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基于LM的双目图像校准算法源码第一部分

發(fā)布時間：2023/12/20 编程问答 26 豆豆

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基于LM的雙目圖像校準(zhǔn)算法源碼
代碼中調(diào)用的部分函數(shù)已作為資源上傳，這個代碼僅供咱們學(xué)習(xí)討論使用，如果需要工程使用，需要進(jìn)一步優(yōu)化。這是多年前寫得代碼，不足之處請批評指正。

float rotate[9]; float distTwoPoint(vect2f_t a,vect2f_t b) {return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y)); } int mvGetPointIndex(vect2f_t *src,int nPoint,int *index,float stepx,float stepy,int isLimit) {float thet0 = PI/2,thet1 = -PI/2;float min = 4000;float initDist,dist;vect2f_t nearpoint0,nearpoint1;int i;while(1){index[0] = rand()%nPoint;index[1] = rand()%nPoint;if(fabs(src[index[0]].x) > (stepx * HOMOGRAPHY_RANGE_POINT_NUM) || fabs(src[index[0]].y) > (stepy * HOMOGRAPHY_RANGE_POINT_NUM)|| fabs(src[index[1]].x) > (stepx * HOMOGRAPHY_RANGE_POINT_NUM) || fabs(src[index[1]].y) > (stepy * HOMOGRAPHY_RANGE_POINT_NUM)){if(isLimit)continue;}initDist = distTwoPoint(src[index[0]],src[index[1]]);if(initDist > 10.0f && initDist < 70.0f)break;}//index[0] = 0;//index[1] = 2;nearpoint0.x = -(src[index[1]].y - src[index[0]].y)*sin(thet0) + src[index[0]].x;nearpoint0.y = (src[index[1]].x - src[index[0]].x)*sin(thet0) + src[index[0]].y;nearpoint1.x = -(src[index[1]].y - src[index[0]].y)*sin(thet1) + src[index[0]].x;nearpoint1.y = (src[index[1]].x - src[index[0]].x)*sin(thet1) + src[index[0]].y;for( i = 0; i < nPoint; ++i ){if(i == index[0] || i == index[1])continue;dist = distTwoPoint(src[i],nearpoint0);if(min > dist){index[2] = i;min = dist;}dist = distTwoPoint(src[i],nearpoint1);if(min > dist){index[2] = i;min = dist;}}nearpoint0.x = -(src[index[0]].y - src[index[2]].y)*sin(thet0) + src[index[2]].x;nearpoint0.y = (src[index[0]].x - src[index[2]].x)*sin(thet0) + src[index[2]].y;nearpoint1.x = -(src[index[0]].y - src[index[2]].y)*sin(thet1) + src[index[2]].x;nearpoint1.y = (src[index[0]].x - src[index[2]].x)*sin(thet1) + src[index[2]].y;min = 4000;for( i = 0; i < nPoint; ++i ){if(i == index[0] || i == index[1]|| i == index[2])continue;dist = distTwoPoint(src[i],nearpoint0);if(min > dist){index[3] = i;min = dist;}dist = distTwoPoint(src[i],nearpoint1);if(min > dist){index[3] = i;min = dist;}}dist = distTwoPoint(src[index[0]],src[index[1]]);//printf("%f ",dist);if(dist < 10.0f || dist > 110.0f)return 0;dist = distTwoPoint(src[index[1]],src[index[2]]);//printf("%f ",dist);if(dist < 1.0f|| dist > 110.0f)return 0;dist = distTwoPoint(src[index[2]],src[index[3]]);//printf("%f ",dist);if(dist < 1.0f|| dist > 110.0f)return 0;dist = distTwoPoint(src[index[0]],src[index[2]]);//printf("%f ",dist);if(dist < 1.0f || dist > 110.0f)return 0;dist = distTwoPoint(src[index[3]],src[index[1]]);//printf("%f ",dist);if(dist < 1.0f || dist > 110.0f)return 0;dist = distTwoPoint(src[index[0]],src[index[3]]);//printf("%f\n",dist);if(dist < 1.0f || dist > 110.0f)return 0;return 1;} float getErrHomography(vect2f_t *src,vect2f_t *dst,float *R,int nPoint,float stepx,float stepy) {int j;float errSum = 0.0f;float x1,y1;int count = 0;for(j = 0;j < nPoint;j++){if(fabs(src[j].x) > (stepx * HOMOGRAPHY_RANGE_POINT_NUM) || fabs(src[j].y) > (stepy * HOMOGRAPHY_RANGE_POINT_NUM)){continue;}x1 = (R[0] * src[j].x + R[1] * src[j].y + R[2])/(R[6] * src[j].x + R[7] * src[j].y + R[8]);y1 = (R[3] * src[j].x + R[4] * src[j].y + R[5])/(R[6] * src[j].x + R[7] * src[j].y + R[8]);errSum += fabs(x1 - dst[j].x);errSum += fabs(y1 - dst[j].y);count++;}errSum = errSum/(2.0f *count);return errSum; } int mvFindHomographyProj2Img(vect2f_t *src,vect2f_t *dst,float *R,int nPoint,float stepx,float stepy,int iterations) {CvMat _J,_B,_JtJiJtB;float J[8][8],eB[8],JtJiJtB[8],filterJtJiJtB[8],Rf[9];memset(R,0,32);double a[8][8];double b[8], x[9];CvMat A = cvMat( 8, 8, CV_64FC1, a );CvMat B = cvMat( 8, 1, CV_64FC1, b );CvMat X = cvMat( 8, 1, CV_64FC1, x );int i,j,k;int index[4];float errSum = 0.0f,minErr = 10000.0f;memset(filterJtJiJtB,0,32);for(k = 0;k < 2000;k++){if(0 == mvGetPointIndex(src,nPoint,index,stepx,stepy,1))continue;for( i = 0; i < 4; ++i ){a[i + 0][0] = src[index[i]].x;a[i + 0][1] = src[index[i]].y;a[i + 0][2] = 1;a[i + 0][3] = 0;a[i + 0][4] = 0;a[i + 0][5] = 0;a[i + 0][6] = -dst[index[i]].x * src[index[i]].x;a[i + 0][7] = -dst[index[i]].x * src[index[i]].y;a[i + 4][0] = 0;a[i + 4][1] = 0;a[i + 4][2] = 0;a[i + 4][3] = src[index[i]].x;a[i + 4][4] = src[index[i]].y;a[i + 4][5] = 1;a[i + 4][6] = -dst[index[i]].y * src[index[i]].x;a[i + 4][7] = -dst[index[i]].y * src[index[i]].y;b[i + 0] = dst[index[i]].x;b[i + 4] = dst[index[i]].y;}cvSolve( &A, &B, &X, CV_SVD );x[8] = 1;for(i = 0;i < 9;i++){Rf[i] = (float)x[i];}errSum = getErrHomography(src,dst,Rf,nPoint,stepx,stepy);if(errSum < 0.01f){minErr = errSum;for(i = 0;i < 9;i++){R[i] = (float)x[i];}break;}if(minErr > errSum){for(i = 0;i < 9;i++){R[i] = (float)x[i];}minErr = errSum;}/*printf("%f %f %f\n",x[0],x[1],x[2]);printf("%f %f %f\n",x[3],x[4],x[5]);printf("%f %f %f\n",x[6],x[7],x[8]);printf("\n");*/}errSum = minErr;if(errSum > 1.0f)return 0;for(k = 0;k < iterations;k++){vect2f_t _dstCalc;if(0 == mvGetPointIndex(src,nPoint,index,stepx,stepy,1))continue;for( i = 0; i < 4; ++i ){_dstCalc.x = (R[0] * src[index[i]].x + R[1] * src[index[i]].y + R[2])/(R[6] * src[index[i]].x + R[7] * src[index[i]].y + R[8]);_dstCalc.y = (R[3] * src[index[i]].x + R[4] * src[index[i]].y + R[5])/(R[6] * src[index[i]].x + R[7] * src[index[i]].y + R[8]);J[i + 0][0] = src[index[i]].x;J[i + 0][1] = src[index[i]].y;J[i + 0][2] = 1;J[i + 0][3] = 0;J[i + 0][4] = 0;J[i + 0][5] = 0;J[i + 0][6] = -dst[index[i]].x * src[index[i]].x;J[i + 0][7] = -dst[index[i]].x * src[index[i]].y;J[i + 4][0] = 0;J[i + 4][1] = 0;J[i + 4][2] = 0;J[i + 4][3] = src[index[i]].x;J[i + 4][4] = src[index[i]].y;J[i + 4][5] = 1;J[i + 4][6] = -dst[index[i]].y * src[index[i]].x;J[i + 4][7] = -dst[index[i]].y * src[index[i]].y;eB[i + 0] = _dstCalc.x - dst[index[i]].x;eB[i + 4] = _dstCalc.y - dst[index[i]].y;b[i + 0] = dst[index[i]].x;b[i + 4] = dst[index[i]].y;}for(i = 0;i <8;i++){for(j = 0;j < 8;j++){a[i][j] = (double)J[i][j];}}cvSolve( &A, &B, &X, CV_SVD );float errSum1 = 0.0f; for(i = 0;i < 9;i++){Rf[i] = (float)x[i];}errSum1 = getErrHomography(src,dst,Rf,nPoint,stepx,stepy);if(errSum1 > 0.001f){continue;}_J = cvMat(8, 8, CV_32FC1, (float *)&J[0][0]);_JtJiJtB = cvMat(8, 1, CV_32FC1,(float *)&JtJiJtB[0]); _B = cvMat(8, 1, CV_32FC1, (float *)&eB[0]);cvSolve( &_J, &_B, &_JtJiJtB, CV_SVD );//cvSolve(&_JtJ,&_JtB,&_JtJiJtB,CV_SVD);//mvMatrixMutl(&JtJi[0][0],8,8,JtB,1,JtJiJtB);float Rtemp[9],JtJiJtBTemp[9];for(j = 0;j < 9;j++){JtJiJtBTemp[j] = filterJtJiJtB[j];Rtemp[j] = R[j];filterJtJiJtB[j] = 0.9f * filterJtJiJtB[j] + 0.1f * JtJiJtB[j];R[j] -= filterJtJiJtB[j];}float errSum2 = 0.0f;errSum2 = getErrHomography(src,dst,R,nPoint,stepx,stepy);if(errSum2 > errSum){for(j = 0;j < 9;j++){R[j] = Rtemp[j];filterJtJiJtB[j] = JtJiJtBTemp[j];}}errSum2 = getErrHomography(src,dst,R,nPoint,stepx,stepy);if(errSum2 < 0.1f){break;}}R[8] = 1.0f;return 1; } float gR[20][3][3]; void mvInitCalibCameraPointTest(const vect2f_t* objectPoints,const vect2f_t* imagePoints, int width,int hight,float stepx,float stepy,int imageCnt) {int i,j,k;vect2f_t *pObjPoint = (vect2f_t *)objectPoints,*pImgPoint = (vect2f_t *)imagePoints;vect3f_t *rotate3dAngle = (vect3f_t *)malloc(imageCnt * sizeof(vect3f_t));vect3f_t *translation3d = (vect3f_t *)malloc(imageCnt * sizeof(vect3f_t));float R[3][3];float k1 = 0.010245f;float k2 = 0.001011245f;float fx = 122.0f,fy = 122.0f;float cx = 150.0f,cy = 50.0f;float lamder = 1.0f,err = 0.0f;float x,y,x1,y1,x2,y2,x3,y3;srand((unsigned) time(NULL)); //cx = (float)(rand() % 200);//cy = (float)(rand() % 200);//printf("fx,fy,cx,cy = %f,%f,%f,%f\n\n",fx,fy,cx,cy);for(i = 0;i < imageCnt;i++){rotate3dAngle[i].x = ((float)(rand() % 90) - 45.0f) * PI/180.0f;rotate3dAngle[i].y = ((float)(rand() % 90) - 45.0f) * PI/180.0f;rotate3dAngle[i].z = ((float)(rand() % 90) - 45.0f) * PI/180.0f;translation3d[i].x = (float)(rand() % 201);translation3d[i].y = (float)(rand() % 201);translation3d[i].z = (float)(400 + (rand() % 100));//(float)(rand() % 51);//printf("z init = %f\n",translation3d[i].z);}for(i = 0;i < imageCnt;i++){float aerf,belt,garmer;aerf = rotate3dAngle[i].z;belt = rotate3dAngle[i].x;garmer = rotate3dAngle[i].y;R[0][0] = cos(aerf) * cos(belt);R[0][1] = cos(aerf) * sin(belt)* sin(garmer) - sin(aerf) * cos(garmer);R[0][2] = cos(aerf) * sin(belt)* cos(garmer) + sin(aerf) * sin(garmer);R[1][0] = sin(aerf) * cos(belt);R[1][1] = sin(aerf) * sin(belt)* sin(garmer) + cos(aerf) * cos(garmer);R[1][2] = sin(aerf) * sin(belt)* cos(garmer) - cos(aerf) * sin(garmer);R[2][0] = -sin(belt);R[2][1] = sin(garmer) * cos(belt);R[2][2] = cos(garmer) * cos(belt); #if 0H[0][0] = fx * R[0][0] + cx * R[2][0];H[0][1] = fx * R[0][1] + cx * R[2][1];H[0][2] = fx * R[0][2] + cx * R[2][2];H[0][3] = fx * translation3d[i].x + cx * translation3d[i].z;H[1][0] = fy * R[1][0] + cy * R[2][0];H[1][1] = fy * R[1][1] + cy * R[2][1];H[1][2] = fy * R[1][2] + cy * R[2][2];H[1][3] = fy * translation3d[i].y + cx * translation3d[i].z;H[2][0] = R[2][0];H[2][1] = R[2][1];H[2][2] = R[2][2];H[2][3] = translation3d[i].z;//printf("%f ",R[0][0] * R[0][0] + R[1][0] * R[1][0] + R[2][0] * R[2][0]);//printf("%f ",R[0][1] * R[0][1] + R[1][1] * R[1][1] + R[2][1] * R[2][1]);//printf("%f\n",R[0][2] * R[0][2] + R[1][2] * R[1][2] + R[2][2] * R[2][2]);R[0][0] = H[0][0];R[0][1] = H[0][1];R[0][2] = H[0][3];R[1][0] = H[1][0];R[1][1] = H[1][1];R[1][2] = H[1][3];R[2][0] = H[2][0];R[2][1] = H[2][1];R[2][2] = H[2][3];gR[i][0][0] = H[0][0];gR[i][0][1] = H[0][1];gR[i][0][2] = H[0][3];gR[i][1][0] = H[1][0];gR[i][1][1] = H[1][1];gR[i][1][2] = H[1][3];gR[i][2][0] = H[2][0];gR[i][2][1] = H[2][1];gR[i][2][2] = H[2][3]; #elsegR[i][0][0] = (float)(fx * R[0][0] + cx * R[2][0]);gR[i][0][1] = (float)(fx * R[0][1] + cx * R[2][1]);gR[i][0][2] = (float)(fx * translation3d[i].x + cx * translation3d[i].z);gR[i][1][0] = (float)(fy * R[1][0] + cy * R[2][0]);gR[i][1][1] = (float)(fy * R[1][1] + cy * R[2][1]);gR[i][1][2] = (float)(fy * translation3d[i].y + cx * translation3d[i].z);gR[i][2][0] = (float)R[2][0];gR[i][2][1] = (float)R[2][1];gR[i][2][2] = (float)(translation3d[i].z);R[0][2] = translation3d[i].x;R[1][2] = translation3d[i].y;R[2][2] = translation3d[i].z; #endiffor(j = 0;j < hight;j++){for(k = 0;k < width;k++){pObjPoint[j * width + k].x = stepx * (k + 1);pObjPoint[j * width + k].y = stepy * (j + 1);x = stepx * (k + 1);y = stepy * (j + 1);x1 = (R[0][0] * x + R[0][1] * y + R[0][2])/(R[2][0] * x + R[2][1] * y + R[2][2]);y1 = (R[1][0] * x + R[1][1] * y + R[1][2])/(R[2][0] * x + R[2][1] * y + R[2][2]);double x2y2square = x1 * x1 + y1 * y1;double square2 = x2y2square * x2y2square;double square3 = x2y2square * x2y2square * x2y2square;double square4 = x2y2square * x2y2square * x2y2square * x2y2square;double scalek1 = k1 * square2;double scalek2 = k2 * square4;x2 = x1 * (1 + k1 * (float)square2 + k2 * (float)square4);y2 = y1 * (1 + k1 * (float)square2 + k2 * (float)square4);x3 = fx * x2 + cx;y3 = fy * y2 + cy;pImgPoint[(j) * width + k].x = (float)x3;pImgPoint[(j) * width + k].y = (float)y3;}}//float estR[9];//mvFindHomography(pObjPoint,pImgPoint,estR,(width - 1) * (hight - 1),200);//printf("%f %f %f\n",estR[0],estR[1],estR[2]);//printf("%f %f %f\n",estR[3],estR[4],estR[5]);//printf("%f %f %f\n",estR[6],estR[7],estR[8]);//printf("\n\n");pObjPoint += width * hight;pImgPoint += width * hight;} }int mvCalibCameraParams(const vect2f_t* objectPoints,const vect2f_t* imagePoints, int width,int hight,int imageCnt,float stepx,float stepy,matrix_t* A) {int hcount = 0;int i,j,k,m,n,p;int homographyCnt = width * hight;float mHt[3][3],**gHt;vect2f_t *pObjPoint = 0,*pImgPoint = 0;double h11,h12,h13,h21,h22,h23;double err = 0.0f;float fx = 0.0f,fy = 0.0f,cx = 0.0f,cy = 0.0f;float maxPoint = 0.0f,minPoint = 100000.0f;float *x0Param = (float *)malloc((imageCnt * imageCnt * imageCnt * imageCnt * imageCnt) * sizeof(float));float *x1Param = (float *)malloc((imageCnt * imageCnt * imageCnt * imageCnt * imageCnt) * sizeof(float));float *y0Param = (float *)malloc((imageCnt * imageCnt * imageCnt * imageCnt * imageCnt) * sizeof(float));float *y1Param = (float *)malloc((imageCnt * imageCnt * imageCnt * imageCnt * imageCnt) * sizeof(float));double *k1k2 = (double *)malloc(4 * homographyCnt * imageCnt * sizeof(double));double *pd = (double *)malloc(2 * homographyCnt * imageCnt * sizeof(double));int *validImage = (int *)malloc(4 * imageCnt);gHt = (float **)malloc(imageCnt * sizeof(*gHt));if(gHt == NULL)return 0;for(i = 0;i < imageCnt;i++){gHt[i] = (float *)malloc(9 * sizeof(float));if(gHt[i] == NULL)return 0;}if(width < 2 || hight < 2 || imageCnt < 10){return 0;}if(objectPoints == NULL || imagePoints == NULL || A == NULL)return 0;/*double mfx = 1.22f,mfy = 1.22f;double mcx = 13.0f,mcy = 12.0f;double mlamder = 0.2f;float mi[9],mit[9],mtim[9];mi[0] = 1/mfx; mi[1] = 0; mi[2] = -mcx/mfx;mi[3] = 0; mi[4] = 1/mfy; mi[5] = -mcy/mfy;mi[6] = 0; mi[7] = 0; mi[8] = 1;mit[0] = 1/mfx; mit[1] = 0; mit[2] = 0;mit[3] = 0; mit[4] = 1/mfy; mit[5] = 0;mit[6] = -mcx/mfx; mit[7] = -mcy/mfy; mit[8] = 1;mvMatrixMutl(mit,3,3,mi,3,mtim);b[0] = 1/(mfx * mfx);b[1] = 0.0f;b[2] = 1/(mfy * mfy);b[3] = -mcx/(mfx * mfx);b[4] = -mcy/(mfy * mfy);b[5] = (mcx/mfx) * (mcx/mfx) + (mcy/mfy) * (mcy/mfy);fx = sqrt(fabs(1.0f/b[0]));fy = sqrt(fabs(1.0f/b[2]));cx = -b[3] * fx * fx;cy = -b[4] * fy * fy;float b[7] = {mtim[0],mtim[1],mtim[4],mtim[6],mtim[7],mtim[8],1.0f};*/pObjPoint = (vect2f_t *)objectPoints;pImgPoint = (vect2f_t *)imagePoints;CvMat _pt1, _pt2,_mHt;double Hdata[7][7],Bb[7],Bres[7];int count = 0,failFalg = 0;for(i = 0;i < imageCnt;i++){float *pGht = gHt[i];/*printf("%f %f %f\n",gR[i][0][0],gR[i][0][1],gR[i][0][2]);printf("%f %f %f\n",gR[i][1][0],gR[i][1][1],gR[i][1][2]);printf("%f %f %f\n",gR[i][2][0],gR[i][2][1],gR[i][2][2]);*/validImage[i] = mvFindHomographyProj2Img(&pObjPoint[i * homographyCnt],&pImgPoint[i * homographyCnt],pGht,homographyCnt,stepx,stepy,200);if(validImage[i] == 0){printf("i falid %d\n",i);continue;}/*if(fabs(gR[i][0][0] - pGht[0]) > 1.0f || fabs(gR[i][0][1] - pGht[1]) > 1.0f){printf("\n");printf("%f %f %f\n",gR[i][0][0],gR[i][0][1],gR[i][0][2]);printf("%f %f %f\n",gR[i][1][0],gR[i][1][1],gR[i][1][2]);printf("%f %f %f\n",gR[i][2][0],gR[i][2][1],gR[i][2][2]);printf("\n");printf("%f %f %f\n",pGht[0],pGht[1],pGht[2]);printf("%f %f %f\n",pGht[3],pGht[4],pGht[5]);printf("%f %f %f\n",pGht[6],pGht[7],pGht[8]);printf("\n\n");}*/}for(p = 0;p < (imageCnt - 2);p++){for(k = p + 1;k < (imageCnt - 1);k++){for(m = k + 1;m < imageCnt;m++){failFalg = 0;int index[3] = {p,k,m};if(validImage[p] == 0)continue;if(validImage[k] == 0)continue;if(validImage[m] == 0)continue;for(n = 0;n < 3;n++){//float estR[9];//cvFindHomography(&_pt1,&_pt2,&_mHt);float *pGht = gHt[index[n]];mHt[0][0] = pGht[0];mHt[0][1] = pGht[1];mHt[0][2] = pGht[2];mHt[1][0] = pGht[3];mHt[1][1] = pGht[4];mHt[1][2] = pGht[5];mHt[2][0] = pGht[6];mHt[2][1] = pGht[7];mHt[2][2] = pGht[8];h11 = mHt[0][0];h12 = mHt[1][0];h13 = mHt[2][0];h21 = mHt[0][1];h22 = mHt[1][1];h23 = mHt[2][1];/*printf("\n");printf("%f %f %f\n",mHt[0][0],mHt[0][1],mHt[0][2]);printf("%f %f %f\n",mHt[1][0],mHt[1][1],mHt[1][2]);printf("%f %f %f\n",mHt[2][0],mHt[2][1],mHt[2][2]);printf("\n");*//*h11 = gR[n][0][0];h12 = gR[n][1][0];h13 = gR[n][2][0];h21 = gR[n][0][1];h22 = gR[n][1][1];h23 = gR[n][2][1];*/double v12[7] = {h11 * h21,h11 * h22 + h12 * h21,h12 * h22,h13 * h21 + h11 * h23,h13 * h22 + h12 * h23,h13 * h23,h13 * h23};double v11[7] = {h11 * h11,h11 * h12 + h12 * h11,h12 * h12,h13 * h11 + h11 * h13,h13 * h12 + h12 * h13,h13 * h13,h13 * h13};double v22[7] = {h21 * h21,h21 * h22 + h22 * h21,h22 * h22,h23 * h21 + h21 * h23,h23 * h22 + h22 * h23,h23 * h23,h23 * h23};for(i = 0;i < 6;i++){Hdata[2 * n][i] = v12[i];}Hdata[2 * n][6] = v12[6];Bb[2 * n + 0] = Hdata[2 * n][0];for(i = 0;i < 6;i++){Hdata[2 * n + 1][i] = (v11[i] - v22[i]);}Hdata[2 * n + 1][6] = (v11[0] - v22[0]);Bb[2 * n + 1] = Hdata[2 * n + 1][0];/*double sum0 = 0.0f, sum1 = 0.0f;for(i = 0;i < 6;i++){sum0 += v12[i] * b[i];sum1 += (v11[i] - v22[i]) * b[i];}if(fabs(sum0) > 0.0001f || fabs(sum1) > 0.0001f ){failFalg = 1;}*/}/*if(failFalg){continue;}*/double max = -10000.0f;for(i = 0;i < 6;i++){for(j = 0;j < 6;j++){if(fabs(Hdata[i][j]) > max){max = fabs(Hdata[i][j]);}}}Hdata[6][0] = 0;Hdata[6][1] = 0;Hdata[6][2] = 0;Hdata[6][3] = 0;Hdata[6][4] = 0;Hdata[6][5] = 0;Hdata[6][6] = 1;for(i = 0;i < 7;i++){for(j = 0;j < 7;j++){Hdata[i][j] = Hdata[i][j]/max;}}Bb[6] = 1.0f;for(i = 0;i < 7;i++){Bb[i] = Bb[i]/max;}//mvMatrixTrans((float *)H.pdata,6,6,(float *)&Ht[0]);//mvMatrixMutl(&Ht[0],6,6,H.pdata,6,&HtH[0]);//mvJacobiEigens_32f(HtH,W,B.pdata,6,0.0001f);_pt1 = cvMat(7, 7, CV_64FC1, (double *)&Hdata[0][0] );_pt2 = cvMat(7, 1, CV_64FC1, (double *)&Bb[0] );_mHt = cvMat(7, 1, CV_64FC1, Bres);cvSolve( &_pt1, &_pt2, &_mHt, CV_SVD );double B11,B12,B13,B22,B23,B33,B00,deltFx,deltFy,deltCx,deltCy;B11 = Bres[0];B12 = Bres[1];B13 = Bres[2];B22 = Bres[3];B23 = Bres[4];B33 = Bres[5];B00 = Bres[6];deltFx = sqrt(fabs(1.0f/B11));deltFy = sqrt(fabs(1.0f/B13));deltCx = fabs(-B22 * deltFx * deltFx);deltCy = fabs(-B23 * deltFy * deltFy);double a1 = mHt[0][0] - deltCx * mHt[2][0] ;double b1 = mHt[0][1] - deltCy * mHt[2][1] ;double scale = deltFx/deltFy;deltFy = sqrt((a1 * a1 + scale * b1 * b1)/fabs(1 - mHt[2][0] * mHt[2][0]));deltFx = scale * deltFy;x0Param[count] = (float)deltCx;y0Param[count] = (float)deltCy;count++;//printf("%d:fx,fy,cx,cy = %f,%f,%f,%f\n",count,deltFx,deltFy,deltCx,deltCy);//printf("%d:fx,fy,cx,cy = %f,%f,%f,%f\n",count,fx,fy,cx,cy);}}}//fx = gR[n][0][0] - cx * gR[n][2][0]//printf("%d:fx,fy,cx,cy = %f,%f,%f,%f\n",count,fx/count,fy/count,cx/count,cy/count);cx = getBestVal(x0Param,count,4.0f);cy = getBestVal(y0Param,count,4.0f);count = 0;for(i = 0;i < imageCnt;i++){if(validImage[i] == 0)continue;float *pGht = gHt[i];mHt[0][0] = pGht[0];mHt[0][1] = pGht[1];mHt[0][2] = pGht[2];mHt[1][0] = pGht[3];mHt[1][1] = pGht[4];mHt[1][2] = pGht[5];mHt[2][0] = pGht[6];mHt[2][1] = pGht[7];mHt[2][2] = pGht[8];double r31,r32;r31 = mHt[2][0];r32 = mHt[2][1]; #if 0deltFx = 122.0f;deltFy = 122.0f;double r11,r12,r21,r22;r31 = mHt[2][0];r32 = mHt[2][1];r11 = (mHt[0][0] - deltCx * r31)/deltFx;r21 = (mHt[1][0] - deltCy * r31)/deltFx;r12 = (mHt[0][1] - deltCx * r32)/deltFy;r22 = (mHt[1][1] - deltCy * r32)/deltFy;double mod0,mod1;mod0 = r11 * r11 + r21 * r21 + r31 * r31;mod1 = r12 * r12 + r22 * r22 + r32 * r32;printf("mod = %f %f\n",mod0 * 40000.0f,mod1 * 40000.0f);if(fabs(mod0 - 1.0f) > 0.1f || fabs(mod1 - 1.0f) > 0.1f){continue;}#endifdouble a,b,c,d,yy;a = (mHt[0][0] - cx * r31);b = (mHt[1][0] - cy * r31);c = (mHt[0][1] - cx * r32);d = (mHt[1][1] - cy * r32);double ff = (a * c * (b * b - d * d) - d * b * (a * a - c * c))/(a * c * (r32 * r32 - r31 * r31) + r31 * r32 * (a * a - c * c));if(fabs(ff) < 0.001f)continue;yy = 1.0f/ff;if(ff < 0.0f)continue;fy = (float)sqrt(ff);fx = (float)sqrt((a * a - c * c)/((r32 * r32 - r31 * r31) - (b * b - d * d) * yy));//fx = scale * deltFy;//printf("f = %f %f\n",fx,fy);x0Param[count] = fx;y0Param[count] = fy;count++;}fx = getBestVal(x0Param,count,4.0f);fy = getBestVal(y0Param,count,4.0f);printf("fx,fy,cx,cy = %f,%f,%f,%f\n",fx,fy,cx,cy);float mi[9],R[9];mi[0] = 1/fx; mi[1] = 0; mi[2] = -cx/fx;mi[3] = 0; mi[4] = 1/fy; mi[5] = -cy/fy;mi[6] = 0; mi[7] = 0; mi[8] = 1;float k1 = 0.0f,k2 = 0.0f;int kCnt = 0;double _k[2];for(n = 0;n < imageCnt;n++){if(validImage[n] == 0)continue;float *pGht = gHt[n];mvMatrixMutl(mi,3,3,pGht,3,R);//printf("%f\n",R[0] * R[0] + R[3] * R[3] + R[6] * R[6]);//printf("%f\n",R[1] * R[1] + R[4] * R[4] + R[7] * R[7]);memcpy(pGht,R,36);double *_k1k2 = &k1k2[4 * kCnt * homographyCnt];double *d = &pd[2 * kCnt * homographyCnt];double x1,y1,x2,y2;for(i = 0;i < homographyCnt;i++){vect2f_t pT = pObjPoint[n * homographyCnt + i];vect2f_t iT = pImgPoint[n * homographyCnt + i];x1 = (R[0] * pT.x + R[1] * pT.y + R[2])/(R[6] * pT.x + R[7] * pT.y + R[8]);y1 = (R[3] * pT.x + R[4] * pT.y + R[5])/(R[6] * pT.x + R[7] * pT.y + R[8]);double x2y2square = x1 * x1 + y1 * y1;double square2 = x2y2square * x2y2square;double square3 = x2y2square * x2y2square * x2y2square;double square4 = x2y2square * x2y2square * x2y2square * x2y2square;x2 = (iT.x - cx)/fx;y2 = (iT.y - cy)/fy;_k1k2[4 * i + 0] = x1 * square2;_k1k2[4 * i + 1] = x1 * square4;d[2 * i + 0] = x2 - x1;_k1k2[4 * i + 2] = y1 * square2;_k1k2[4 * i + 3] = y1 * square4;d[2 * i + 1] = y2 - y1;}//x0Param[2 * kCnt + 0] = sqrt(1.0f/(R[0] * R[0] + R[3] * R[3] + R[6] * R[6]));//x0Param[2 * kCnt + 1] = sqrt(1.0f/(R[1] * R[1] + R[4] * R[4] + R[7] * R[7]));//printf("z0 = %f\n",sqrt(1.0f/(R[0] * R[0] + R[3] * R[3] + R[6] * R[6])));//printf("z1 = %f\n",sqrt(1.0f/(R[1] * R[1] + R[4] * R[4] + R[7] * R[7])));kCnt++;}_pt1 = cvMat(kCnt * homographyCnt * 2, 2, CV_64FC1, k1k2);_pt2 = cvMat(kCnt * homographyCnt * 2, 1, CV_64FC1, pd );_mHt = cvMat(2, 1, CV_64FC1, _k);cvSolve( &_pt1, &_pt2, &_mHt, CV_SVD );_k[0] = _k[0] * 2.0f;_k[1] = _k[1] * 1.2f;//float z = getBestVal(x0Param,kCnt * 2,4.0f);//printf("k1,k2 = %f,%f\n",_k[0],_k[1]);A->pdata[0] = fx;A->pdata[1] = 0;A->pdata[2] = cx;A->pdata[3] = 0;A->pdata[4] = fy;A->pdata[5] = cy;A->pdata[6] = 0;A->pdata[7] = 0;A->pdata[8] = 1;mvBPCalcCameraParams(objectPoints,imagePoints,validImage,width,hight,imageCnt,stepx,stepy,A,_k,gHt);for(i = 0;i < imageCnt;i++){free(gHt[i]);}free(gHt);free(x0Param);free(x1Param);free(y0Param);free(y1Param);free(k1k2);free(pd);free(validImage);return 1;} float yt[1000]; float xt[1000]; float getBestVal(float *pVal,int count,float limit) {float maxValid = 0;int validCnt;int i,j;float validVal = 0.0f;float validSum = 0.0f;for(i = 0;i < (count - 1);i++){validCnt = 0;for(j = i;j < count;j++){if(fabs(pVal[i] - pVal[j]) < limit){validCnt++;}}if(validCnt > (int)maxValid){maxValid = (float)validCnt;validVal = pVal[i];}}validCnt = 0;for(j = 0;j < count;j++){if(fabs(validVal - pVal[j]) < limit){validCnt++;validSum += pVal[j];}}return (validSum/validCnt); } void LMTest(void) {int i,j;float a1 = 1;float b1 = 1;float c1 = 1;float d1 = 1;#define LM_SIZE 4#define PARAM_NUM 16for(i = 0;i < 1000;i++){xt[i] = (i - 500) * 0.1f;float temp = 2.5f * xt[i];yt[i] = 2.36f* temp * temp + 3.345f * temp + 4.1f;}float J[LM_SIZE][LM_SIZE],Jt[LM_SIZE][LM_SIZE],JtJ[LM_SIZE][LM_SIZE],P[LM_SIZE],e[LM_SIZE],Je[LM_SIZE],JtJi[LM_SIZE][LM_SIZE],JtJiJ[LM_SIZE][LM_SIZE];CvMat _J, _Jt,_JtJ,_P,_e,_Je,_JtJi;_J = cvMat(LM_SIZE, LM_SIZE, CV_32FC1, (double *)&J[0][0] );_Jt = cvMat(LM_SIZE, LM_SIZE, CV_32FC1, (double *)&Jt[0][0] );_JtJ = cvMat(LM_SIZE, LM_SIZE, CV_32FC1, (double *)&JtJ[0][0] );_JtJi = cvMat(LM_SIZE, LM_SIZE, CV_32FC1, (double *)&JtJi[0][0] );_P = cvMat(LM_SIZE, 1, CV_32FC1, P);_e = cvMat(LM_SIZE, 1, CV_32FC1, e);_Je = cvMat(LM_SIZE, 1, CV_32FC1, Je);float temp; for(j = 0;j < 6000;j++){for(i = 0;i < LM_SIZE;i++){int idx = rand() % 1000;printf("idx = %d\n",idx);temp = d1 * xt[idx];float ytt0 = a1 * temp * temp + b1 * temp + c1;J[i][0] = temp * temp;J[i][1] = temp;J[i][2] = 1;J[i][3] = (2.0f * a1 * temp + b1) * xt[idx];e[i] = ytt0 - yt[idx];}mvMatrixTrans((float *)&J[0][0],LM_SIZE,LM_SIZE,(float *)&Jt[0][0]);mvMatrixMutl((float *)&Jt[0][0],LM_SIZE,LM_SIZE,(float *)&J[0][0],LM_SIZE,(float *)&JtJ[0][0]);cvInvert(&_JtJ,&_JtJi,CV_SVD);mvMatrixMutl((float *)&JtJi[0][0],LM_SIZE,LM_SIZE,(float *)&Jt[0][0],LM_SIZE,(float *)&JtJiJ[0][0]);mvMatrixMutl((float *)&JtJiJ[0][0],LM_SIZE,LM_SIZE,(float *)e,1,(float *)&P[0]);//cvGEMM(&_J,&_e,1,NULL,1,&_Je);//cvGEMM(&_JtJi,&_Je,1,NULL,1,&_P);//cvSolve( &_J, &_e, &_P, CV_SVD );a1 = a1 - 0.2f * P[0];b1 = b1 - 0.2f * P[1];c1 = c1 - 0.2f * P[2];d1 = d1 - 0.2f * P[3];float err = 0.0f;float ytt0;for(i = 0;i < 1000;i++){temp = d1 * xt[i];ytt0 = a1 * temp * temp + b1 * temp + c1;err += ytt0 - yt[i];}printf("err = %f\n",err);}printf("a,b,c = %f,%f,%f",a1,b1,c1); } double getErrHomParams(vect2f_t *src,vect2f_t *dst,float *H,double fx,double fy,double cx,double cy,int nPoint) {double x1,y1,x3,y3;float *pGht = H;float mi[9],R[9];int i;double errSum = 0.0f;mi[0] = (float)1/(float)fx; mi[1] = 0; mi[2] = -(float)cx/(float)fx;mi[3] = 0; mi[4] = (float)1/(float)fy; mi[5] = -(float)cy/(float)fy;mi[6] = 0; mi[7] = 0; mi[8] = 1;mvMatrixMutl(mi,3,3,H,3,R);vect2f_t *_imgPoint = src;vect2f_t *_prjPoint = dst;for(i = 0;i < nPoint;i++){vect2f_t pT = _prjPoint[i];x1 = (R[0] * pT.x + R[1] * pT.y + R[2])/(R[6] * pT.x + R[7] * pT.y + R[8]);y1 = (R[3] * pT.x + R[4] * pT.y + R[5])/(R[6] * pT.x + R[7] * pT.y + R[8]); /*double x2y2square = x1 * x1 + y1 * y1;double square2 = x2y2square * x2y2square;double square3 = x2y2square * x2y2square * x2y2square;double square4 = x2y2square * x2y2square * x2y2square * x2y2square;double scalek1 = k1 * square2;double scalek2 = k2 * square4;x2 = x1 * (1 + k1 * square2 + k2 * square4);y2 = y1 * (1 + k1 * square2 + k2 * square4); */ x3 = fx * x1 + cx;y3 = fy * y1 + cy;errSum += fabs(x3 - _imgPoint[i].x);errSum += fabs(y3 - _imgPoint[i].y);}errSum = errSum/(2.0f *nPoint);return errSum; }double getErrCameraParams(vect2f_t *src,vect2f_t *dst,double *param,int nPoint) {int j;double errSum = 0.0f;double x,y,x1,y1,x2,y2,x3,y3;double fx,fy,cx,cy,k1,k2,R[3][3];fx = param[0];fy = param[1];cx = param[2];cy = param[3];k1 = param[4];k2 = param[5];R[0][0] = param[6];R[0][1] = param[7];R[0][2] = param[8];R[1][0] = param[9];R[1][1] = param[10];R[1][2] = param[11];R[2][0] = param[12];R[2][1] = param[13];R[2][2] = param[14];for(j = 0;j < nPoint;j++){x = (double)src[j].x;y = (double)src[j].y;x1 = (double)(R[0][0] * x + R[0][1] * y + R[0][2])/(R[2][0] * x + R[2][1] * y + R[2][2]);y1 = (double)(R[1][0] * x + R[1][1] * y + R[1][2])/(R[2][0] * x + R[2][1] * y + R[2][2]);double x2y2square = x1 * x1 + y1 * y1;double square2 = x2y2square * x2y2square;double square3 = x2y2square * x2y2square * x2y2square;double square4 = x2y2square * x2y2square * x2y2square * x2y2square;x2 = x1 * (1 + k1 * square2 + k2 * square4);y2 = y1 * (1 + k1 * square2 + k2 * square4);x3 = fx * x2 + cx;y3 = fy * y2 + cy;errSum += fabs(x3 - dst[j].x);errSum += fabs(y3 - dst[j].y);}errSum = errSum/(2.0f *nPoint);return errSum; }void mvBPCalcCameraParams(const vect2f_t* objectPoints,const vect2f_t* imagePoints, int *validImage,int width,int hight,int imageCnt, float stepx,float stepy,matrix_t* A,double *k,float **gHt) {double deltFx = 0.0f,deltFy = 0.0f,deltCx = 0.0f,deltCy = 0.0f,deltK1 = 0.0f,deltK2 = 0.0f;double deltR11 = 0.0f,deltR12 = 0.0f,deltTx = 0.0f;double deltR21 = 0.0f,deltR22 = 0.0f,deltTy = 0.0f;double deltR31 = 0.0f,deltR32 = 0.0f,deltTz = 0.0f;//float dFx,dFy,dCx,dCy,dK1,dK2,dR11,dR12,dR13,dR21,dR22,dR23,dR31,dR32,dR33;double J[16][15],e[16],delt[15],filterDelt[15],param[15],filterDeltTemp[15],paramTemp[15];double k1,k2,fx,fy,cx,cy;double x,y,x1,y1,x2,y2,x3,y3;int j;float miu = 0.2f;float scale = 0.2f;double R[3][3];int iner = 0;k1 = 0.000001f;k2 = 0.000000000001f;fx = A->pdata[0];fy = A->pdata[4];cx = A->pdata[2];cy = A->pdata[5];//LMTest();CvMat _pt1, _pt2,_delt;_pt1 = cvMat(16, 15, CV_64FC1, (double *)&J[0][0] );_pt2 = cvMat(16, 1, CV_64FC1, (double *)&e[0] );_delt = cvMat(15, 1, CV_64FC1, delt);param[0] = fx;param[1] = fy;param[2] = cx;param[3] = cy;param[4] = k[0];param[5] = k[1];double lastErr = 10000.0f;double gErr;for(int n = 0;n < imageCnt;n++){vect2f_t *pObjectPoints = (vect2f_t *)&objectPoints[n * width * hight];vect2f_t *pImagePoints = (vect2f_t *)&imagePoints[n * width * hight];if(validImage[n] == 0)continue;memset(filterDelt,0,15 * sizeof(double));float *pGht = gHt[n];R[0][0] = pGht[0];R[0][1] = pGht[1];R[0][2] = pGht[2];R[1][0] = pGht[3];R[1][1] = pGht[4];R[1][2] = pGht[5];R[2][0] = pGht[6];R[2][1] = pGht[7];R[2][2] = pGht[8];param[6] = R[0][0];param[7] = R[0][1];param[8] = R[0][2];param[9] = R[1][0];param[10] = R[1][1];param[11] = R[1][2];param[12] = R[2][0];param[13] = R[2][1];param[14] = R[2][2];gErr = getErrCameraParams(pObjectPoints,pImagePoints,param,(width * hight));if(gErr > lastErr){continue;}lastErr = gErr;iner = 0;for(;;){fx = param[0];fy = param[1];cx = param[2];cy = param[3];k1 = param[4];k2 = param[5];R[0][0] = param[6];R[0][1] = param[7];R[0][2] = param[8];R[1][0] = param[9];R[1][1] = param[10];R[1][2] = param[11];R[2][0] = param[12];R[2][1] = param[13];R[2][2] = param[14];int idxrtan[8];while(!mvGetPointIndex(pObjectPoints,width * hight,&idxrtan[0],stepx,stepy,0));while(!mvGetPointIndex(pObjectPoints,width * hight,&idxrtan[4],stepx,stepy,0));for(j = 0;j < 8;j++){int idx = idxrtan[j];x = (double)pObjectPoints[idx].x;y = (double)pObjectPoints[idx].y;x1 = (double)(R[0][0] * x + R[0][1] * y + R[0][2])/(R[2][0] * x + R[2][1] * y + R[2][2]);y1 = (double)(R[1][0] * x + R[1][1] * y + R[1][2])/(R[2][0] * x + R[2][1] * y + R[2][2]);double x2y2square = x1 * x1 + y1 * y1;double square2 = x2y2square * x2y2square;double square3 = x2y2square * x2y2square * x2y2square;double square4 = x2y2square * x2y2square * x2y2square * x2y2square;x2 = x1 * (1 + k1 * square2 + k2 * square4);y2 = y1 * (1 + k1 * square2 + k2 * square4);x3 = fx * x2 + cx;y3 = fy * y2 + cy;double dx3dx2 = fx;double dy3dy2 = fy;double dx2dx1 = 1 + k1 * x2y2square \+ 4.0f * x1 * x1 * x2y2square + k2 * square4\+ 8.0f * k2 * x1 * x1 * square3;double dy2dy1 = 1 + k1 * x2y2square \+ 4.0f * y1 * y1 * x2y2square + k2 * square4\+ 8.0f * k2 * y1 * y1 * square3;J[2 * j + 0][0] = x2;J[2 * j + 0][1] = 0;J[2 * j + 0][2] = 1;J[2 * j + 0][3] = 0;J[2 * j + 0][4] = dx3dx2 * x1 * square2;J[2 * j + 0][5] = dx3dx2 * x1 * square4;J[2 * j + 0][6] = fx * dx2dx1 * (x);J[2 * j + 0][7] = fx * dx2dx1 * (y);J[2 * j + 0][8] = fx * dx2dx1 * (1);J[2 * j + 0][9] = fx * dx2dx1 * (0);J[2 * j + 0][10] = fx * dx2dx1 * (0);J[2 * j + 0][11] = fx * dx2dx1 * (0);J[2 * j + 0][12] = fx * dx2dx1 * (-x1 * x);J[2 * j + 0][13] = fx * dx2dx1 * (-x1 * y);J[2 * j + 0][14] = fx * dx2dx1 * (x1);e[2 * j + 0] = x3 - pImagePoints[idx].x;J[2 * j + 1][0] = 0;J[2 * j + 1][1] = y2;J[2 * j + 1][2] = 0;J[2 * j + 1][3] = 1;J[2 * j + 1][4] = dy3dy2 * y1 * square2;J[2 * j + 1][5] = dy3dy2 * y1 * square4;J[2 * j + 1][6] = fy * dy2dy1 * (0);J[2 * j + 1][7] = fy * dy2dy1 * (0);J[2 * j + 1][8] = fy * dy2dy1 * (0);J[2 * j + 1][9] = fy * dy2dy1 * (x);J[2 * j + 1][10] = fy * dy2dy1 * (y);J[2 * j + 1][11] = fy * dy2dy1 * (1);J[2 * j + 1][12] = fy * dy2dy1 * (-y1 * x);J[2 * j + 1][13] = fy * dy2dy1 * (-y1 * y);J[2 * j + 1][14] = fy * dy2dy1 * (y1);e[2 * j + 1] = y3 - pImagePoints[idx].y;}cvSolve( &_pt1, &_pt2, &_delt, CV_SVD );memcpy(filterDeltTemp,filterDelt,sizeof(filterDelt));memcpy(paramTemp,param,sizeof(param));for(j = 0;j < 15;j++){filterDelt[j] = 0.8f * filterDelt[j] + 0.2f * delt[j];}for(j = 0;j < 15;j++){param[j] = param[j] - 0.2f * filterDelt[j];}gErr = getErrCameraParams(pObjectPoints,pImagePoints,param,(width * hight));if(gErr > lastErr){memcpy(filterDelt,filterDeltTemp,sizeof(filterDelt));memcpy(param,paramTemp,sizeof(param));//break;}else{lastErr = gErr;}iner++;if(iner > 5000){n = imageCnt;break;}if(gErr < 0.1f){n = imageCnt;break;}}}k[0] = k1 * 1.2f;k[1] = k2 * 1.2f;printf("best = %f,%f,%f,%f,%f,%f\n",fx,fy,cx,cy,k1,k2);printf("ERR = %f\n",gErr);if(gErr > 0.1f){printf("calib image failed!\n\n\n\n");}A->pdata[0] = (float)fx;A->pdata[1] = 0;A->pdata[2] = (float)cx;A->pdata[3] = 0;A->pdata[4] = (float)fy;A->pdata[5] = (float)cy;A->pdata[6] = 0;A->pdata[7] = 0;A->pdata[8] = 1;}

歡迎使用Markdown編輯器

你好！這是你第一次使用 Markdown編輯器 所展示的歡迎頁。如果你想學(xué)習(xí)如何使用Markdown編輯器, 可以仔細(xì)閱讀這篇文章，了解一下Markdown的基本語法知識。

新的改變

我們對Markdown編輯器進(jìn)行了一些功能拓展與語法支持，除了標(biāo)準(zhǔn)的Markdown編輯器功能，我們增加了如下幾點(diǎn)新功能，幫助你用它寫博客：

全新的界面設(shè)計(jì) ，將會帶來全新的寫作體驗(yàn)；

在創(chuàng)作中心設(shè)置你喜愛的代碼高亮樣式，Markdown 將代碼片顯示選擇的高亮樣式 進(jìn)行展示；

增加了 圖片拖拽 功能，你可以將本地的圖片直接拖拽到編輯區(qū)域直接展示；

全新的 KaTeX數(shù)學(xué)公式 語法；

增加了支持甘特圖的mermaid語法¹ 功能；

增加了 多屏幕編輯 Markdown文章功能；

增加了 焦點(diǎn)寫作模式、預(yù)覽模式、簡潔寫作模式、左右區(qū)域同步滾輪設(shè)置 等功能，功能按鈕位于編輯區(qū)域與預(yù)覽區(qū)域中間；

增加了 檢查列表 功能。

功能快捷鍵

撤銷：Ctrl/Command + Z
重做：Ctrl/Command + Y
加粗：Ctrl/Command + B
斜體：Ctrl/Command + I
標(biāo)題：Ctrl/Command + Shift + H
無序列表：Ctrl/Command + Shift + U
有序列表：Ctrl/Command + Shift + O
檢查列表：Ctrl/Command + Shift + C
插入代碼：Ctrl/Command + Shift + K
插入鏈接：Ctrl/Command + Shift + L
插入圖片：Ctrl/Command + Shift + G

合理的創(chuàng)建標(biāo)題，有助于目錄的生成

直接輸入1次#，并按下space后，將生成1級標(biāo)題。
輸入2次#，并按下space后，將生成2級標(biāo)題。
以此類推，我們支持6級標(biāo)題。有助于使用TOC語法后生成一個完美的目錄。

如何改變文本的樣式

強(qiáng)調(diào)文本強(qiáng)調(diào)文本

加粗文本 加粗文本

標(biāo)記文本

刪除文本

引用文本

H₂O is是液體。

2¹⁰ 運(yùn)算結(jié)果是 1024.

插入鏈接與圖片

鏈接: link.

圖片:

帶尺寸的圖片:

居中的圖片:

居中并且?guī)С叽绲膱D片:

當(dāng)然，我們?yōu)榱俗層脩舾颖憬?#xff0c;我們增加了圖片拖拽功能。

如何插入一段漂亮的代碼片

去博客設(shè)置頁面，選擇一款你喜歡的代碼片高亮樣式，下面展示同樣高亮的代碼片.

// An highlighted block var foo = 'bar';

生成一個適合你的列表

項(xiàng)目
- 項(xiàng)目
  - 項(xiàng)目

項(xiàng)目1

項(xiàng)目2

項(xiàng)目3

計(jì)劃任務(wù)
完成任務(wù)

創(chuàng)建一個表格

一個簡單的表格是這么創(chuàng)建的：

項(xiàng)目Value

電腦	$1600
手機(jī)	$12
導(dǎo)管	$1

設(shè)定內(nèi)容居中、居左、居右

使用:---------:居中
使用:----------居左
使用----------:居右

第一列第二列第三列

第一列文本居中

第二列文本居右

第三列文本居左

SmartyPants

SmartyPants將ASCII標(biāo)點(diǎn)字符轉(zhuǎn)換為“智能”印刷標(biāo)點(diǎn)HTML實(shí)體。例如：

TYPEASCIIHTML

Single backticks	'Isn't this fun?'	‘Isn’t this fun?’
Quotes	"Isn't this fun?"	“Isn’t this fun?”
Dashes	-- is en-dash, --- is em-dash	– is en-dash, — is em-dash

創(chuàng)建一個自定義列表

Markdown

Text-to-HTML conversion tool

Authors

John

Luke

如何創(chuàng)建一個注腳

一個具有注腳的文本。²

注釋也是必不可少的

Markdown將文本轉(zhuǎn)換為 HTML。

KaTeX數(shù)學(xué)公式

您可以使用渲染LaTeX數(shù)學(xué)表達(dá)式 KaTeX:

Gamma公式展示 $Γ(n)=(n?1)!?n∈N\Gamma(n) = (n-1)!\quad\forall n\in\mathbb N$ 是通過歐拉積分

$Γ(z)=∫0∞tz?1e?tdt .\Gamma(z) = \int_0^\infty t^{z-1}e^{-t}dt\,.$

你可以找到更多關(guān)于的信息 LaTeX 數(shù)學(xué)表達(dá)式here.

新的甘特圖功能，豐富你的文章

Mon 06Mon 13Mon 20已完成進(jìn)行中計(jì)劃一計(jì)劃二現(xiàn)有任務(wù)Adding GANTT diagram functionality to mermaid

關(guān)于 甘特圖 語法，參考這兒,

UML 圖表

可以使用UML圖表進(jìn)行渲染。 Mermaid. 例如下面產(chǎn)生的一個序列圖：:

張三李四王五你好！李四, 最近怎么樣?你最近怎么樣，王五？我很好，謝謝!我很好，謝謝!李四想了很長時間,文字太長了不適合放在一行.打量著王五...很好... 王五, 你怎么樣?張三李四王五

這將產(chǎn)生一個流程圖。:

鏈接長方形圓圓角長方形菱形

關(guān)于 Mermaid 語法，參考這兒,

FLowchart流程圖

我們依舊會支持flowchart的流程圖：

Created with Rapha?l 2.2.0開始我的操作確認(rèn)？結(jié)束yesno

關(guān)于 Flowchart流程圖 語法，參考這兒.

導(dǎo)出與導(dǎo)入

導(dǎo)出

如果你想嘗試使用此編輯器, 你可以在此篇文章任意編輯。當(dāng)你完成了一篇文章的寫作, 在上方工具欄找到 文章導(dǎo)出 ，生成一個.md文件或者.html文件進(jìn)行本地保存。

導(dǎo)入

如果你想加載一篇你寫過的.md文件，在上方工具欄可以選擇導(dǎo)入功能進(jìn)行對應(yīng)擴(kuò)展名的文件導(dǎo)入，
繼續(xù)你的創(chuàng)作。

mermaid語法說明 ??

注腳的解釋 ??

總結(jié)

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