INIT_MU; opts[1]=1E-12; opts[2]=1E-12; opts[3]=1E-15;
opts[4]=LM_DIFF_DELTA; // relevant only if the finite difference Jacobian version is used
m=NUM_RTPARAMS; n=2*ninl; // two measurements per point
if((x=(double *)malloc(n*sizeof(double)))==NULL){
fprintf(stderr, "Memory allocation request failed in refinePoseRT()\n");
exit(1);
}
for(i=0; i<ninl; ++i){
j=i<<1; // 2*i
x[j] =data->pts2D[data->inliersidx[i]][0];
x[j+1]=data->pts2D[data->inliersidx[i]][1];
}
err=ptsProjRT;
jacerr=ptsProjRTJac;
if(doMLSL)
{
double lb[NUM_RTPARAMS], ub[NUM_RTPARAMS], minL2sq;
double scl[NUM_RTPARAMS];
/* setup bounds & expected magnitudes; translation in mm -- CHECKME */
if(!inpl){
if(verbose) printf("PnP pose: %g %g %g %g %g %g\n", p[0], p[1], p[2], p[3], p[4], p[5]);
scl[0]=1.0; scl[1]=2.0; scl[2]=1.0;
scl[3]=300.; scl[4]=300.; scl[5]=1500.;
lb[0]=-1.5+p[0]; ub[0]=1.5+p[0];
lb[1]=-1.5+p[1]; ub[1]=1.5+p[1];
lb[2]=-1.5+p[2]; ub[2]=1.5+p[2];
lb[3]=-300.+p[3]; ub[3]=300.+p[3];
lb[4]=-300.+p[4]; ub[4]=300.+p[4];
lb[5]=-700.+p[5]; ub[5]=700.+p[5];
}
else{ // in-place
if(verbose) printf("Init refinement to PnP pose (in-place): %g %g %g %g %g %g\n", p[0], p[1], p[2], p[3], p[4], p[5]);
scl[0]=1.0; scl[1]=1.0; scl[2]=1.0;
scl[3]=fabs(p[3]); scl[4]=fabs(p[4]); scl[5]=fabs(p[5]);
lb[0]=-1.5+p[0]; ub[0]=1.5+p[0];
lb[1]=-1.5+p[1]; ub[1]=1.5+p[1];
lb[2]=-1.5+p[2]; ub[2]=1.5+p[2];
lb[3]=-1000.+p[3]; ub[3]=1000.+p[3];
lb[4]=-1000.+p[4]; ub[4]=1000.+p[4];
lb[5]=-1500.+p[5]; ub[5]=1500.+p[5];
}
# if 0
printf("L bounds: %g %g %g %g %g %g\n", lb[0], lb[1], lb[2], lb[3], lb[4], lb[5]);
printf("U bounds: %g %g %g %g %g %g\n", ub[0], ub[1], ub[2], ub[3], ub[4], ub[5]);
#endif
/* refine PnP pose and use it to initiate MLSL */
ret=dlevmar_der(err, jacerr, p, x, m, n, 1000, opts, info, NULL, NULL, (void *)data); // with analytic Jacobian
mlsl_dlevmar_der(err, jacerr, p, x, m, n, lb, ub, scl, 500, opts, info, NULL, NULL, (void *)data, &minL2sq, 5, 1, verbose);
if(verbose) printf("MLSL pose: %g %g %g %g %g %g, error %g\n", p[0], p[1], p[2], p[3], p[4], p[5], minL2sq/ninl);
}
#if USE_ROBUST_LM==0
ret=dlevmar_der(err, jacerr, p, x, m, n, 1000, opts, info, NULL, NULL, (void *)data); // with analytic Jacobian
//ret=dlevmar_dif(err, p, x, m, n, 1000, opts, info, NULL, NULL, (void *)data); // no Jacobian
#else
{ double rp[2];
# if 0
// attempt to estimate scale from the data
double ls[2];
int est=LM_HAMPEL_LOCSCL; // LM_ROUSSEEUW_LOCSCL
ret=dlevmar_der(err, jacerr, p, x, m, n, 1000, opts, info, NULL, NULL, (void *)data); // with analytic Jacobian
dlevmar_locscale(err, p, x, m, n, (void *)data, est, ls, NULL);
# endif
/* use convex cost function first, then non-convex */
rp[0] = ME_FAIR; rp[1]= 1.3998; // Fair 0.6
ret=dlevmar_rob_der(err, jacerr, p, x, m, n, rp, 1000, opts, info, NULL, NULL, (void *)data);
//rp[0] = ME_TUKEY; rp[1] = 4.6851;//; // Tukey 0.20
rp[0] = ME_GEMANMCCLURE; rp[1] = 2.3849; // Geman-McClure 0.25
ret=dlevmar_rob_der(err, jacerr, p, x, m, n, rp, 100, opts, info, NULL, NULL, (void *)data);
}
#endif /* USE_ROBUST_LM */
if(verbose){
fprintf(stdout, "\nRefinement using %d measurements, %d variables\n", n, m);
fprintf(stdout, "LM returned %d in %g iter, reason %g, error %g [initial %g], %d/%d func/fjac evals\n",
ret, info[5], info[6], info[1]/ninl, info[0]/ninl, (int)info[7], (int)info[8]);
#if 0
fprintf(stdout, "\nSolution: ");
for(i=0; i<m; ++i)
fprintf(stdout, "%.7g ", p[i]);
fprintf(stdout, "\n");
#endif
}
free(x);
return ret;
}
/* nonlinear refinement of camera pose using an in-place parameterization;
* based on minimizing reprojection error
*
* Posest computes the pose Rp,t transforming points from bundler to camera frame:
* Mc=Rp*Mb + tp (1)
* The in-place refinement computes a correction dR,dt so that
* Mc'=dR*(Mc-C) + C + dt (2), with C being the center of rotation (the point's
* centroid). Therefore, substituting (1) into (2) gives
* Mc'=dR*Rp*Mb + dR*(tp-C) + C + dt,
* which gives the overall pose in posest's convention (bundler to camera) as
* R=dR*Rp, t=dR*(tp-C) + C + dt
*
* Note also that (2) implies that dR,C+dt can be estimated with refinePoseRT()
* applied to the transformed input points (Mc-C)
*/
static int refinePoseRT_inplace(double *p, struct RTdata *data, int doMLSL, int verbose)
{
register int i, j;
int ninl=data->numInliers;
int *inliersidx=data->inliersidx;
double (*pts3D)[3]=data->pts3D, X, Y, Z, dp[NUM_RTPARAMS];
double cent[3], // C
Rp[9], tp[3], // PnP pose estimate (from RANSAC)
tp_cent[3], // tp-C
dR[9], totR[9];
int ret;
if(verbose) printf("PnP pose: %g %g %g %g %g %g\n", p[0], p[1], p[2], p[3], p[4], p[5]);
/* compute points centroid */
cent[0]=cent[1]=cent[2]=0.0;
for(i=0; i<ninl; ++i){
j=data->inliersidx[i];
cent[0]+=pts3D[j][0];
cent[1]+=pts3D[j][1];
cent[2]+=pts3D[j][2];
}
cent[0]/=(double)ninl; cent[1]/=(double)ninl; cent[2]/=(double)ninl;
/* transform 3D points with supplied pose & translate centroid to origin: Rp*M+tp-cent */
rvec2rotmat(p, Rp);
tp[0]=p[3]; tp[1]=p[4]; tp[2]=p[5];
tp_cent[0]=tp[0]-cent[0]; tp_cent[1]=tp[1]-cent[1]; tp_cent[2]=tp[2]-cent[2];
for(i=0; i<ninl; ++i){
j=data->inliersidx[i];
X=pts3D[j][0]; Y=pts3D[j][1]; Z=pts3D[j][2];
pts3D[j][0]=Rp[0]*X + Rp[1]*Y + Rp[2]*Z + tp_cent[0];
pts3D[j][1]=Rp[3]*X + Rp[4]*Y + Rp[5]*Z + tp_cent[1];
pts3D[j][2]=Rp[6]*X + Rp[7]*Y + Rp[8]*Z + tp_cent[2];
}
/* estimate in-place pose refinement */
dp[0]=1E-04; dp[1]=dp[2]=0.0; // dR=I, avoid singular case with r=[0 0 0]
dp[3]=cent[0]; dp[4]=cent[1]; dp[5]=cent[2]; // we are actually estimating C+dt, initial dt=[0 0 0]
ret=refinePoseRT(dp, data, doMLSL, 1, verbose);
/* undo changes to 3D points: Rp'*(M-(tp-cent)) */
for(i=0; i<ninl; ++i){
j=data->inliersidx[i];
X=pts3D[j][0]-(tp_cent[0]); Y=pts3D[j][1]-(tp_cent[1]); Z=pts3D[j][2]-(tp_cent[2]);
pts3D[j][0]=Rp[0]*X + Rp[3]*Y + Rp[6]*Z;
pts3D[j][1]=Rp[1]*X + Rp[4]*Y + Rp[7]*Z;
pts3D[j][2]=Rp[2]*X + Rp[5]*Y + Rp[8]*Z;
}
if(ret==LM_ERROR) goto bailout;
/* incorporate estimated in-place pose to p */
rvec2rotmat(dp, dR);
/* totR=dR*Rp */
for(i=0; i<3; ++i)
for(j=0; j<3; ++j)
totR[i*3+j]=dR[i*3]*Rp[j] + dR[i*3+1]*Rp[3+j] + dR[i*3+2]*Rp[2*3+j];
rotmat2rodr(totR, p); // sets p[0:2]
/* dR*(tp-cent) + C+dt */
p[3]=dR[0]*tp_cent[0] + dR[1]*tp_cent[1] + dR[2]*tp_cent[2] + dp[3];
p[4]=dR[3]*tp_cent[0] + dR[4]*tp_cent[1] + dR[5]*tp_cent[2] + dp[4];
p[5]=dR[6]*tp_cent[0] + dR[7]*tp_cent[1] + dR[8]*tp_cent[2] + dp[5];
if(verbose){
#if 0
fprintf(stdout, "\nSolution: ");
for(i=0; i<NUM_RTPARAMS; ++i)
fprintf(stdout, "%.7g ", p[i]);
fprintf(stdout, "\n");
#endif
}
bailout:
return ret;
}
/* Robust, non-linear 2D-3D pose estimation from "nmatches" matched point features, possibly
* including outliers. "pts2D", "pts3D" contain the matched 2D-3D point coordinates,
* "inlPcent" is the expected percentage of inliers (>=0.5), "rt" contains the estimated pose
* parameters upon return, "NLrefine" specifies which cost function should be employed for the
* non-linear refinement step (see posest.h for appropriate values), "idxOutliers" points to
* sufficiently large memory which upon return is set to the indices of the detected outlying
* points (pass NULL if don't care), "nbOutliers" contains the number of outliers, "verbose"
* specifies the verbosity level
*/
static int posestRT(double (*pts2D)[2], double (*pts3D)[3], int nmatches, double inlPcent, double K[9],
double rt[NUM_RTPARAMS], int NLrefine, int *idxOutliers, int *nbOutliers, int verbose)
{
register int i, j;
int isSqr=1, maxNbSol;
double gate=2.0, premResid=-1.0, sampleProb=0.99, outlierThresh;
int *outliersMap, ret, **sets=NULL, nbSets=0;
struct RTdata dat;
int verbosein=verbose;
if(nmatches<NUM_PNPMATCHES) return POSEST_ERR; // too few matches
#if (USE_LQS_FIT==1) || (USE_RANSAC_FIT==1) || (USE_MLESAC_FIT==1)
nbSets=10*lqs_numtries(NUM_PNPMATCHES, inlPcent, sampleProb); // ten times those theoretically necessary
sets=lqs_allocsets(NUM_PNPMATCHES, nbSets);
#ifdef USE_BUCKETS
nbSets=posest_genRandomSetsWithBuckets(pts2D, NUM_PNPMATCHES, nmatches, nbSets, sets);
#else
nbSets=posest_genRandomSetsNoBuckets(NUM_PNPMATCHES, nmatches, nbSets, sets);
#endif /* USE_BUCKETS */
#endif /* (USE_LQS_FIT==1) || (USE_RANSAC_FIT==1) || (USE_MLESAC_FIT==1) */
dat.pts2D=pts2D; dat.pts3D=pts3D;
dat.K=K;
p3p_set_calib(&dat.cal, K);
dat.inliersidx=NULL;
if(!(outliersMap=(int *)malloc(nmatches*sizeof(int)))){
fprintf(stderr, "Error: not enough memory for 'outliersMap' in posestRT()\n");
exit(1);
}
verbose=verbose>1;
maxNbSol=(NUM_PNPMATCHES==3)? MAX_NUM_P3P_SOL : 1;
#if USE_LQS_FIT==1
j=lqsfit(nmatches, NUM_PNPMATCHES, sets, nbSets, poseRTResidualsGeom, estP3PPose,
isSqr, verbose, maxNbSol, gate, premResid, NUM_RTPARAMS, inlPcent, (void *)&dat,
rt, NULL, outliersMap, nbOutliers, &outlierThresh);
#elif (USE_RANSAC_FIT==1) || (USE_PROSAC_FIT==1) || (USE_MLESAC_FIT==1)
gate=premResid=0; /* -Wall */
//outlierThresh=ransac_getthresh(0.8, 2); // assume s=.8, symmetric distance involves 2 squared terms
//outlierThresh=sqrt(0.8*0.8*9.210340372); // assume s=.8, symmetric distance involves 2 squared terms
outlierThresh=RANSAC_OUTL_THRESH;
# if USE_RANSAC_FIT==1
j=ransacfit(nmatches, NUM_PNPMATCHES, sets, nbSets, poseRTResidualsGeom, estP3PPose,
isSqr, verbose, maxNbSol, outlierThresh, 0, NUM_RTPARAMS, inlPcent, (void *)&dat,
rt, NULL, outliersMap, nbOutliers);
# elif USE_MLESAC_FIT==1
j=mlesacfit(nmatches, NUM_PNPMATCHES, sets, nbSets, poseRTResidualsGeom, estP3PPose,
isSqr, verbose, maxNbSol, outlierThresh, 0, NUM_RTPARAMS, inlPcent, (void *)&dat,
rt, NULL, outliersMap, nbOutliers);
# else
j=prosacfit(nmatches, NUM_PNPMATCHES, poseRTResidualsGeom, estP3PPose,
isSqr, verbose, maxNbSol, outlierThresh, 0, NUM_RTPARAMS, inlPcent, (void *)&dat,
rt, NULL, outliersMap, nbOutliers);
# endif
#endif /* USE_LQS_FIT */
if(verbose){
fprintf(stderr, "Outlier threshold: %g\n", outlierThresh);
fprintf(stderr, "posestRT(): robust fit returned %d, %d outliers [out of %d]\n", j, *nbOutliers, nmatches);
}
if(sets) lqs_freesets(sets);
dat.numInliers=nmatches - *nbOutliers;
if(j!=0){
dat.inliersidx=(int *)malloc(dat.numInliers*sizeof(int));
if(!dat.inliersidx){
fprintf(stderr, "Error: not enough memory for 'dat.inliersidx' in posestRT()\n");
exit(1);
}
for(i=j=0; i<nmatches; ++i)
if(!outliersMap[i]) dat.inliersidx[j++]=i;
#if 0
/* LS estimation on inliers */
estP3PPose(rt, dat.numInliers, dat.inliersidx, (void *)&dat);
#endif
/* expose outliers */
if(idxOutliers!=NULL)
for(i=j=0; i<nmatches; ++i)
if(outliersMap[i]) idxOutliers[j++]=i;
#if 0
if(verbose){
fputs("Outliers: ", stderr);
for(i=j=0; i<nmatches; ++i)
if(outliersMap[i]) fprintf(stderr, "%d ", i);
fputc('\n', stderr);
}
#endif
ret=POSEST_OK;
#if 0
/* include the following code fragment to print the matching 3D-2D points found to be inlying */
for(i=0; i<dat.numInliers; ++i){
printf("%.4lf %.4lf %.4lf %.4lf %.4lf\n", pts3D[dat.inliersidx[i]][0], pts3D[dat.inliersidx[i]][1], pts3D[dat.inliersidx[i]][2],
pts2D[dat.inliersidx[i]][0], pts2D[dat.inliersidx[i]][1]);
}
#endif
}
else{ /* robust fit failed */
memset(rt, 0, NUM_RTPARAMS*sizeof(double));
*nbOutliers=nmatches;
dat.numInliers=0; /* makes sure the non-linear refinement below is avoided */
ret=POSEST_ERR;
}
/* the initial estimate has now been computed. Time for the non-linear refinement */
if(2*dat.numInliers>=NUM_RTPARAMS && NLrefine!=POSEST_REPR_ERR_NO_NLN_REFINE){
int withMLSL=(NLrefine==POSEST_REPR_ERR_NLN_MLSL_REFINE);
sam_rvecnorm(rt); // map rotation angle to [-pi, pi]
# if USE_INPLACE_REFN==0
j=refinePoseRT(rt, &dat, withMLSL, 0, verbosein);
# else
j=refinePoseRT_inplace(rt, &dat, withMLSL, verbosein);
# endif
ret=(j!=LM_ERROR)? POSEST_OK : POSEST_ERR;
sam_rvecnorm(rt); // map rotation angle to [-pi, pi]
}
if(dat.inliersidx) free(dat.inliersidx);
free(outliersMap);
return ret;
}
/***** robust nonlinear estimation of focal length, rotation and translation *****/
/* variables used by various estimation routines */
struct RTFdata {
double u0v0[2]; // principal point
double (*pts2D)[2], (*pts3D)[3];
int *inliersidx, numInliers;
};
/* estimate "point" pose P=K[R t] s.t. m=P*M, with m, M specified by ptsidx */
static int estP4PfPose(double *rtf, int npts, int *ptsidx, void *adata)
{
int nposes;
struct RTFdata *dat=(struct RTFdata *)adata;
double (*pts2D)[2]=dat->pts2D, (*pts3D)[3]=dat->pts3D;
double *m0, *m1, *m2, *m3, *M0, *M1, *M2, *M3;
double m[4][2], M[4][3], *prtf;
double R[MAX_NUM_P4PF_SOL][3][3], t[MAX_NUM_P4PF_SOL][3], foc[MAX_NUM_P4PF_SOL];
register int i, j;
if(npts<NUM_P4PFMATCHES) return 0; // not enough points
m0=pts2D[ptsidx[0]]; M0=pts3D[ptsidx[0]];
m1=pts2D[ptsidx[1]]; M1=pts3D[ptsidx[1]];
m2=pts2D[ptsidx[2]]; M2=pts3D[ptsidx[2]];
m3=pts2D[ptsidx[3]]; M3=pts3D[ptsidx[3]];
#if 0
/* print matching points for matlab */
printf("\n=======================================\n");
printf("m=[");
for(i=0; i<2; ++i)
printf("%g %g %g %g\n", m0[i], m1[i], m2[i], m3[i]);
printf("]\nM=[");
for(i=0; i<3; ++i)
printf("%g %g %g %g\n", M0[i], M1[i], M2[i], M3[i]);
printf("]\n");
printf("\n=======================================\n");
fflush(stdout);
#endif
for(i=0; i<2; ++i){
m[0][i]=m0[i]; m[1][i]=m1[i]; m[2][i]=m2[i]; m[3][i]=m3[i];
M[0][i]=M0[i]; M[1][i]=M1[i]; M[2][i]=M2[i]; M[3][i]=M3[i];
}
M[0][2]=M0[2]; M[1][2]=M1[2]; M[2][2]=M2[2]; M[3][2]=M3[2];
/* solve P4Pf */
nposes=p4pf_solve(m, M, R, t, foc);
for(i=j=0; i<nposes; ++i){
prtf=rtf+j*NUM_RTFPARAMS;
if(!rotmat2rodr((double *)R[i], prtf)){
prtf[3]=t[i][0];
prtf[4]=t[i][1];
prtf[5]=t[i][2];
prtf[6]=foc[i];
++j;
}
}
return j;
}
/* compute the geometric residuals corresponding to pose as the (squared) distance between actual and predicted point */
static void poseRTFResidualsGeom(double rtf[NUM_RTFPARAMS], int numres, void *adata, double *resid)
{
register int i;
double K[9], P[NUM_PPARAMS], X, Y, Z, s, ppt[2];
struct RTFdata *dat=(struct RTFdata *)adata;
double (*pts2D)[2]=dat->pts2D, (*pts3D)[3]=dat->pts3D;
/* NOTE: no u0v0 here! */
K[0]=rtf[NUM_RTFPARAMS-1]; K[1]=0.0; K[2]=0.0;
K[3]=0.0; K[4]=K[0]; K[5]=0.0;
K[6]=0.0; K[7]=0.0; K[8]=1.0;
/* P=K[R t] */
posest_PfromKRt(P, K, rtf);
for(i=0; i<numres; ++i){
/* project 3D point */
X=pts3D[i][0]; Y=pts3D[i][1]; Z=pts3D[i][2];
s=1.0/(P[8]*X + P[9]*Y + P[10]*Z + P[11]);
ppt[0]=(P[0]*X + P[1]*Y + P[2]*Z + P[3])*s;
ppt[1]=(P[4]*X + P[5]*Y + P[6]*Z + P[7])*s;
ppt[0]-=pts2D[i][0]; ppt[1]-=pts2D[i][1];
resid[i]=(SQR(ppt[0]) + SQR(ppt[1]));
}
}
/* reprojection error and Jacobian */
static void ptsProjRTF(double *rtf, double *x, int m, int n, void *adata)
{
struct RTFdata *dat=(struct RTFdata *)adata;
int ninl=dat->numInliers, *inlidx=dat->inliersidx;
double (*pts3D)[3]=dat->pts3D, *u0v0=dat->u0v0;
register int i;
for(i=0; i<ninl; ++i){
calc_poseProjRTF(rtf, u0v0, pts3D[inlidx[i]], x+i*2);
}
}
static void ptsProjRTFJac(double *rtf, double *jac, int m, int n, void *adata)
{
register int i;
struct RTFdata *dat=(struct RTFdata *)adata;
int ninl=dat->numInliers, *inlidx=dat->inliersidx;
double (*pts3D)[3]=dat->pts3D, *u0v0=dat->u0v0;
register double *jacrow;
//memset(jac, 0, m*n*sizeof(double));
for(i=0, jacrow=jac; i<ninl; ++i, jacrow+=2*m){
calc_poseProjRTFJac(rtf, u0v0, pts3D[inlidx[i]], jacrow, jacrow+m);
}
}
/* nonlinear refinement of camera pose & foc. length; based on minimizing reprojection error */
/** NOTE: MLSL not implemented for this case yet!*/
static int refinePoseRTF(double *p, struct RTFdata *data, int verbose)
{