/* * 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