1 /*
2 * Copyright (C) 2011 The Android Open Source Project
3 *
4 * Licensed under the Apache License, Version 2.0 (the "License");
5 * you may not use this file except in compliance with the License.
6 * You may obtain a copy of the License at
7 *
8 * http://www.apache.org/licenses/LICENSE-2.0
9 *
10 * Unless required by applicable law or agreed to in writing, software
11 * distributed under the License is distributed on an "AS IS" BASIS,
12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13 * See the License for the specific language governing permissions and
14 * limitations under the License.
15 */
16
17 /* $Id: db_image_homography.cpp,v 1.2 2011/06/17 14:03:31 mbansal Exp $ */
18
19 #include "db_utilities.h"
20 #include "db_image_homography.h"
21 #include "db_framestitching.h"
22 #include "db_metrics.h"
23
24
25
26 /*****************************************************************
27 * Lean and mean begins here *
28 *****************************************************************/
29
30 /*Compute the linear constraint on H obtained by requiring that the
31 ratio between coordinate i_num and i_den of xp is equal to the ratio
32 between coordinate i_num and i_den of Hx. i_zero should be set to
33 the coordinate not equal to i_num or i_den. No normalization is used*/
db_SProjImagePointPointConstraint(double c[9],int i_num,int i_den,int i_zero,double xp[3],double x[3])34 inline void db_SProjImagePointPointConstraint(double c[9],int i_num,int i_den,int i_zero,
35 double xp[3],double x[3])
36 {
37 db_MultiplyScalarCopy3(c+3*i_den,x, xp[i_num]);
38 db_MultiplyScalarCopy3(c+3*i_num,x, -xp[i_den]);
39 db_Zero3(c+3*i_zero);
40 }
41
42 /*Compute two constraints on H generated by the correspondence (Xp,X),
43 assuming that Xp ~= H*X. No normalization is used*/
db_SProjImagePointPointConstraints(double c1[9],double c2[9],double xp[3],double x[3])44 inline void db_SProjImagePointPointConstraints(double c1[9],double c2[9],double xp[3],double x[3])
45 {
46 int ma_ind;
47
48 /*Find index of coordinate of Xp with largest absolute value*/
49 ma_ind=db_MaxAbsIndex3(xp);
50
51 /*Generate 2 constraints,
52 each constraint is generated by considering the ratio between a
53 coordinate and the largest absolute value coordinate*/
54 switch(ma_ind)
55 {
56 case 0:
57 db_SProjImagePointPointConstraint(c1,1,0,2,xp,x);
58 db_SProjImagePointPointConstraint(c2,2,0,1,xp,x);
59 break;
60 case 1:
61 db_SProjImagePointPointConstraint(c1,0,1,2,xp,x);
62 db_SProjImagePointPointConstraint(c2,2,1,0,xp,x);
63 break;
64 default:
65 db_SProjImagePointPointConstraint(c1,0,2,1,xp,x);
66 db_SProjImagePointPointConstraint(c2,1,2,0,xp,x);
67 }
68 }
69
db_SAffineImagePointPointConstraints(double c1[7],double c2[7],double xp[3],double x[3])70 inline void db_SAffineImagePointPointConstraints(double c1[7],double c2[7],double xp[3],double x[3])
71 {
72 double ct1[9],ct2[9];
73
74 db_SProjImagePointPointConstraints(ct1,ct2,xp,x);
75 db_Copy6(c1,ct1); c1[6]=ct1[8];
76 db_Copy6(c2,ct2); c2[6]=ct2[8];
77 }
78
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])79 void db_StitchProjective2D_4Points(double H[9],
80 double x1[3],double x2[3],double x3[3],double x4[3],
81 double xp1[3],double xp2[3],double xp3[3],double xp4[3])
82 {
83 double c[72];
84
85 /*Collect the constraints*/
86 db_SProjImagePointPointConstraints(c ,c+9 ,xp1,x1);
87 db_SProjImagePointPointConstraints(c+18,c+27,xp2,x2);
88 db_SProjImagePointPointConstraints(c+36,c+45,xp3,x3);
89 db_SProjImagePointPointConstraints(c+54,c+63,xp4,x4);
90 /*Solve for the nullvector*/
91 db_NullVector8x9Destructive(H,c);
92 }
93
db_StitchAffine2D_3Points(double H[9],double x1[3],double x2[3],double x3[3],double xp1[3],double xp2[3],double xp3[3])94 void db_StitchAffine2D_3Points(double H[9],
95 double x1[3],double x2[3],double x3[3],
96 double xp1[3],double xp2[3],double xp3[3])
97 {
98 double c[42];
99
100 /*Collect the constraints*/
101 db_SAffineImagePointPointConstraints(c ,c+7 ,xp1,x1);
102 db_SAffineImagePointPointConstraints(c+14,c+21,xp2,x2);
103 db_SAffineImagePointPointConstraints(c+28,c+35,xp3,x3);
104 /*Solve for the nullvector*/
105 db_NullVector6x7Destructive(H,c);
106 db_MultiplyScalar6(H,db_SafeReciprocal(H[6]));
107 H[6]=H[7]=0; H[8]=1.0;
108 }
109
110 /*Compute up to three solutions for the focal length given two point correspondences
111 generated by a rotation with a common unknown focal length. No specific normalization
112 of the input points is required. If signed_disambiguation is true, the points are
113 required to be in front of the camera*/
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)114 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)
115 {
116 double m,ax,ay,apx,apy,bx,by,bpx,bpy;
117 double p1[2],p2[2],p3[2],p4[2],p5[2],p6[2];
118 double p7[3],p8[4],p9[5],p10[3],p11[4];
119 double roots[3];
120 int nr_roots,i,j;
121
122 /*Solve for focal length using the equation
123 <a,b>^2*<ap,ap><bp,bp>=<ap,bp>^2*<a,a><b,b>
124 where a and ap are the homogenous vectors in the first image
125 after focal length scaling and b,bp are the vectors in the
126 second image*/
127
128 /*Normalize homogenous coordinates so that last coordinate is one*/
129 m=db_SafeReciprocal(x1[2]);
130 ax=x1[0]*m;
131 ay=x1[1]*m;
132 m=db_SafeReciprocal(xp1[2]);
133 apx=xp1[0]*m;
134 apy=xp1[1]*m;
135 m=db_SafeReciprocal(x2[2]);
136 bx=x2[0]*m;
137 by=x2[1]*m;
138 m=db_SafeReciprocal(xp2[2]);
139 bpx=xp2[0]*m;
140 bpy=xp2[1]*m;
141
142 /*Compute cubic in l=1/(f^2)
143 by dividing out the root l=0 from the equation
144 (l(ax*bx+ay*by)+1)^2*(l(apx^2+apy^2)+1)*(l(bpx^2+bpy^2)+1)=
145 (l(apx*bpx+apy*bpy)+1)^2*(l(ax^2+ay^2)+1)*(l(bx^2+by^2)+1)*/
146 p1[1]=ax*bx+ay*by;
147 p2[1]=db_sqr(apx)+db_sqr(apy);
148 p3[1]=db_sqr(bpx)+db_sqr(bpy);
149 p4[1]=apx*bpx+apy*bpy;
150 p5[1]=db_sqr(ax)+db_sqr(ay);
151 p6[1]=db_sqr(bx)+db_sqr(by);
152 p1[0]=p2[0]=p3[0]=p4[0]=p5[0]=p6[0]=1;
153
154 db_MultiplyPoly1_1(p7,p1,p1);
155 db_MultiplyPoly1_2(p8,p2,p7);
156 db_MultiplyPoly1_3(p9,p3,p8);
157
158 db_MultiplyPoly1_1(p10,p4,p4);
159 db_MultiplyPoly1_2(p11,p5,p10);
160 db_SubtractPolyProduct1_3(p9,p6,p11);
161 /*Cubic starts at p9[1]*/
162 db_SolveCubic(roots,&nr_roots,p9[4],p9[3],p9[2],p9[1]);
163
164 for(j=0,i=0;i<nr_roots;i++)
165 {
166 if(roots[i]>0)
167 {
168 if((!signed_disambiguation) || (db_PolyEval1(p1,roots[i])*db_PolyEval1(p4,roots[i])>0))
169 {
170 fsol[j++]=db_SafeSqrtReciprocal(roots[i]);
171 }
172 }
173 }
174 *nr_sols=j;
175 }
176
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)177 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)
178 {
179 double fsol[3];
180 int nr_sols,i,best_sol,done;
181 double cost,best_cost;
182 double m,hyp[27],x1_temp[3],x2_temp[3],xp1_temp[3],xp2_temp[3];
183 double *hyp_point,ft;
184 double y[2];
185
186 db_CommonFocalLengthFromRotation_2Point(fsol,&nr_sols,x1,x2,xp1,xp2,signed_disambiguation);
187 if(nr_sols)
188 {
189 db_DeHomogenizeImagePoint(y,xp3);
190 done=0;
191 for(i=0;i<nr_sols;i++)
192 {
193 ft=fsol[i];
194 m=db_SafeReciprocal(ft);
195 x1_temp[0]=x1[0]*m;
196 x1_temp[1]=x1[1]*m;
197 x1_temp[2]=x1[2];
198 x2_temp[0]=x2[0]*m;
199 x2_temp[1]=x2[1]*m;
200 x2_temp[2]=x2[2];
201 xp1_temp[0]=xp1[0]*m;
202 xp1_temp[1]=xp1[1]*m;
203 xp1_temp[2]=xp1[2];
204 xp2_temp[0]=xp2[0]*m;
205 xp2_temp[1]=xp2[1]*m;
206 xp2_temp[2]=xp2[2];
207
208 hyp_point=hyp+9*i;
209 db_StitchCameraRotation_2Points(hyp_point,x1_temp,x2_temp,xp1_temp,xp2_temp);
210 hyp_point[2]*=ft;
211 hyp_point[5]*=ft;
212 hyp_point[6]*=m;
213 hyp_point[7]*=m;
214 cost=db_SquaredReprojectionErrorHomography(y,hyp_point,x3);
215
216 if(!done || cost<best_cost)
217 {
218 done=1;
219 best_cost=cost;
220 best_sol=i;
221 }
222 }
223
224 if(f) *f=fsol[best_sol];
225 db_Copy9(H,hyp+9*best_sol);
226 return(1);
227 }
228 else
229 {
230 db_Identity3x3(H);
231 if(f) *f=1.0;
232 return(0);
233 }
234 }
235
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)236 void db_StitchSimilarity2DRaw(double *scale,double R[4],double t[2],
237 double **Xp,double **X,int nr_points,int orientation_preserving,
238 int allow_scaling,int allow_rotation,int allow_translation)
239 {
240 int i;
241 double c[2],cp[2],r[2],rp[2],M[4],s,sp,sc;
242 double *temp,*temp_p;
243 double Aacc,Bacc,Aacc2,Bacc2,divisor,divisor2,m,Am,Bm;
244
245 if(allow_translation)
246 {
247 db_PointCentroid2D(c,X,nr_points);
248 db_PointCentroid2D(cp,Xp,nr_points);
249 }
250 else
251 {
252 db_Zero2(c);
253 db_Zero2(cp);
254 }
255
256 db_Zero4(M);
257 s=sp=0;
258 for(i=0;i<nr_points;i++)
259 {
260 temp= *X++;
261 temp_p= *Xp++;
262 r[0]=(*temp++)-c[0];
263 r[1]=(*temp++)-c[1];
264 rp[0]=(*temp_p++)-cp[0];
265 rp[1]=(*temp_p++)-cp[1];
266
267 M[0]+=r[0]*rp[0];
268 M[1]+=r[0]*rp[1];
269 M[2]+=r[1]*rp[0];
270 M[3]+=r[1]*rp[1];
271
272 s+=db_sqr(r[0])+db_sqr(r[1]);
273 sp+=db_sqr(rp[0])+db_sqr(rp[1]);
274 }
275
276 /*Compute scale*/
277 if(allow_scaling) sc=sqrt(db_SafeDivision(sp,s));
278 else sc=1.0;
279 *scale=sc;
280
281 /*Compute rotation*/
282 if(allow_rotation)
283 {
284 /*orientation preserving*/
285 Aacc=M[0]+M[3];
286 Bacc=M[2]-M[1];
287 /*orientation reversing*/
288 Aacc2=M[0]-M[3];
289 Bacc2=M[2]+M[1];
290 if(Aacc!=0.0 || Bacc!=0.0)
291 {
292 divisor=sqrt(Aacc*Aacc+Bacc*Bacc);
293 m=db_SafeReciprocal(divisor);
294 Am=Aacc*m;
295 Bm=Bacc*m;
296 R[0]= Am;
297 R[1]= Bm;
298 R[2]= -Bm;
299 R[3]= Am;
300 }
301 else
302 {
303 db_Identity2x2(R);
304 divisor=0.0;
305 }
306 if(!orientation_preserving && (Aacc2!=0.0 || Bacc2!=0.0))
307 {
308 divisor2=sqrt(Aacc2*Aacc2+Bacc2*Bacc2);
309 if(divisor2>divisor)
310 {
311 m=db_SafeReciprocal(divisor2);
312 Am=Aacc2*m;
313 Bm=Bacc2*m;
314 R[0]= Am;
315 R[1]= Bm;
316 R[2]= Bm;
317 R[3]= -Am;
318 }
319 }
320 }
321 else db_Identity2x2(R);
322
323 /*Compute translation*/
324 if(allow_translation)
325 {
326 t[0]=cp[0]-sc*(R[0]*c[0]+R[1]*c[1]);
327 t[1]=cp[1]-sc*(R[2]*c[0]+R[3]*c[1]);
328 }
329 else db_Zero2(t);
330 }
331
332
333