void arGetInitRot2_sub2(real_t &err, mat33_t &R, vec3_t &t, const vec3_array &_model, const vec3_array &_iprts, const options_t _options)
{
mat33_t Rlu_;
vec3_t tlu_;
unsigned int it1_;
real_t obj_err1_;
real_t img_err1_;
vec3_array model(_model.begin(),_model.end());
vec3_array iprts(_iprts.begin(),_iprts.end());
options_t options;
memcpy(&options,&_options,sizeof(options_t));
mat33_clear(Rlu_);
vec3_clear(tlu_);
it1_ = 0;
obj_err1_ = 0;
img_err1_ = 0;
objpose(R, t, it1_, obj_err1_, img_err1_, false, model, iprts, options);
/*pose_vec sol;
sol.clear();
get2ndPose_Exact(sol,iprts,model,Rlu_,tlu_,0);
int min_err_idx = (-1);
real_t min_err = MAX_FLOAT;
for(unsigned int i=0; i<sol.size(); i++)
{
mat33_copy(options.initR,sol[i].R);
objpose(Rlu_, tlu_, it1_, obj_err1_, img_err1_, true, model, iprts, options);
mat33_copy(sol[i].PoseLu_R,Rlu_);
vec3_copy(sol[i].PoseLu_t,tlu_);
sol[i].obj_err = obj_err1_;
if(sol[i].obj_err < min_err)
{
min_err = sol[i].obj_err;
min_err_idx = i;
}
}
if(min_err_idx >= 0)
{
mat33_copy(R,sol[min_err_idx].PoseLu_R);
vec3_copy(t,sol[min_err_idx].PoseLu_t);
err = sol[min_err_idx].obj_err;
}
else
{
mat33_clear(R);
vec3_clear(t);
err = MAX_FLOAT;
}*/
}
void get2ndPose_Exact(pose_t *sol, const vec3_t *v, const vec3_t *P,
const mat33_t R, const vec3_t t, const real_t DB, const int n, int *sol_n)
{
vec3_t cent, _v1;
vec3_t _va1[n];
normRv2(&*_va1, v, n);
vec3_array_mean(&_v1, &*_va1, n);
normRv(¢, &_v1);
mat33_t Rim;
vec3_clear(&_v1);
_v1.v[2] = 1.0;
GetRotationbyVector(&Rim, &_v1, ¢);
vec3_t v_[n];
vec3_array_mult_vec2(&*v_, &Rim, v, n);
normRv2(&*_va1, &*v_, n);
vec3_array_mean(&_v1, &*_va1, n);
normRv(¢, &_v1);
mat33_t R_;
vec3_t t_;
mat33_mult_mat2(&R_, &Rim, &R);
vec3_mult_mat(&t_, &Rim, &t);
int res_n = 0;
getRfor2ndPose_V_Exact(sol, &*v_, P, R_, t_, DB, n, &res_n);
// Re normalize it
mat33_t Rim_tr;
mat33_transpose(&Rim_tr, Rim);
int i;
vec3_t _t;
mat33_t _R;
for(i=0; i<res_n; i++)
{
vec3_mult_mat(&_t, &Rim_tr, &sol[i].t);
mat33_mult_mat2(&_R, &Rim_tr, &sol[i].R);
vec3_copy(&sol[i].t, &_t);
mat33_copy(&sol[i].R, &_R);
}
*sol_n = res_n;
}
void optimal_t(vec3_t *t ,const mat33_t *R, const mat33_t *G,
const mat33_t *F,const vec3_t *P, int n){
vec3_t _sum;
vec3_clear(&_sum);
int i;
for(i=0; i<n; i++)
{
vec3_t _v1, _v2;
vec3_mult_mat(&_v1, R, &P[i]);
vec3_mult_mat(&_v2, &F[i], &_v1);
vec3_add_vec(&_sum, &_v2);
}
vec3_mult_mat(t, G, &_sum);
}
// =====================================================================================
// function returns two solutions to the pose problem (1st has the lower Error !!!!!!
// ====================================================================================
void robust_pose(real_t *err, mat33_t *R , vec3_t *t,
real_t *errb, mat33_t *Rb, vec3_t *tb,
const vec3_t *_model, const vec3_t *_iprts, const options_t _options, const int n)
{
mat33_t Rlu_;
vec3_t tlu_;
int it1_, i;
real_t obj_err1_;
real_t img_err1_;
vec3_t model[n];
vec3_t iprts[n];
memcpy(&*model, _model, n * sizeof(vec3_t));
memcpy(&*iprts, _iprts, n * sizeof(vec3_t));
options_t options;
memcpy(&options, &_options, sizeof(options_t));
mat33_clear(&Rlu_);
vec3_clear(&tlu_);
it1_ = 0;
obj_err1_ = 0;
img_err1_ = 0;
objpose(&Rlu_, &tlu_, &it1_, &obj_err1_, &img_err1_, CALC_IMAGE_ERROR, &*model, &*iprts, options, n);
pose_t sol[10];
int sol_n = 0;
get2ndPose_Exact(&*sol, &*iprts, &*model, Rlu_, tlu_, 0, n, &sol_n);
// refine all poses
for(i=0; i<sol_n; i++)
{
mat33_copy(&options.initR, &sol[i].R);
objpose(&Rlu_, &tlu_, &it1_, &obj_err1_, &img_err1_, CALC_IMAGE_ERROR, &*model, &*iprts, options, n);
mat33_copy(&sol[i].PoseLu_R, &Rlu_);
vec3_copy(&sol[i].PoseLu_t, &tlu_);
sol[i].obj_err = obj_err1_;
}
// from all solutions get the best
int min_err_idx = (-1);
real_t min_err = MAX_FLOAT;
for(i=0; i<sol_n; i++)
if(sol[i].obj_err < min_err)
{
min_err = sol[i].obj_err;
min_err_idx = i;
}
// Copy the best solution !!!
if(min_err_idx >= 0)
{
mat33_copy(R, &sol[min_err_idx].PoseLu_R);
vec3_copy(t, &sol[min_err_idx].PoseLu_t);
*err = sol[min_err_idx].obj_err;
}
else
{
mat33_clear(R);
vec3_clear(t);
*err = MAX_FLOAT;
}
// from all solutions get the 2nd Best one !!
int min_err_idx2 = min_err_idx;
min_err = MAX_FLOAT;
for(i=0; i < sol_n; i++)
{
if(sol[i].obj_err < min_err &&
(min_err_idx2 != i) )
{
min_err = sol[i].obj_err;
min_err_idx = i;
}
}
// Copy the 2nd best solution !!!
if(min_err_idx >= 0)
{
mat33_copy(Rb, &sol[min_err_idx].PoseLu_R);
vec3_copy(tb, &sol[min_err_idx].PoseLu_t);
*errb = sol[min_err_idx].obj_err;
}
else
{
mat33_clear(R);
vec3_clear(t);
*err = MAX_FLOAT;
}
}
void getRotationY_wrtT(double *al_ret, vec3_t *tnew, const vec3_t *v,
const vec3_t *p, const vec3_t *t, const real_t *DB,
const mat33_t *Rz, const int n, int *res_n)
{
int i,j,k;
mat33_t V[n];
for(i=0; i<n; i++)
{
vec3_mul_vec3trans(&V[i], &v[i], &v[i]);
mat33_div(&V[i], vec3trans_mul_vec3(&v[i], &v[i]));
}
mat33_t G, _g1, _g2, _g3;
mat33_array_sum(&_g1, &*V, n);
mat33_eye(&_g2);
mat33_div(&_g1, (real_t)(n));
mat33_sub_mat2(&_g3, &_g2, &_g1);
mat33_inv(&G, &_g3);
mat33_div(&G, (real_t)(n));
mat33_t _opt_t;
mat33_clear(&_opt_t);
for(i=0; i<n; i++)
{
const real_t v11 = V[i].m[0];
const real_t v21 = V[i].m[3];
const real_t v31 = V[i].m[6];
const real_t v12 = V[i].m[1];
const real_t v22 = V[i].m[4];
const real_t v32 = V[i].m[7];
const real_t v13 = V[i].m[2];
const real_t v23 = V[i].m[5];
const real_t v33 = V[i].m[8];
const real_t px = p[i].v[0];
const real_t py = p[i].v[1];
const real_t pz = p[i].v[2];
const real_t r1 = Rz->m[0];
const real_t r2 = Rz->m[1];
const real_t r3 = Rz->m[2];
const real_t r4 = Rz->m[3];
const real_t r5 = Rz->m[4];
const real_t r6 = Rz->m[5];
const real_t r7 = Rz->m[6];
const real_t r8 = Rz->m[7];
const real_t r9 = Rz->m[8];
mat33_t _o;
_o.m[0] = (((v11-(real_t)(1))*r2+v12*r5+v13*r8)*py+(-(v11-(real_t)(1))*r1-v12*r4-v13*r7)*px+(-(v11-(real_t)(1))*r3-v12*r6-v13*r9)*pz);
_o.m[1] = (((real_t)(2)*(v11-(real_t)(1))*r1+(real_t)(2)*v12*r4+(real_t)(2)*v13*r7)*pz+(-(real_t)(2)*(v11-(real_t)(1))*r3-(real_t)(2)*v12*r6-(real_t)(2)*v13*r9)*px);
_o.m[2] = ((v11-(real_t)(1))*r1+v12*r4+v13*r7)*px+((v11-(real_t)(1))*r3+v12*r6+v13*r9)*pz+((v11-(real_t)(1))*r2+v12*r5+v13*r8)*py;
_o.m[3] = ((v21*r2+(v22-(real_t)(1))*r5+v23*r8)*py+(-v21*r1-(v22-(real_t)(1))*r4-v23*r7)*px+(-v21*r3-(v22-(real_t)(1))*r6-v23*r9)*pz);
_o.m[4] = (((real_t)(2)*v21*r1+(real_t)(2)*(v22-(real_t)(1))*r4+(real_t)(2)*v23*r7)*pz+(-(real_t)(2)*v21*r3-(real_t)(2)*(v22-(real_t)(1))*r6-(real_t)(2)*v23*r9)*px);
_o.m[5] = (v21*r1+(v22-(real_t)(1))*r4+v23*r7)*px+(v21*r3+(v22-(real_t)(1))*r6+v23*r9)*pz+(v21*r2+(v22-(real_t)(1))*r5+v23*r8)*py;
_o.m[6] = ((v31*r2+v32*r5+(v33-(real_t)(1))*r8)*py+(-v31*r1-v32*r4-(v33-(real_t)(1))*r7)*px+(-v31*r3-v32*r6-(v33-(real_t)(1))*r9)*pz);
_o.m[7] = (((real_t)(2)*v31*r1+(real_t)(2)*v32*r4+(real_t)(2)*(v33-(real_t)(1))*r7)*pz+(-(real_t)(2)*v31*r3-(real_t)(2)*v32*r6-(real_t)(2)*(v33-(real_t)(1))*r9)*px);
_o.m[8] = (v31*r1+v32*r4+(v33-(real_t)(1))*r7)*px+(v31*r3+v32*r6+(v33-(real_t)(1))*r9)*pz+(v31*r2+v32*r5+(v33-(real_t)(1))*r8)*py;
mat33_add(&_opt_t, &_o);
}
mat33_t opt_t;
mat33_mult_mat2(&opt_t, &G, &_opt_t);
real_t E_2[5] = {0,0,0,0,0};
for(i=0; i<n; i++)
{
const real_t px = p[i].v[0];
const real_t py = p[i].v[1];
const real_t pz = p[i].v[2];
mat33_t Rpi;
mat33_assign(&Rpi, -px, (real_t)(2)*pz,px,py,(real_t)(0),py,-pz,-(real_t)(2)*px,pz);
mat33_t E,_e1,_e2;
mat33_eye(&_e1);
mat33_sub(&_e1, &V[i]);
mat33_mult_mat2(&_e2, Rz, &Rpi);
mat33_add(&_e2, &opt_t);
mat33_mult_mat2(&E,&_e1,&_e2);
vec3_t e2,e1,e0;
mat33_to_col_vec3(&e2,&e1,&e0,&E);
vec3_t _E2_0,_E2_1,_E2_2,_E2_3,_E2_4;
vec3_copy(&_E2_0,&e2);
vec3_mult_vec(&_E2_0,&e2);
vec3_copy(&_E2_1,&e1);
vec3_mult_vec(&_E2_1,&e2);
vec3_mult(&_E2_1,2.0);
vec3_copy(&_E2_2,&e0);
vec3_mult_vec(&_E2_2,&e2);
vec3_mult(&_E2_2,2.0);
vec3_t _e1_sq;
vec3_copy(&_e1_sq,&e1);
vec3_mult_vec(&_e1_sq,&e1);
vec3_add_vec(&_E2_2,&_e1_sq);
vec3_copy(&_E2_3,&e0);
vec3_mult_vec(&_E2_3,&e1);
vec3_mult(&_E2_3,2.0);
vec3_copy(&_E2_4,&e0);
vec3_mult_vec(&_E2_4,&e0);
E_2[0] += vec3_sum(&_E2_0);
E_2[1] += vec3_sum(&_E2_1);
E_2[2] += vec3_sum(&_E2_2);
E_2[3] += vec3_sum(&_E2_3);
E_2[4] += vec3_sum(&_E2_4);
}
//scalar_array _a;
//_a.resize(5);
double _a[5];
_a[4] = -E_2[1];
_a[3] = (real_t)(4)*E_2[0] - (real_t)(2)*E_2[2];
_a[2] = -(real_t)(3)*E_2[3] + (real_t)(3)*E_2[1];
_a[1] = -(real_t)(4)*E_2[4] + (real_t)(2)*E_2[2];
_a[0] = E_2[3];
double at_sol[5];
int num_sol = solve_polynomial(&*at_sol, &*_a, 5);
double e[num_sol];
scalar_array_clear(&*e, num_sol);
double at[num_sol];
if(COMPLICATED_ERROR_CMP)
{
// get the error in a complicate way
scalar_array_clear(&*e, num_sol);
scalar_array_add(&*e, _a[0], num_sol);
//at.clear();
//at.assign(at_sol.begin(),at_sol.end());
memcpy(&*at, &*at_sol, num_sol*sizeof(double));
scalar_array_mult(&*at, _a[1], num_sol);
scalar_array_add_vec(&*e, &*at, num_sol);
for(j=2; j<=4; j++)
{
//at.clear();
//at.assign(at_sol.begin(),at_sol.end());
memcpy(&*at, &*at_sol, num_sol*sizeof(double));
scalar_array_pow(&*at, (real_t)(j), num_sol);
scalar_array_mult(&*at, _a[j], num_sol);
scalar_array_add_vec(&*e, &*at, num_sol);
}
}
else
{
// Or in a fast one
scalar_array_add(&*e, _a[4], num_sol);
for(j=3;j>0;j--)
{
// multiply with at & add a_
for(k=0;k<num_sol;k++)
{
e[k] = e[k]*at_sol[k] + _a[j] ;
}
}
}
memcpy(&*at, &*at_sol, num_sol*sizeof(double));
// get the angle al
//scalar_array sa(at.begin(),at.end());
double sa[num_sol];
memcpy(&*sa, &*at, num_sol*sizeof(double));
scalar_array_mult(&*sa, 2.0, num_sol);
//scalar_array _ca1(at.begin(),at.end());
double _ca1[num_sol];
memcpy(&*_ca1, &*at, num_sol*sizeof(double));
scalar_array_pow(&*_ca1,2.0, num_sol);
scalar_array_add(&*_ca1,1.0, num_sol);
//scalar_array ca(at.begin(),at.end());
double ca[num_sol];
memcpy(&*ca, &*at, num_sol*sizeof(double));
scalar_array_pow(&*ca,2, num_sol);
scalar_array_negate(&*ca, num_sol);
scalar_array_add(&*ca,1.0, num_sol);
scalar_array_div_vec(&*ca, &*_ca1, num_sol);
scalar_array_div_vec(&*sa, &*_ca1, num_sol);
double al[num_sol];
scalar_array_atan2(&*al, &*sa, &*ca, num_sol);
// check the sign of the derivative
scalar_array_mult(&*al, (real_t)(180./CONST_PI), num_sol);
double _c_tMaxMin[num_sol];
//_c_tMaxMin.resize(at.size());
scalar_array_clear(&*_c_tMaxMin, num_sol);
scalar_array_add(&*_c_tMaxMin, _a[1], num_sol);
double _at[num_sol];
//_at.clear();
//_at.assign(at.begin(),at.end());
memcpy(&*_at, &*at, num_sol*sizeof(double));
scalar_array_mult(&*_at, _a[2], num_sol);
scalar_array_mult(&*_at, 2.0, num_sol);
scalar_array_add_vec(&*_c_tMaxMin, &*_at, num_sol);
for(j=3; j<=4; j++)
{
memcpy(&*_at, &*at, num_sol*sizeof(double));
scalar_array_pow(&*_at, (real_t)(j)-(real_t)(1.0), num_sol);
scalar_array_mult(&*_at, _a[j], num_sol);
scalar_array_mult(&*_at, (real_t)(j), num_sol);
scalar_array_add_vec(&*_c_tMaxMin, &*_at, num_sol);
}
double tMaxMin[num_sol];
double al_[num_sol];
int al_idx = 0, a;
memcpy(&*tMaxMin, &*_c_tMaxMin, num_sol*sizeof(double));
for(i=0; i<num_sol; i++)
{
if(tMaxMin[i] > 0) al_[al_idx++] = al[i];
}
for(a=0; a<al_idx; a++)
{
vec3_t rpy;
vec3_assign(&rpy, (real_t)0, (real_t)(al_[a] * CONST_PI / (real_t)(180)), (real_t)(0));
mat33_t R, Ry_;
rpyMat(&Ry_, &rpy);
mat33_mult_mat2(&R, Rz, &Ry_);
vec3_t t_opt;
vec3_clear(&t_opt);
for(i=0; i<n; i++)
{
mat33_t _m1, _eye3;
mat33_eye(&_eye3);
mat33_copy(&_m1, &V[i]);
mat33_sub(&_m1, &_eye3);
vec3_t _v1, _v2;
vec3_mult_mat(&_v1, &R, &p[i]);
vec3_mult_mat(&_v2, &_m1, &_v1);
vec3_add_vec(&t_opt, &_v2);
}
vec3_t t_opt_;
vec3_mult_mat(&t_opt_, &G, &t_opt);
tnew[a] = t_opt_;
}
memcpy(al_ret, &*al_, al_idx*sizeof(double));
*res_n = al_idx;
}
void objpose(mat33_t *R, vec3_t *t, int *it, real_t *obj_err, real_t *img_err,
bool calc_img_err, const vec3_t *_P, const vec3_t *Qp, const options_t options, const int n)
{
int i, j;
//vec3_array P(_P.begin(),_P.end());
vec3_t P[n];
memcpy(&*P, _P, n*sizeof(vec3_t));
//const int n = (unsigned int) P.size();
vec3_t pbar;
vec3_array_sum(&pbar, &*P, n);
vec3_div(&pbar, (real_t)(n));
vec3_array_sub(&*P, &pbar, n);
//vec3_array Q(Qp.begin(),Qp.end());
vec3_t Q[n];
memcpy(&*Q, Qp, n*sizeof(vec3_t));
vec3_t ones;
ones.v[0] = 1;
ones.v[1] = 1;
ones.v[2] = 1;
const bool mask_z[3] = {0,0,1};
vec3_array_set(&*Q, &ones, mask_z, n);
//mat33_array F;
//F.resize(n);
mat33_t F[n];
vec3_t V;
for(i=0; i<n; i++)
{
V.v[0] = Q[i].v[0] / Q[i].v[2];
V.v[1] = Q[i].v[1] / Q[i].v[2];
V.v[2] = 1.0;
mat33_t _m;
vec3_mul_vec3trans(&_m, &V, &V);
mat33_div(&_m, vec3trans_mul_vec3(&V,&V));
F[i] = _m;
}
mat33_t tFactor;
mat33_t _m1,_m2,_m3;
mat33_eye(&_m1);
mat33_array_sum(&_m2, &*F, n);
mat33_div(&_m2, (real_t)(n));
mat33_sub_mat2(&_m3, &_m1, &_m2);
mat33_inv(&tFactor, &_m3);
mat33_div(&tFactor, (real_t)(n));
*it = 0;
int initR_approximate = mat33_all_zeros(&options.initR);
mat33_t Ri;
vec3_t ti;
//vec3_array Qi;
//Qi.resize(n);
vec3_t Qi[n];
real_t old_err = 0.0, new_err = 0.0;
// ----------------------------------------------------------------------------------------
if(initR_approximate == 0)
{
mat33_copy(&Ri, &options.initR);
vec3_t _sum;
vec3_t _v1, _v2;
mat33_t _m1,_m2;
vec3_clear(&_sum);
for(j=0; j<n; j++)
{
mat33_eye(&_m1);
mat33_sub_mat2(&_m2, &F[j], &_m1);
vec3_mult_mat(&_v1, &Ri, &P[j]);
vec3_mult_mat(&_v2, &_m2, &_v1);
vec3_add_vec(&_sum, &_v2);
}
vec3_mult_mat(&ti,&tFactor,&_sum);
xform(&*Qi, &*P, &Ri, &ti, n);
old_err = 0;
vec3_t _v;
for(j=0; j<n; j++)
{
mat33_eye(&_m1);
mat33_sub_mat2(&_m2, &F[j], &_m1);
vec3_mult_mat(&_v, &_m2, &Qi[j]);
old_err += vec3_dot(&_v, &_v);
}
// ----------------------------------------------------------------------------------------
}
else
{
abskernel(&Ri, &ti, &*Qi, &old_err, &*P, &*Q, &*F, &tFactor, n);
*it = 1;
}
// ----------------------------------------------------------------------------------------
abskernel(&Ri, &ti, &*Qi, &new_err, &*P, &*Qi, &*F, &tFactor, n);
*it = *it + 1;
while((_abs((old_err-new_err)/old_err) > options.tol) && (new_err > options.epsilon) &&
(options.max_iter == 0 || *it < options.max_iter))
{
old_err = new_err;
abskernel(&Ri, &ti, &*Qi, &new_err, &*P, &*Qi, &*F, &tFactor, n);
*it = *it + 1;
}
mat33_copy(R, &Ri);
vec3_copy(t, &ti);
*obj_err = _sqrt(new_err/(real_t)(n));
if(calc_img_err == 1)
{
//vec3_array Qproj;
//Qproj.resize(n);
vec3_t Qproj[n];
xformproj(&*Qproj, &*P, &Ri, &ti, n);
*img_err = 0;
vec3_t _v;
for(j=0; j<n; j++)
{
vec3_sub_vec2(&_v, &Qproj[j], &Qp[j]);
*img_err += vec3_dot(&_v, &_v);
}
*img_err = _sqrt(*img_err/(real_t)(n));
}
if(t->v[2] < 0)
{
mat33_mult(R, -1.0);
vec3_mult(t, -1.0);
}
vec3_t _ts;
vec3_mult_mat(&_ts, &Ri, &pbar);
vec3_sub_vec(t, &_ts);
}
