feature_stab/db_vlvm/db_image_homography.cpp

/*
 * 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_image_homography.cpp,v 1.2 2011/06/17 14:03:31 mbansal Exp $ */

#include "db_utilities.h"
#include "db_image_homography.h"
#include "db_framestitching.h"
#include "db_metrics.h"


/*****************************************************************
*    Lean and mean begins here                                   *
*****************************************************************/

/*Compute the linear constraint on H obtained by requiring that the
ratio between coordinate i_num and i_den of xp is equal to the ratio
between coordinate i_num and i_den of Hx. i_zero should be set to
the coordinate not equal to i_num or i_den. No normalization is used*/
inline void db_SProjImagePointPointConstraint(double c[9],int i_num,int i_den,int i_zero,
                           double xp[3],double x[3])
{
    db_MultiplyScalarCopy3(c+3*i_den,x,  xp[i_num]);
    db_MultiplyScalarCopy3(c+3*i_num,x, -xp[i_den]);
    db_Zero3(c+3*i_zero);
}

/*Compute two constraints on H generated by the correspondence (Xp,X),
assuming that Xp ~= H*X. No normalization is used*/
inline void db_SProjImagePointPointConstraints(double c1[9],double c2[9],double xp[3],double x[3])
{
    int ma_ind;

    /*Find index of coordinate of Xp with largest absolute value*/
    ma_ind=db_MaxAbsIndex3(xp);

    /*Generate 2 constraints,
    each constraint is generated by considering the ratio between a
    coordinate and the largest absolute value coordinate*/
    switch(ma_ind)
    {
    case 0:
        db_SProjImagePointPointConstraint(c1,1,0,2,xp,x);
        db_SProjImagePointPointConstraint(c2,2,0,1,xp,x);
        break;
    case 1:
        db_SProjImagePointPointConstraint(c1,0,1,2,xp,x);
        db_SProjImagePointPointConstraint(c2,2,1,0,xp,x);
        break;
    default:
        db_SProjImagePointPointConstraint(c1,0,2,1,xp,x);
        db_SProjImagePointPointConstraint(c2,1,2,0,xp,x);
    }
}

inline void db_SAffineImagePointPointConstraints(double c1[7],double c2[7],double xp[3],double x[3])
{
    double ct1[9],ct2[9];

    db_SProjImagePointPointConstraints(ct1,ct2,xp,x);
    db_Copy6(c1,ct1); c1[6]=ct1[8];
    db_Copy6(c2,ct2); c2[6]=ct2[8];
}

void db_StitchProjective2D_4Points(double H[9],
                                      double x1[3],double x2[3],double x3[3],double x4[3],
                                      double xp1[3],double xp2[3],double xp3[3],double xp4[3])
{
    double c[72];

    /*Collect the constraints*/
    db_SProjImagePointPointConstraints(c   ,c+9 ,xp1,x1);
    db_SProjImagePointPointConstraints(c+18,c+27,xp2,x2);
    db_SProjImagePointPointConstraints(c+36,c+45,xp3,x3);
    db_SProjImagePointPointConstraints(c+54,c+63,xp4,x4);
    /*Solve for the nullvector*/
    db_NullVector8x9Destructive(H,c);
}

void db_StitchAffine2D_3Points(double H[9],
                                      double x1[3],double x2[3],double x3[3],
                                      double xp1[3],double xp2[3],double xp3[3])
{
    double c[42];

    /*Collect the constraints*/
    db_SAffineImagePointPointConstraints(c   ,c+7 ,xp1,x1);
    db_SAffineImagePointPointConstraints(c+14,c+21,xp2,x2);
    db_SAffineImagePointPointConstraints(c+28,c+35,xp3,x3);
    /*Solve for the nullvector*/
    db_NullVector6x7Destructive(H,c);
    db_MultiplyScalar6(H,db_SafeReciprocal(H[6]));
    H[6]=H[7]=0; H[8]=1.0;
}

/*Compute up to three solutions for the focal length given two point correspondences
generated by a rotation with a common unknown focal length. No specific normalization
of the input points is required. If signed_disambiguation is true, the points are
required to be in front of the camera*/
inline void db_CommonFocalLengthFromRotation_2Point(double fsol[3],int *nr_sols,double x1[3],double x2[3],double xp1[3],double xp2[3],int signed_disambiguation=1)
{
    double m,ax,ay,apx,apy,bx,by,bpx,bpy;
    double p1[2],p2[2],p3[2],p4[2],p5[2],p6[2];
    double p7[3],p8[4],p9[5],p10[3],p11[4];
    double roots[3];
    int nr_roots,i,j;

    /*Solve for focal length using the equation
    <a,b>^2*<ap,ap><bp,bp>=<ap,bp>^2*<a,a><b,b>
    where a and ap are the homogenous vectors in the first image
    after focal length scaling and b,bp are the vectors in the
    second image*/

    /*Normalize homogenous coordinates so that last coordinate is one*/
    m=db_SafeReciprocal(x1[2]);
    ax=x1[0]*m;
    ay=x1[1]*m;
    m=db_SafeReciprocal(xp1[2]);
    apx=xp1[0]*m;
    apy=xp1[1]*m;
    m=db_SafeReciprocal(x2[2]);
    bx=x2[0]*m;
    by=x2[1]*m;
    m=db_SafeReciprocal(xp2[2]);
    bpx=xp2[0]*m;
    bpy=xp2[1]*m;

    /*Compute cubic in l=1/(f^2)
    by dividing out the root l=0 from the equation
    (l(ax*bx+ay*by)+1)^2*(l(apx^2+apy^2)+1)*(l(bpx^2+bpy^2)+1)=
    (l(apx*bpx+apy*bpy)+1)^2*(l(ax^2+ay^2)+1)*(l(bx^2+by^2)+1)*/
    p1[1]=ax*bx+ay*by;
    p2[1]=db_sqr(apx)+db_sqr(apy);
    p3[1]=db_sqr(bpx)+db_sqr(bpy);
    p4[1]=apx*bpx+apy*bpy;
    p5[1]=db_sqr(ax)+db_sqr(ay);
    p6[1]=db_sqr(bx)+db_sqr(by);
    p1[0]=p2[0]=p3[0]=p4[0]=p5[0]=p6[0]=1;

    db_MultiplyPoly1_1(p7,p1,p1);
    db_MultiplyPoly1_2(p8,p2,p7);
    db_MultiplyPoly1_3(p9,p3,p8);

    db_MultiplyPoly1_1(p10,p4,p4);
    db_MultiplyPoly1_2(p11,p5,p10);
    db_SubtractPolyProduct1_3(p9,p6,p11);
    /*Cubic starts at p9[1]*/
    db_SolveCubic(roots,&nr_roots,p9[4],p9[3],p9[2],p9[1]);

    for(j=0,i=0;i<nr_roots;i++)
    {
        if(roots[i]>0)
        {
            if((!signed_disambiguation) || (db_PolyEval1(p1,roots[i])*db_PolyEval1(p4,roots[i])>0))
            {
                fsol[j++]=db_SafeSqrtReciprocal(roots[i]);
            }
        }
    }
    *nr_sols=j;
}

int db_StitchRotationCommonFocalLength_3Points(double H[9],double x1[3],double x2[3],double x3[3],double xp1[3],double xp2[3],double xp3[3],double *f,int signed_disambiguation)
{
    double fsol[3];
    int nr_sols,i,best_sol,done;
    double cost,best_cost;
    double m,hyp[27],x1_temp[3],x2_temp[3],xp1_temp[3],xp2_temp[3];
    double *hyp_point,ft;
    double y[2];

    db_CommonFocalLengthFromRotation_2Point(fsol,&nr_sols,x1,x2,xp1,xp2,signed_disambiguation);
    if(nr_sols)
    {
        db_DeHomogenizeImagePoint(y,xp3);
        done=0;
        for(i=0;i<nr_sols;i++)
        {
            ft=fsol[i];
            m=db_SafeReciprocal(ft);
            x1_temp[0]=x1[0]*m;
            x1_temp[1]=x1[1]*m;
            x1_temp[2]=x1[2];
            x2_temp[0]=x2[0]*m;
            x2_temp[1]=x2[1]*m;
            x2_temp[2]=x2[2];
            xp1_temp[0]=xp1[0]*m;
            xp1_temp[1]=xp1[1]*m;
            xp1_temp[2]=xp1[2];
            xp2_temp[0]=xp2[0]*m;
            xp2_temp[1]=xp2[1]*m;
            xp2_temp[2]=xp2[2];

            hyp_point=hyp+9*i;
            db_StitchCameraRotation_2Points(hyp_point,x1_temp,x2_temp,xp1_temp,xp2_temp);
            hyp_point[2]*=ft;
            hyp_point[5]*=ft;
            hyp_point[6]*=m;
            hyp_point[7]*=m;
            cost=db_SquaredReprojectionErrorHomography(y,hyp_point,x3);

            if(!done || cost<best_cost)
            {
                done=1;
                best_cost=cost;
                best_sol=i;
            }
        }

        if(f) *f=fsol[best_sol];
        db_Copy9(H,hyp+9*best_sol);
        return(1);
    }
    else
    {
        db_Identity3x3(H);
        if(f) *f=1.0;
        return(0);
    }
}

void db_StitchSimilarity2DRaw(double *scale,double R[4],double t[2],
                            double **Xp,double **X,int nr_points,int orientation_preserving,
                            int allow_scaling,int allow_rotation,int allow_translation)
{
    int i;
    double c[2],cp[2],r[2],rp[2],M[4],s,sp,sc;
    double *temp,*temp_p;
    double Aacc,Bacc,Aacc2,Bacc2,divisor,divisor2,m,Am,Bm;

    if(allow_translation)
    {
        db_PointCentroid2D(c,X,nr_points);
        db_PointCentroid2D(cp,Xp,nr_points);
    }
    else
    {
        db_Zero2(c);
        db_Zero2(cp);
    }

    db_Zero4(M);
    s=sp=0;
    for(i=0;i<nr_points;i++)
    {
        temp=   *X++;
        temp_p= *Xp++;
        r[0]=(*temp++)-c[0];
        r[1]=(*temp++)-c[1];
        rp[0]=(*temp_p++)-cp[0];
        rp[1]=(*temp_p++)-cp[1];

        M[0]+=r[0]*rp[0];
        M[1]+=r[0]*rp[1];
        M[2]+=r[1]*rp[0];
        M[3]+=r[1]*rp[1];

        s+=db_sqr(r[0])+db_sqr(r[1]);
        sp+=db_sqr(rp[0])+db_sqr(rp[1]);
    }

    /*Compute scale*/
    if(allow_scaling) sc=sqrt(db_SafeDivision(sp,s));
    else sc=1.0;
    *scale=sc;

    /*Compute rotation*/
    if(allow_rotation)
    {
        /*orientation preserving*/
        Aacc=M[0]+M[3];
        Bacc=M[2]-M[1];
        /*orientation reversing*/
        Aacc2=M[0]-M[3];
        Bacc2=M[2]+M[1];
        if(Aacc!=0.0 || Bacc!=0.0)
        {
            divisor=sqrt(Aacc*Aacc+Bacc*Bacc);
            m=db_SafeReciprocal(divisor);
            Am=Aacc*m;
            Bm=Bacc*m;
            R[0]=  Am;
            R[1]=  Bm;
            R[2]= -Bm;
            R[3]=  Am;
        }
        else
        {
            db_Identity2x2(R);
            divisor=0.0;
        }
        if(!orientation_preserving && (Aacc2!=0.0 || Bacc2!=0.0))
        {
            divisor2=sqrt(Aacc2*Aacc2+Bacc2*Bacc2);
            if(divisor2>divisor)
            {
                m=db_SafeReciprocal(divisor2);
                Am=Aacc2*m;
                Bm=Bacc2*m;
                R[0]=  Am;
                R[1]=  Bm;
                R[2]=  Bm;
                R[3]= -Am;
            }
        }
    }
    else db_Identity2x2(R);

    /*Compute translation*/
    if(allow_translation)
    {
        t[0]=cp[0]-sc*(R[0]*c[0]+R[1]*c[1]);
        t[1]=cp[1]-sc*(R[2]*c[0]+R[3]*c[1]);
    }
    else db_Zero2(t);
}