| /* |
| * Copyright (C) 2011 The Android Open Source Project |
| * |
| * Licensed under the Apache License, Version 2.0 (the "License"); |
| * you may not use this file except in compliance with the License. |
| * You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| |
| /* $Id: db_metrics.h,v 1.3 2011/06/17 14:03:31 mbansal Exp $ */ |
| |
| #ifndef DB_METRICS |
| #define DB_METRICS |
| |
| |
| |
| /***************************************************************** |
| * Lean and mean begins here * |
| *****************************************************************/ |
| |
| #include "db_utilities.h" |
| /*! |
| * \defgroup LMMetrics (LM) Metrics |
| */ |
| /*\{*/ |
| |
| |
| |
| |
| /*! |
| Compute function value fp and Jacobian J of robustifier given input value f*/ |
| inline void db_CauchyDerivative(double J[4],double fp[2],const double f[2],double one_over_scale2) |
| { |
| double x2,y2,r,r2,r2s,one_over_r2,fu,r_fu,one_over_r_fu; |
| double one_plus_r2s,half_dfu_dx,half_dfu_dy,coeff,coeff2,coeff3; |
| int at_zero; |
| |
| /*The robustifier takes the input (x,y) and makes a new |
| vector (xp,yp) where |
| xp=sqrt(log(1+(x^2+y^2)*one_over_scale2))*x/sqrt(x^2+y^2) |
| yp=sqrt(log(1+(x^2+y^2)*one_over_scale2))*y/sqrt(x^2+y^2) |
| The new vector has the property |
| xp^2+yp^2=log(1+(x^2+y^2)*one_over_scale2) |
| i.e. when it is square-summed it gives the robust |
| reprojection error |
| Define |
| r2=(x^2+y^2) and |
| r2s=r2*one_over_scale2 |
| fu=log(1+r2s)/r2 |
| then |
| xp=sqrt(fu)*x |
| yp=sqrt(fu)*y |
| and |
| d(r2)/dx=2x |
| d(r2)/dy=2y |
| and |
| dfu/dx=d(r2)/dx*(r2s/(1+r2s)-log(1+r2s))/(r2*r2) |
| dfu/dy=d(r2)/dy*(r2s/(1+r2s)-log(1+r2s))/(r2*r2) |
| and |
| d(xp)/dx=1/(2sqrt(fu))*(dfu/dx)*x+sqrt(fu) |
| d(xp)/dy=1/(2sqrt(fu))*(dfu/dy)*x |
| d(yp)/dx=1/(2sqrt(fu))*(dfu/dx)*y |
| d(yp)/dy=1/(2sqrt(fu))*(dfu/dy)*y+sqrt(fu) |
| */ |
| |
| x2=db_sqr(f[0]); |
| y2=db_sqr(f[1]); |
| r2=x2+y2; |
| r=sqrt(r2); |
| |
| if(r2<=0.0) at_zero=1; |
| else |
| { |
| one_over_r2=1.0/r2; |
| r2s=r2*one_over_scale2; |
| one_plus_r2s=1.0+r2s; |
| fu=log(one_plus_r2s)*one_over_r2; |
| r_fu=sqrt(fu); |
| if(r_fu<=0.0) at_zero=1; |
| else |
| { |
| one_over_r_fu=1.0/r_fu; |
| fp[0]=r_fu*f[0]; |
| fp[1]=r_fu*f[1]; |
| /*r2s is always >= 0*/ |
| coeff=(r2s/one_plus_r2s*one_over_r2-fu)*one_over_r2; |
| half_dfu_dx=f[0]*coeff; |
| half_dfu_dy=f[1]*coeff; |
| coeff2=one_over_r_fu*half_dfu_dx; |
| coeff3=one_over_r_fu*half_dfu_dy; |
| |
| J[0]=coeff2*f[0]+r_fu; |
| J[1]=coeff3*f[0]; |
| J[2]=coeff2*f[1]; |
| J[3]=coeff3*f[1]+r_fu; |
| at_zero=0; |
| } |
| } |
| if(at_zero) |
| { |
| /*Close to zero the robustifying mapping |
| becomes identity*sqrt(one_over_scale2)*/ |
| fp[0]=0.0; |
| fp[1]=0.0; |
| J[0]=sqrt(one_over_scale2); |
| J[1]=0.0; |
| J[2]=0.0; |
| J[3]=J[0]; |
| } |
| } |
| |
| inline double db_SquaredReprojectionErrorHomography(const double y[2],const double H[9],const double x[3]) |
| { |
| double x0,x1,x2,mult; |
| double sd; |
| |
| x0=H[0]*x[0]+H[1]*x[1]+H[2]*x[2]; |
| x1=H[3]*x[0]+H[4]*x[1]+H[5]*x[2]; |
| x2=H[6]*x[0]+H[7]*x[1]+H[8]*x[2]; |
| mult=1.0/((x2!=0.0)?x2:1.0); |
| sd=db_sqr((y[0]-x0*mult))+db_sqr((y[1]-x1*mult)); |
| |
| return(sd); |
| } |
| |
| inline double db_SquaredInhomogenousHomographyError(const double y[2],const double H[9],const double x[2]) |
| { |
| double x0,x1,x2,mult; |
| double sd; |
| |
| x0=H[0]*x[0]+H[1]*x[1]+H[2]; |
| x1=H[3]*x[0]+H[4]*x[1]+H[5]; |
| x2=H[6]*x[0]+H[7]*x[1]+H[8]; |
| mult=1.0/((x2!=0.0)?x2:1.0); |
| sd=db_sqr((y[0]-x0*mult))+db_sqr((y[1]-x1*mult)); |
| |
| return(sd); |
| } |
| |
| /*! |
| Return a constant divided by likelihood of a Cauchy distributed |
| reprojection error given the image point y, homography H, image point |
| point x and the squared scale coefficient one_over_scale2=1.0/(scale*scale) |
| where scale is the half width at half maximum (hWahM) of the |
| Cauchy distribution*/ |
| inline double db_ExpCauchyInhomogenousHomographyError(const double y[2],const double H[9],const double x[2], |
| double one_over_scale2) |
| { |
| double sd; |
| sd=db_SquaredInhomogenousHomographyError(y,H,x); |
| return(1.0+sd*one_over_scale2); |
| } |
| |
| /*! |
| Compute residual vector f between image point y and homography Hx of |
| image point x. Also compute Jacobian of f with respect |
| to an update dx of H*/ |
| inline void db_DerivativeInhomHomographyError(double Jf_dx[18],double f[2],const double y[2],const double H[9], |
| const double x[2]) |
| { |
| double xh,yh,zh,mult,mult2,xh_mult2,yh_mult2; |
| /*The Jacobian of the inhomogenous coordinates with respect to |
| the homogenous is |
| [1/zh 0 -xh/(zh*zh)] |
| [ 0 1/zh -yh/(zh*zh)] |
| The Jacobian of the homogenous coordinates with respect to dH is |
| [x0 x1 1 0 0 0 0 0 0] |
| [ 0 0 0 x0 x1 1 0 0 0] |
| [ 0 0 0 0 0 0 x0 x1 1] |
| The output Jacobian is minus their product, i.e. |
| [-x0/zh -x1/zh -1/zh 0 0 0 x0*xh/(zh*zh) x1*xh/(zh*zh) xh/(zh*zh)] |
| [ 0 0 0 -x0/zh -x1/zh -1/zh x0*yh/(zh*zh) x1*yh/(zh*zh) yh/(zh*zh)]*/ |
| |
| /*Compute warped point, which is the same as |
| homogenous coordinates of reprojection*/ |
| xh=H[0]*x[0]+H[1]*x[1]+H[2]; |
| yh=H[3]*x[0]+H[4]*x[1]+H[5]; |
| zh=H[6]*x[0]+H[7]*x[1]+H[8]; |
| mult=1.0/((zh!=0.0)?zh:1.0); |
| /*Compute inhomogenous residual*/ |
| f[0]=y[0]-xh*mult; |
| f[1]=y[1]-yh*mult; |
| /*Compute Jacobian*/ |
| mult2=mult*mult; |
| xh_mult2=xh*mult2; |
| yh_mult2=yh*mult2; |
| Jf_dx[0]= -x[0]*mult; |
| Jf_dx[1]= -x[1]*mult; |
| Jf_dx[2]= -mult; |
| Jf_dx[3]=0; |
| Jf_dx[4]=0; |
| Jf_dx[5]=0; |
| Jf_dx[6]=x[0]*xh_mult2; |
| Jf_dx[7]=x[1]*xh_mult2; |
| Jf_dx[8]=xh_mult2; |
| Jf_dx[9]=0; |
| Jf_dx[10]=0; |
| Jf_dx[11]=0; |
| Jf_dx[12]=Jf_dx[0]; |
| Jf_dx[13]=Jf_dx[1]; |
| Jf_dx[14]=Jf_dx[2]; |
| Jf_dx[15]=x[0]*yh_mult2; |
| Jf_dx[16]=x[1]*yh_mult2; |
| Jf_dx[17]=yh_mult2; |
| } |
| |
| /*! |
| Compute robust residual vector f between image point y and homography Hx of |
| image point x. Also compute Jacobian of f with respect |
| to an update dH of H*/ |
| inline void db_DerivativeCauchyInhomHomographyReprojection(double Jf_dx[18],double f[2],const double y[2],const double H[9], |
| const double x[2],double one_over_scale2) |
| { |
| double Jf_dx_loc[18],f_loc[2]; |
| double J[4],J0,J1,J2,J3; |
| |
| /*Compute reprojection Jacobian*/ |
| db_DerivativeInhomHomographyError(Jf_dx_loc,f_loc,y,H,x); |
| /*Compute robustifier Jacobian*/ |
| db_CauchyDerivative(J,f,f_loc,one_over_scale2); |
| |
| /*Multiply the robustifier Jacobian with |
| the reprojection Jacobian*/ |
| J0=J[0];J1=J[1];J2=J[2];J3=J[3]; |
| Jf_dx[0]=J0*Jf_dx_loc[0]; |
| Jf_dx[1]=J0*Jf_dx_loc[1]; |
| Jf_dx[2]=J0*Jf_dx_loc[2]; |
| Jf_dx[3]= J1*Jf_dx_loc[12]; |
| Jf_dx[4]= J1*Jf_dx_loc[13]; |
| Jf_dx[5]= J1*Jf_dx_loc[14]; |
| Jf_dx[6]=J0*Jf_dx_loc[6]+J1*Jf_dx_loc[15]; |
| Jf_dx[7]=J0*Jf_dx_loc[7]+J1*Jf_dx_loc[16]; |
| Jf_dx[8]=J0*Jf_dx_loc[8]+J1*Jf_dx_loc[17]; |
| Jf_dx[9]= J2*Jf_dx_loc[0]; |
| Jf_dx[10]=J2*Jf_dx_loc[1]; |
| Jf_dx[11]=J2*Jf_dx_loc[2]; |
| Jf_dx[12]= J3*Jf_dx_loc[12]; |
| Jf_dx[13]= J3*Jf_dx_loc[13]; |
| Jf_dx[14]= J3*Jf_dx_loc[14]; |
| Jf_dx[15]=J2*Jf_dx_loc[6]+J3*Jf_dx_loc[15]; |
| Jf_dx[16]=J2*Jf_dx_loc[7]+J3*Jf_dx_loc[16]; |
| Jf_dx[17]=J2*Jf_dx_loc[8]+J3*Jf_dx_loc[17]; |
| } |
| /*! |
| Compute residual vector f between image point y and rotation of |
| image point x by R. Also compute Jacobian of f with respect |
| to an update dx of R*/ |
| inline void db_DerivativeInhomRotationReprojection(double Jf_dx[6],double f[2],const double y[2],const double R[9], |
| const double x[2]) |
| { |
| double xh,yh,zh,mult,mult2,xh_mult2,yh_mult2; |
| /*The Jacobian of the inhomogenous coordinates with respect to |
| the homogenous is |
| [1/zh 0 -xh/(zh*zh)] |
| [ 0 1/zh -yh/(zh*zh)] |
| The Jacobian at zero of the homogenous coordinates with respect to |
| [sin(phi) sin(ohm) sin(kap)] is |
| [-rx2 0 rx1 ] |
| [ 0 rx2 -rx0 ] |
| [ rx0 -rx1 0 ] |
| The output Jacobian is minus their product, i.e. |
| [1+xh*xh/(zh*zh) -xh*yh/(zh*zh) -yh/zh] |
| [xh*yh/(zh*zh) -1-yh*yh/(zh*zh) xh/zh]*/ |
| |
| /*Compute rotated point, which is the same as |
| homogenous coordinates of reprojection*/ |
| xh=R[0]*x[0]+R[1]*x[1]+R[2]; |
| yh=R[3]*x[0]+R[4]*x[1]+R[5]; |
| zh=R[6]*x[0]+R[7]*x[1]+R[8]; |
| mult=1.0/((zh!=0.0)?zh:1.0); |
| /*Compute inhomogenous residual*/ |
| f[0]=y[0]-xh*mult; |
| f[1]=y[1]-yh*mult; |
| /*Compute Jacobian*/ |
| mult2=mult*mult; |
| xh_mult2=xh*mult2; |
| yh_mult2=yh*mult2; |
| Jf_dx[0]= 1.0+xh*xh_mult2; |
| Jf_dx[1]= -yh*xh_mult2; |
| Jf_dx[2]= -yh*mult; |
| Jf_dx[3]= -Jf_dx[1]; |
| Jf_dx[4]= -1-yh*yh_mult2; |
| Jf_dx[5]= xh*mult; |
| } |
| |
| /*! |
| Compute robust residual vector f between image point y and rotation of |
| image point x by R. Also compute Jacobian of f with respect |
| to an update dx of R*/ |
| inline void db_DerivativeCauchyInhomRotationReprojection(double Jf_dx[6],double f[2],const double y[2],const double R[9], |
| const double x[2],double one_over_scale2) |
| { |
| double Jf_dx_loc[6],f_loc[2]; |
| double J[4],J0,J1,J2,J3; |
| |
| /*Compute reprojection Jacobian*/ |
| db_DerivativeInhomRotationReprojection(Jf_dx_loc,f_loc,y,R,x); |
| /*Compute robustifier Jacobian*/ |
| db_CauchyDerivative(J,f,f_loc,one_over_scale2); |
| |
| /*Multiply the robustifier Jacobian with |
| the reprojection Jacobian*/ |
| J0=J[0];J1=J[1];J2=J[2];J3=J[3]; |
| Jf_dx[0]=J0*Jf_dx_loc[0]+J1*Jf_dx_loc[3]; |
| Jf_dx[1]=J0*Jf_dx_loc[1]+J1*Jf_dx_loc[4]; |
| Jf_dx[2]=J0*Jf_dx_loc[2]+J1*Jf_dx_loc[5]; |
| Jf_dx[3]=J2*Jf_dx_loc[0]+J3*Jf_dx_loc[3]; |
| Jf_dx[4]=J2*Jf_dx_loc[1]+J3*Jf_dx_loc[4]; |
| Jf_dx[5]=J2*Jf_dx_loc[2]+J3*Jf_dx_loc[5]; |
| } |
| |
| |
| |
| /*! |
| // remove the outliers whose projection error is larger than pre-defined |
| */ |
| inline int db_RemoveOutliers_Homography(const double H[9], double *x_i,double *xp_i, double *wp,double *im, double *im_p, double *im_r, double *im_raw,double *im_raw_p,int point_count,double scale, double thresh=DB_OUTLIER_THRESHOLD) |
| { |
| double temp_valueE, t2; |
| int c; |
| int k1=0; |
| int k2=0; |
| int k3=0; |
| int numinliers=0; |
| int ind1; |
| int ind2; |
| int ind3; |
| int isinlier; |
| |
| // experimentally determined |
| t2=1.0/(thresh*thresh*thresh*thresh); |
| |
| // count the inliers |
| for(c=0;c<point_count;c++) |
| { |
| ind1=c<<1; |
| ind2=c<<2; |
| ind3=3*c; |
| |
| temp_valueE=db_SquaredInhomogenousHomographyError(im_p+ind3,H,im+ind3); |
| |
| isinlier=((temp_valueE<=t2)?1:0); |
| |
| // if it is inlier, then copy the 3d and 2d correspondences |
| if (isinlier) |
| { |
| numinliers++; |
| |
| x_i[k1]=x_i[ind1]; |
| x_i[k1+1]=x_i[ind1+1]; |
| |
| xp_i[k1]=xp_i[ind1]; |
| xp_i[k1+1]=xp_i[ind1+1]; |
| |
| k1=k1+2; |
| |
| // original normalized pixel coordinates |
| im[k3]=im[ind3]; |
| im[k3+1]=im[ind3+1]; |
| im[k3+2]=im[ind3+2]; |
| |
| im_r[k3]=im_r[ind3]; |
| im_r[k3+1]=im_r[ind3+1]; |
| im_r[k3+2]=im_r[ind3+2]; |
| |
| im_p[k3]=im_p[ind3]; |
| im_p[k3+1]=im_p[ind3+1]; |
| im_p[k3+2]=im_p[ind3+2]; |
| |
| // left and right raw pixel coordinates |
| im_raw[k3] = im_raw[ind3]; |
| im_raw[k3+1] = im_raw[ind3+1]; |
| im_raw[k3+2] = im_raw[ind3+2]; // the index |
| |
| im_raw_p[k3] = im_raw_p[ind3]; |
| im_raw_p[k3+1] = im_raw_p[ind3+1]; |
| im_raw_p[k3+2] = im_raw_p[ind3+2]; // the index |
| |
| k3=k3+3; |
| |
| // 3D coordinates |
| wp[k2]=wp[ind2]; |
| wp[k2+1]=wp[ind2+1]; |
| wp[k2+2]=wp[ind2+2]; |
| wp[k2+3]=wp[ind2+3]; |
| |
| k2=k2+4; |
| |
| } |
| } |
| |
| return numinliers; |
| } |
| |
| |
| |
| |
| |
| /*\}*/ |
| |
| #endif /* DB_METRICS */ |