{"id":109570,"date":"2026-09-24T14:08:53","date_gmt":"2026-09-24T06:08:53","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/109570.html"},"modified":"2026-09-24T14:08:53","modified_gmt":"2026-09-24T06:08:53","slug":"%e5%8d%a1%e5%b0%ba%e7%ae%97%e6%b3%95%e6%b5%81%e7%a8%8b%e8%af%a6%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/109570.html","title":{"rendered":"\u5361\u5c3a\u7b97\u6cd5\u6d41\u7a0b\u8be6\u89e3"},"content":{"rendered":"

\u5361\u5c3a\u7b97\u6cd5\u6d41\u7a0b\u8be6\u89e3<\/h2>\n

\u5bf9\u5e94 detection – EdgeDetection \u6a21\u5757\u7684 RulerLinePoints \/ RulerCirclePoints \u4e24\u4e2a\u51fd\u6570\u3002<\/p>\n

1. \u5361\u5c3a\u7b97\u6cd5\u662f\u4ec0\u4e48<\/h3>\n

\u5361\u5c3a\u7b97\u6cd5（Caliper\/Ruler Algorithm）\u662f\u57fa\u4e8e 1D \u91c7\u6837\u7684\u8fb9\u7f18\u68c0\u6d4b\u65b9\u6cd5，\u6cbf\u6307\u5b9a\u65b9\u5411（\u76f4\u7ebf\u6216\u5706\u5468）\u5b9a\u4f4d\u8fb9\u7f18\u70b9\u3002\u505a\u6cd5\u662f：<\/p>\n

  • \u6cbf\u68c0\u6d4b\u7ebf\u7b49\u95f4\u8ddd\u653e\u7f6e\u591a\u4e2a"\u5361\u5c3a"<\/li>\n
  • \u6bcf\u4e2a\u5361\u5c3a\u5782\u76f4\u4e8e\u68c0\u6d4b\u7ebf\u65b9\u5411\u91c7\u6837\u56fe\u50cf\u50cf\u7d20<\/li>\n
  • \u5bf9\u91c7\u6837\u6570\u636e\u6ee4\u6ce2\u3001\u505a\u5cf0\u503c\u68c0\u6d4b<\/li>\n
  • \u5b9a\u4f4d\u4e9a\u50cf\u7d20\u7cbe\u5ea6\u7684\u8fb9\u7f18\u4f4d\u7f6e<\/li>\n

    \u7528\u5f97\u591a\u7684\u573a\u5408：\u5de5\u4e1a\u6d4b\u91cf\u7684\u96f6\u4ef6\u5c3a\u5bf8\u68c0\u6d4b\u3001\u8fb9\u7f18\u4f4d\u7f6e\u504f\u5dee\u7c7b\u7684\u7f3a\u9677\u68c0\u6d4b\u3001\u57fa\u4e8e\u8fb9\u7f18\u70b9\u7684\u56fe\u50cf\u914d\u51c6\u3001\u76f4\u7ebf\/\u5706\u5f62\u7684\u51e0\u4f55\u53c2\u6570\u4f30\u8ba1\u3002<\/p>\n

    \n

    2. RulerLinePoints \u6d41\u7a0b<\/h3>\n

    2.1 \u5b8c\u6574\u6d41\u7a0b<\/h4>\n

    \u5f00\u59cb
    \n \u2502
    \n \u251c\u2500 \u53c2\u6570\u68c0\u67e5 \u2500\u2500 \u5931\u8d25 \u2192 \u8fd4\u56de\u9519\u8bef
    \n \u2502 \u6210\u529f \u2192 \u521d\u59cb\u5316\u53d8\u91cf
    \n \u2502
    \n \u251c\u2500 \u9700\u8981\u663e\u793a\u7ed3\u679c？
    \n \u2502 \u662f \u2192 \u5148\u7ed8\u5236\u4e3b\u76f4\u7ebf
    \n \u2502 \u5426 \u2192 \u8df3\u8fc7
    \n \u2502
    \n \u251c\u2500 \u521b\u5efa\u6ee4\u6ce2\u5668\u5185\u6838
    \n \u2502
    \n \u251c\u2500 \u5916\u5c42\u5faa\u73af：n = 1 \u2026 ruler_nums，\u6bcf\u4e2a\u5361\u5c3a\u4e00\u8f6e
    \n \u2502 \u2502
    \n \u2502 \u251c\u2500 \u8ba1\u7b97\u5361\u5c3a\u4e2d\u5fc3\u4f4d\u7f6e
    \n \u2502 \u2502
    \n \u2502 \u251c\u2500 \u91c7\u6837，\u53cc\u91cd\u5faa\u73af：
    \n \u2502 \u2502 \u5916\u5c42 m = 0 \u2026 ruler_width
    \n \u2502 \u2502 \u5185\u5c42 ir = -ruler_height \u2026 ruler_height
    \n \u2502 \u2502 \u5750\u6807\u5728\u56fe\u50cf\u5185？
    \n \u2502 \u2502 \u5426 \u2192 \u91c7\u6837\u503c\u7f6e -1
    \n \u2502 \u2502 \u662f \u2192 \u53cc\u7ebf\u6027\u63d2\u503c
    \n \u2502 \u2502 \u5b58\u50a8\u91c7\u6837\u503c
    \n \u2502 \u2502 ir++ \u626b\u5b8c ruler_height \u540e m++，\u76f4\u5230\u626b\u5b8c ruler_width
    \n \u2502 \u2502
    \n \u2502 \u251c\u2500 \u8ba1\u7b97\u6295\u5f71\u5e73\u5747\u503c
    \n \u2502 \u251c\u2500 \u5e94\u7528\u6ee4\u6ce2\u5668
    \n \u2502 \u251c\u2500 \u5cf0\u503c\u68c0\u6d4b
    \n \u2502 \u2502 \u65e0\u5cf0\u503c \u2192 \u76f4\u63a5\u8fdb\u5165\u4e0b\u4e00\u4e2a n
    \n \u2502 \u2502 \u6709\u5cf0\u503c \u2192 \u6839\u636e\u9009\u62e9\u6a21\u5f0f\u7b5b\u9009\u5cf0\u503c
    \n \u2502 \u251c\u2500 \u9009\u62e9\u5cf0\u503c\u70b9
    \n \u2502 \u251c\u2500 \u4e9a\u50cf\u7d20\u5b9a\u4f4d
    \n \u2502 \u251c\u2500 \u8ba1\u7b97\u8fb9\u7f18\u5750\u6807，\u5b58\u50a8\u8fb9\u7f18\u70b9
    \n \u2502 \u2514\u2500 \u9700\u8981\u663e\u793a\u7ed3\u679c \u2192 \u7ed8\u5236\u8be5\u5361\u5c3a\u53ca\u8fb9\u7f18
    \n \u2502
    \n \u2502 n++；n > ruler_nums \u65f6\u9000\u51fa\u5faa\u73af
    \n \u2502
    \n \u2514\u2500 \u8fd4\u56de SUCCESS<\/p>\n

    2.2 \u6838\u5fc3\u6b65\u9aa4\u8be6\u89e3<\/h4>\n

    \u6b65\u9aa4 1: \u53c2\u6570\u68c0\u67e5\u4e0e\u521d\u59cb\u5316<\/h5>\n

    \/\/ \u53c2\u6570\u9a8c\u8bc1<\/span>
    \nCHECK_MAT_NOT_EMPTY<\/span>(<\/span>image)<\/span>;<\/span> \/\/ \u56fe\u50cf\u975e\u7a7a<\/span>
    \nCHECK_MAT_TYPE<\/span>(<\/span>image,<\/span> CV_8UC1)<\/span>;<\/span> \/\/ \u7070\u5ea6\u56fe\u50cf<\/span>
    \nCHECK_POINT_NOT_EMPTY<\/span>(<\/span>line.<\/span>pt1)<\/span>;<\/span> \/\/ \u8d77\u70b9\u6709\u6548<\/span>
    \nCHECK_POINT_NOT_EMPTY<\/span>(<\/span>line.<\/span>pt2)<\/span>;<\/span> \/\/ \u7ec8\u70b9\u6709\u6548<\/span><\/p>\n

    \/\/ \u521d\u59cb\u5316\u53c2\u6570<\/span>
    \nbool<\/span> show_result =<\/span> !<\/span>result_image.<\/span>empty<\/span>(<\/span>)<\/span>;<\/span> \/\/ \u662f\u5426\u663e\u793a\u7ed3\u679c<\/span>
    \nruler_width =<\/span> ruler_width <=<\/span> 0<\/span> ?<\/span> 10<\/span> :<\/span> ruler_width –<\/span> 1<\/span>;<\/span>
    \nruler_height =<\/span> ruler_height <=<\/span> 0<\/span> ?<\/span> 8<\/span> :<\/span> ruler_height;<\/span>
    \nruler_nums =<\/span> ruler_nums <=<\/span> 0<\/span> ?<\/span> 5<\/span> :<\/span> ruler_nums;<\/span><\/p>\n

    \u6b65\u9aa4 2: \u8ba1\u7b97\u76f4\u7ebf\u53c2\u6570<\/h5>\n

    \/\/ \u8f6c\u6362\u5750\u6807<\/span>
    \ncv::<\/span>Point line_st =<\/span> cv2d::<\/span>PointToCVPoint<\/span>(<\/span>line.<\/span>pt1)<\/span>;<\/span>
    \ncv::<\/span>Point line_ed =<\/span> cv2d::<\/span>PointToCVPoint<\/span>(<\/span>line.<\/span>pt2)<\/span>;<\/span><\/p>\n

    \/\/ \u8ba1\u7b97\u76f4\u7ebf\u89d2\u5ea6<\/span>
    \ndouble<\/span> t =<\/span> atan2<\/span>(<\/span>line_ed.<\/span>y –<\/span> line_st.<\/span>y,<\/span> line_ed.<\/span>x –<\/span> line_st.<\/span>x)<\/span>;<\/span><\/p>\n

    \/\/ \u8ba1\u7b97\u76f4\u7ebf\u957f\u5ea6<\/span>
    \nfloat<\/span> L =<\/span> (<\/span>float<\/span>)<\/span>cv::<\/span>norm<\/span>(<\/span>cv::<\/span>Point2d<\/span>(<\/span>line_st.<\/span>x,<\/span> line_st.<\/span>y)<\/span> –<\/span>
    \n cv::<\/span>Point2d<\/span>(<\/span>line_ed.<\/span>x,<\/span> line_ed.<\/span>y)<\/span>)<\/span>;<\/span><\/p>\n

    \/\/ \u8ba1\u7b97\u5361\u5c3a\u95f4\u8ddd<\/span>
    \nfloat<\/span> plus_step =<\/span> (<\/span>L –<\/span> ruler_nums *<\/span> ruler_width)<\/span> \/<\/span> (<\/span>ruler_nums +<\/span> 1.0f<\/span>)<\/span>;<\/span><\/p>\n

    \u6b65\u9aa4 3: \u521b\u5efa\u6ee4\u6ce2\u5668<\/h5>\n

    \/\/ \u5dee\u5206\u6ee4\u6ce2\u5668（\u8fb9\u7f18\u68c0\u6d4b）<\/span>
    \nstd::<\/span>vector<<\/span>float<\/span>><\/span> filter_kernal<\/span>(<\/span>2<\/span> *<\/span> filter_size +<\/span> 1<\/span>,<\/span> 0.0f<\/span>)<\/span>;<\/span>
    \nfor<\/span> (<\/span>int<\/span> n =<\/span> 0<\/span>;<\/span> n <<\/span> filter_size;<\/span> n++<\/span>)<\/span> {<\/span>
    \n filter_kernal[<\/span>n]<\/span> =<\/span> 1<\/span>;<\/span> \/\/ \u6b63\u7cfb\u6570（\u5de6\u4fa7）<\/span>
    \n filter_kernal[<\/span>2<\/span> *<\/span> filter_size –<\/span> n]<\/span> =<\/span> –<\/span>1<\/span>;<\/span> \/\/ \u8d1f\u7cfb\u6570（\u53f3\u4fa7）<\/span>
    \n}<\/span><\/p>\n

    \u6ee4\u6ce2\u5668\u5c31\u662f [1, 1, \u2026, -1, -1] \u5f62\u5f0f\u7684\u5dee\u5206\u6838，\u7528\u6765\u68c0\u6d4b\u7070\u5ea6\u68af\u5ea6\u53d8\u5316\u2014\u2014\u8fb9\u7f18\u5904（\u7070\u5ea6\u7a81\u53d8）\u4f1a\u8f93\u51fa\u5cf0\u503c\u3002<\/p>\n

    \u6b65\u9aa4 4: \u5faa\u73af\u5904\u7406\u6bcf\u4e2a\u5361\u5c3a<\/h5>\n

    for<\/span> (<\/span>int<\/span> n =<\/span> 1<\/span>;<\/span> n <=<\/span> ruler_nums;<\/span> n++<\/span>)<\/span> {<\/span>
    \n \/\/ 4.1 \u8ba1\u7b97\u5361\u5c3a\u4e2d\u5fc3\u4f4d\u7f6e<\/span>
    \n float<\/span> offset =<\/span> n *<\/span> (<\/span>plus_step +<\/span> ruler_width)<\/span> –<\/span> ruler_width +<\/span> ruler_width \/<\/span> 2.0f<\/span>;<\/span>
    \n cv::<\/span>Point2f center<\/span>(<\/span>
    \n line_st.<\/span>x +<\/span> offset *<\/span> cos<\/span>(<\/span>t)<\/span>,<\/span>
    \n line_st.<\/span>y +<\/span> offset *<\/span> sin<\/span>(<\/span>t)<\/span>
    \n )<\/span>;<\/span><\/p>\n

    \/\/ 4.2 \u6cbf\u5782\u76f4\u65b9\u5411\u91c7\u6837<\/span>
    \n std::<\/span>vector<<\/span>float<\/span>><\/span> samples;<\/span>
    \n for<\/span> (<\/span>float<\/span> m =<\/span> –<\/span>ruler_width \/<\/span> 2.0f<\/span>;<\/span> m <=<\/span> ruler_width \/<\/span> 2.0f<\/span>;<\/span> m +=<\/span> 1.0f<\/span>)<\/span> {<\/span>
    \n for<\/span> (<\/span>int<\/span> ir =<\/span> –<\/span>ruler_height;<\/span> ir <=<\/span> ruler_height;<\/span> ir++<\/span>)<\/span> {<\/span>
    \n \/\/ \u8ba1\u7b97\u91c7\u6837\u5750\u6807<\/span>
    \n float<\/span> x =<\/span> center.<\/span>x +<\/span> ir *<\/span> cos<\/span>(<\/span>t +<\/span> PI\/<\/span>2<\/span>)<\/span> +<\/span> m *<\/span> cos<\/span>(<\/span>t)<\/span>;<\/span>
    \n float<\/span> y =<\/span> center.<\/span>y +<\/span> ir *<\/span> sin<\/span>(<\/span>t +<\/span> PI\/<\/span>2<\/span>)<\/span> +<\/span> m *<\/span> sin<\/span>(<\/span>t)<\/span>;<\/span><\/p>\n

    \/\/ \u53cc\u7ebf\u6027\u63d2\u503c<\/span>
    \n float<\/span> value =<\/span> BilinearInterpolation<\/span>(<\/span>image,<\/span> x,<\/span> y)<\/span>;<\/span>
    \n samples.<\/span>push_back<\/span>(<\/span>value)<\/span>;<\/span>
    \n }<\/span>
    \n }<\/span><\/p>\n

    \/\/ 4.3 \u8ba1\u7b97\u6295\u5f71（\u6cbf\u5361\u5c3a\u5bbd\u5ea6\u65b9\u5411\u5e73\u5747）<\/span>
    \n std::<\/span>vector<<\/span>float<\/span>><\/span> projection;<\/span>
    \n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> 2<\/span> *<\/span> ruler_height +<\/span> 1<\/span>;<\/span> i++<\/span>)<\/span> {<\/span>
    \n float<\/span> sum =<\/span> 0<\/span>;<\/span>
    \n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <=<\/span> ruler_width;<\/span> j++<\/span>)<\/span> {<\/span>
    \n sum +=<\/span> samples[<\/span>i *<\/span> (<\/span>ruler_width +<\/span> 1<\/span>)<\/span> +<\/span> j]<\/span>;<\/span>
    \n }<\/span>
    \n projection.<\/span>push_back<\/span>(<\/span>sum \/<\/span> (<\/span>ruler_width +<\/span> 1<\/span>)<\/span>)<\/span>;<\/span>
    \n }<\/span><\/p>\n

    \/\/ 4.4 \u5e94\u7528\u6ee4\u6ce2\u5668<\/span>
    \n std::<\/span>vector<<\/span>float<\/span>><\/span> filtered =<\/span> ApplyFilter<\/span>(<\/span>projection,<\/span> filter_kernal)<\/span>;<\/span><\/p>\n

    \/\/ 4.5 \u5cf0\u503c\u68c0\u6d4b<\/span>
    \n std::<\/span>vector<<\/span>int<\/span>><\/span> peeks =<\/span> FindPeaks<\/span>(<\/span>filtered,<\/span> threshold)<\/span>;<\/span><\/p>\n

    \/\/ 4.6 \u9009\u62e9\u6700\u4f73\u5cf0\u503c<\/span>
    \n int<\/span> selected =<\/span> SelectBestPeak<\/span>(<\/span>peeks,<\/span> selection_mode)<\/span>;<\/span><\/p>\n

    \/\/ 4.7 \u4e9a\u50cf\u7d20\u5b9a\u4f4d<\/span>
    \n float<\/span> subpixel_pos =<\/span> SubpixelRefinement<\/span>(<\/span>filtered,<\/span> selected)<\/span>;<\/span><\/p>\n

    \/\/ 4.8 \u8ba1\u7b97\u8fb9\u7f18\u5750\u6807<\/span>
    \n cv::<\/span>Point2f edge_point<\/span>(<\/span>
    \n center.<\/span>x +<\/span> subpixel_pos *<\/span> cos<\/span>(<\/span>t +<\/span> PI\/<\/span>2<\/span>)<\/span>,<\/span>
    \n center.<\/span>y +<\/span> subpixel_pos *<\/span> sin<\/span>(<\/span>t +<\/span> PI\/<\/span>2<\/span>)<\/span>
    \n )<\/span>;<\/span><\/p>\n

    edge_points.<\/span>push_back<\/span>(<\/span>edge_point)<\/span>;<\/span>
    \n}<\/span><\/p>\n

    \u6b65\u9aa4 5: \u4e9a\u50cf\u7d20\u5b9a\u4f4d<\/h5>\n

    \u5bf9\u5cf0\u503c\u70b9\u53ca\u5176\u5de6\u53f3\u90bb\u57df\u505a\u4e09\u70b9\u629b\u7269\u7ebf\u62df\u5408：<\/p>\n

    \/\/ \u4e09\u70b9\u629b\u7269\u7ebf\u62df\u5408<\/span>
    \nint<\/span> m =<\/span> peak_index;<\/span> \/\/ \u5cf0\u503c\u70b9<\/span>
    \nint<\/span> l =<\/span> m –<\/span> 1<\/span>;<\/span> \/\/ \u5de6\u90bb\u57df<\/span>
    \nint<\/span> r =<\/span> m +<\/span> 1<\/span>;<\/span> \/\/ \u53f3\u90bb\u57df<\/span><\/p>\n

    float<\/span> a =<\/span> filtered[<\/span>l]<\/span>;<\/span> \/\/ \u5de6\u70b9\u68af\u5ea6<\/span>
    \nfloat<\/span> b =<\/span> filtered[<\/span>m]<\/span>;<\/span> \/\/ \u5cf0\u503c\u70b9\u68af\u5ea6<\/span>
    \nfloat<\/span> c =<\/span> filtered[<\/span>r]<\/span>;<\/span> \/\/ \u53f3\u70b9\u68af\u5ea6<\/span><\/p>\n

    \/\/ \u4e9a\u50cf\u7d20\u504f\u79fb\u516c\u5f0f<\/span>
    \nfloat<\/span> u =<\/span> 0.5f<\/span> *<\/span> (<\/span>a –<\/span> c)<\/span> \/<\/span> (<\/span>a –<\/span> 2<\/span>*<\/span>b +<\/span> c)<\/span>;<\/span><\/p>\n

    \/\/ \u6700\u7ec8\u4f4d\u7f6e（\u8303\u56f4：m-0.5 \u5230 m+0.5）<\/span>
    \nfloat<\/span> subpixel_pos =<\/span> m +<\/span> u;<\/span><\/p>\n

    \n

    3. RulerCirclePoints \u6d41\u7a0b<\/h3>\n

    3.1 \u5b8c\u6574\u6d41\u7a0b<\/h4>\n

    \u5f00\u59cb
    \n \u2502
    \n \u251c\u2500 \u53c2\u6570\u68c0\u67e5 \u2500\u2500 \u5931\u8d25 \u2192 \u8fd4\u56de\u9519\u8bef
    \n \u2502 \u6210\u529f \u2192 \u521d\u59cb\u5316\u53d8\u91cf
    \n \u2502
    \n \u251c\u2500 \u9700\u8981\u663e\u793a\u7ed3\u679c？
    \n \u2502 \u662f \u2192 \u5148\u7ed8\u5236\u4e3b\u5706
    \n \u2502 \u5426 \u2192 \u8df3\u8fc7
    \n \u2502
    \n \u251c\u2500 \u521b\u5efa\u6ee4\u6ce2\u5668
    \n \u2502
    \n \u251c\u2500 \u8ba1\u7b97\u89d2\u5ea6\u6b65\u957f plus_step = 2\u03c0 \/ ruler_nums
    \n \u2502
    \n \u251c\u2500 \u5faa\u73af：t = -\u03c0 \u2026 \u03c0，\u6b65\u957f plus_step
    \n \u2502 \u2502
    \n \u2502 \u251c\u2500 \u8ba1\u7b97\u5361\u5c3a\u4e2d\u5fc3 cx, cy = center + radius\u00b7(cos t, sin t)
    \n \u2502 \u251c\u2500 \u91c7\u6837\u5706\u5468\u65b9\u5411（\u5f84\u5411）
    \n \u2502 \u251c\u2500 \u8ba1\u7b97\u6295\u5f71\u5e73\u5747\u503c
    \n \u2502 \u251c\u2500 \u5e94\u7528\u6ee4\u6ce2\u5668
    \n \u2502 \u251c\u2500 \u5cf0\u503c\u68c0\u6d4b
    \n \u2502 \u2502 \u65e0\u5cf0\u503c \u2192 t += plus_step
    \n \u2502 \u2502 \u6709\u5cf0\u503c \u2192 \u6839\u636e\u9009\u62e9\u6a21\u5f0f\u7b5b\u9009\u5cf0\u503c
    \n \u2502 \u251c\u2500 \u4e9a\u50cf\u7d20\u5b9a\u4f4d
    \n \u2502 \u251c\u2500 \u8ba1\u7b97\u8fb9\u7f18\u5750\u6807，\u5b58\u50a8\u8fb9\u7f18\u70b9
    \n \u2502 \u2514\u2500 \u9700\u8981\u663e\u793a\u7ed3\u679c \u2192 \u7ed8\u5236\u8be5\u5361\u5c3a\u53ca\u8fb9\u7f18
    \n \u2502
    \n \u2502 t += plus_step；t \u2265 \u03c0 \u65f6\u9000\u51fa\u5faa\u73af
    \n \u2502
    \n \u2514\u2500 \u8fd4\u56de SUCCESS<\/p>\n

    3.2 \u4e0e\u76f4\u7ebf\u5361\u5c3a\u7684\u533a\u522b<\/h4>\n\n\u7279\u6027RulerLinePointsRulerCirclePoints<\/tr>\n\n\n\n\n\n\n
    \u68c0\u6d4b\u8def\u5f84<\/td>\n\u76f4\u7ebf<\/td>\n\u5706\u5468<\/td>\n<\/tr>\n
    \u5750\u6807\u8ba1\u7b97<\/td>\n\u7ebf\u6027\u63d2\u503c<\/td>\n\u6781\u5750\u6807\u8f6c\u6362<\/td>\n<\/tr>\n
    \u89d2\u5ea6\u8ba1\u7b97<\/td>\n\u56fa\u5b9a\u89d2\u5ea6 t = atan2(dy, dx)<\/td>\n\u53ef\u53d8\u89d2\u5ea6 t = -\u03c0 to \u03c0<\/td>\n<\/tr>\n
    \u5361\u5c3a\u95f4\u8ddd<\/td>\n\u7ebf\u6027\u95f4\u8ddd<\/td>\n\u89d2\u5ea6\u95f4\u8ddd plus_step = 2\u03c0\/ruler_nums<\/td>\n<\/tr>\n
    \u5361\u5c3a\u65b9\u5411<\/td>\n\u5782\u76f4\u4e8e\u76f4\u7ebf<\/td>\n\u5f84\u5411（\u5706\u5fc3\u5411\u5916）<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
    \n

    4. \u5361\u5c3a\u751f\u6210\u8fc7\u7a0b\u53ef\u89c6\u5316<\/h3>\n

    4.1 \u5361\u5c3a\u7ed3\u6784\u793a\u610f<\/h4>\n

    \u5361\u5c3a（Caliper）\u7ed3\u6784：<\/p>\n

    \u2191 \u641c\u7d22\u65b9\u5411
    \n |
    \n | ruler_height (\u9ad8\u5ea6)
    \n |
    \n \u2193
    \n \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510
    \n \u2502 \u2502 ruler_width (\u5bbd\u5ea6)
    \n \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u91c7\u6837\u7ebf \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u2502
    \n \u2502 \u2502
    \n \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u91c7\u6837\u7ebf \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u2502
    \n \u2502 \u2502
    \n \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u91c7\u6837\u7ebf \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u2502
    \n \u2502 \u2502
    \n \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u91c7\u6837\u7ebf \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u2502
    \n \u2502 \u2502
    \n \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u91c7\u6837\u7ebf \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u2502
    \n \u2502 \u2502
    \n \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518
    \n \u2191
    \n |
    \n \u4e2d\u5fc3\u70b9
    \n (\u5728\u68c0\u6d4b\u7ebf\u4e0a）<\/p>\n

    4.2 \u76f4\u7ebf\u5361\u5c3a\u751f\u6210\u8fc7\u7a0b<\/h4>\n

    \u793a\u4f8b\u914d\u7f6e：\u56fe\u50cf 800 \u00d7 600，\u76f4\u7ebf (100, 300) \u2192 (700, 300)，ruler_nums = 5，ruler_width = 10，ruler_height = 20\u3002<\/p>\n

    \u751f\u6210\u8fc7\u7a0b：<\/p>\n

    \u6b65\u9aa4 1: \u7ed8\u5236\u4e3b\u76f4\u7ebf
    \n (100,300) \u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501 (700,300)<\/p>\n

    \u6b65\u9aa4 2: \u8ba1\u7b97\u5361\u5c3a\u95f4\u8ddd
    \n \u76f4\u7ebf\u957f\u5ea6: 600 \u50cf\u7d20
    \n ruler_nums: 5
    \n ruler_width: 10
    \n \u5361\u5c3a\u603b\u5bbd\u5ea6: 5 \u00d7 10 = 50
    \n \u53ef\u7528\u957f\u5ea6: 600 – 50 = 550
    \n \u5361\u5c3a\u95f4\u8ddd: 550 \/ 6 \u2248 91.67 \u50cf\u7d20<\/p>\n

    \u6b65\u9aa4 3: \u751f\u6210\u5361\u5c3a\u4f4d\u7f6e<\/p>\n

    \u5361\u5c3a1: x = 100 + 91.67 + 5 = 196.67
    \n \u5361\u5c3a2: x = 100 + 2\u00d791.67 + 15 = 298.34
    \n \u5361\u5c3a3: x = 100 + 3\u00d791.67 + 25 = 400.00
    \n \u5361\u5c3a4: x = 100 + 4\u00d791.67 + 35 = 501.67
    \n \u5361\u5c3a5: x = 100 + 5\u00d791.67 + 45 = 603.34<\/p>\n

    \u6b65\u9aa4 4: \u6cbf\u5782\u76f4\u65b9\u5411\u91c7\u6837<\/p>\n

    (100,300) \u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501 (700,300)
    \n \u2502 \u2502 \u2502 \u2502 \u2502
    \n \u2502 \u2502 \u2502 \u2502 \u2514\u2500 \u5361\u5c3a5 (603.34, 300)
    \n \u2502 \u2502 \u2502 \u2514\u2500\u2500\u2500\u2500\u2500\u2500 \u5361\u5c3a4 (501.67, 300)
    \n \u2502 \u2502 \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u5361\u5c3a3 (400.00, 300)
    \n \u2502 \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u5361\u5c3a2 (298.34, 300)
    \n \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u5361\u5c3a1 (196.67, 300)<\/p>\n

    \u6bcf\u4e2a\u5361\u5c3a\u7684\u91c7\u6837\u533a\u57df (ruler_height = 20, ruler_width = 10):<\/p>\n

    \u2191
    \n 20px \u2502 \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf
    \n \u2502 \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf
    \n \u2502 \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf
    \n \u2502 \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf
    \n \u2502 \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf
    \n \u2502 \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf
    \n \u2502 \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf
    \n \u2502 \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf
    \n \u2502 \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf
    \n \u2502 \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf
    \n -20px \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf \u25cf
    \n \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500
    \n 10px \u5bbd\u5ea6<\/p>\n

    4.3 \u5706\u5f62\u5361\u5c3a\u751f\u6210\u8fc7\u7a0b<\/h4>\n

    \u793a\u4f8b\u914d\u7f6e：\u5706\u5fc3 (400, 300)，\u534a\u5f84 150，ruler_nums = 8（\u6bcf 45\u00b0 \u4e00\u4e2a\u5361\u5c3a），ruler_width = 10，ruler_height = 20\u3002<\/p>\n

    \u751f\u6210\u8fc7\u7a0b：<\/p>\n

    \u6b65\u9aa4 1: \u7ed8\u5236\u4e3b\u5706
    \n \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510
    \n \u250c\u2500\u2500\u2500\u2524 \u251c\u2500\u2500\u2500\u2510
    \n \u250c\u2500\u2524 \u2502 \u2502 \u251c\u2500\u2510
    \n \u250c\u2500\u2524 \u2502 \u25cf(400,300) \u2502 \u251c\u2500\u2510
    \n \u2502 \u2502 \u2502 \u2502 \u2502 \u2502
    \n \u2514\u2500\u2524 \u2502 \u2502 \u251c\u2500\u2518
    \n \u2514\u2500\u2524 \u2502 \u2502 \u251c\u2500\u2518
    \n \u2514\u2500\u2500\u2500\u2524 \u251c\u2500\u2500\u2500\u2518
    \n \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518<\/p>\n

    \u6b65\u9aa4 2: \u8ba1\u7b97\u5361\u5c3a\u4f4d\u7f6e（\u5706\u5468\u4e0a8\u4e2a\u70b9）<\/p>\n

    \u89d2\u5ea6\u6b65\u957f: plus_step = 2\u03c0 \/ 8 = 45\u00b0<\/p>\n

    \u5361\u5c3a1: t = -180\u00b0 \u2192 (-150, 300)
    \n \u5361\u5c3a2: t = -135\u00b0 \u2192 (294, 194)
    \n \u5361\u5c3a3: t = -90\u00b0 \u2192 (400, 150)
    \n \u5361\u5c3a4: t = -45\u00b0 \u2192 (506, 194)
    \n \u5361\u5c3a5: t = 0\u00b0 \u2192 (550, 300)
    \n \u5361\u5c3a6: t = 45\u00b0 \u2192 (506, 406)
    \n \u5361\u5c3a7: t = 90\u00b0 \u2192 (400, 450)
    \n \u5361\u5c3a8: t = 135\u00b0 \u2192 (294, 406)<\/p>\n

    \u6b65\u9aa4 3: \u5f84\u5411\u91c7\u6837（\u6cbf\u5706\u5fc3\u5411\u5916）<\/p>\n

    \u5361\u5c3a3 (400,150)
    \n \u2191
    \n \u2502
    \n \u2502
    \n \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u25cf(400,300)\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500
    \n \u2502
    \n \u2502
    \n \u2193
    \n \u5361\u5c3a7 (400,450)<\/p>\n

    4.4 \u91c7\u6837\u6570\u636e\u6d41<\/h4>\n

    \u539f\u59cb\u56fe\u50cf (\u7070\u5ea6)
    \n \u2193
    \n\u91c7\u6837 (\u6cbf\u5361\u5c3a\u65b9\u5411)
    \n \u2193
    \n\u91c7\u6837\u6570\u636e\u77e9\u9635 (height \u00d7 width)
    \n \u2193
    \n\u6295\u5f71 (\u6cbf\u5bbd\u5ea6\u65b9\u5411\u5e73\u5747)
    \n [v1, v2, v3, …, v(2*height+1)]
    \n \u2193
    \n\u6ee4\u6ce2 (\u5dee\u5206\u6ee4\u6ce2\u5668)
    \n [g1, g2, g3, …, g(2*height+1)]
    \n \u2193
    \n\u5cf0\u503c\u68c0\u6d4b
    \n \u627e\u5230\u68af\u5ea6\u6700\u5927\u7684\u4f4d\u7f6e
    \n \u2193
    \n\u4e9a\u50cf\u7d20\u5b9a\u4f4d
    \n \u629b\u7269\u7ebf\u62df\u5408\u5f97\u5230\u4e9a\u50cf\u7d20\u7cbe\u5ea6
    \n \u2193
    \n\u8fb9\u7f18\u70b9\u5750\u6807
    \n \u8f6c\u6362\u56de\u56fe\u50cf\u5750\u6807\u7cfb<\/p>\n

    \n

    5. \u5173\u952e\u7b97\u6cd5\u8be6\u89e3<\/h3>\n

    5.1 \u53cc\u7ebf\u6027\u63d2\u503c<\/h4>\n

    \u91c7\u6837\u5750\u6807\u5927\u591a\u4e0d\u662f\u6574\u6570，\u7528\u5468\u56f4 4 \u4e2a\u50cf\u7d20\u52a0\u6743\u53d6\u503c：<\/p>\n

    \u5bf9\u4e8e\u5750\u6807 (x, y)，\u8bbe：
    \n– x0 = floor(x), x1 = x0 + 1
    \n– y0 = floor(y), y1 = y0 + 1
    \n– dx = x – x0, dy = y – y0<\/p>\n

    \u63d2\u503c\u503c = (1-dx)(1-dy)I(x0,y0) + dx(1-dy)I(x1,y0) +
    \n (1-dx)dy I(x0,y1) + dx dy I(x1,y1)<\/p>\n

    5.2 \u5cf0\u503c\u68c0\u6d4b<\/h4>\n

    \u601d\u8def\u662f\u76f8\u90bb\u70b9\u505a\u5dee\u5206，\u68c0\u6d4b\u7b26\u53f7\u53d8\u5316（\u6b63\u2192\u8d1f），\u518d\u7b5b\u6389\u4e0d\u8d85\u8fc7\u9608\u503c\u7684：<\/p>\n

    void<\/span> FindPeak<\/span>(<\/span>int<\/span> size,<\/span> float<\/span> data[<\/span>]<\/span>,<\/span> float<\/span> threshold,<\/span> std::<\/span>vector<<\/span>int<\/span>><\/span>&<\/span> peaks)<\/span> {<\/span>
    \n std::<\/span>vector<<\/span>int<\/span>><\/span> sign;<\/span>
    \n for<\/span> (<\/span>int<\/span> i =<\/span> 1<\/span>;<\/span> i <<\/span> size;<\/span> i++<\/span>)<\/span> {<\/span>
    \n float<\/span> diff =<\/span> data[<\/span>i]<\/span> –<\/span> data[<\/span>i–<\/span>1<\/span>]<\/span>;<\/span>
    \n if<\/span> (<\/span>diff <<\/span> 0.0f<\/span>)<\/span> sign.<\/span>push_back<\/span>(<\/span>–<\/span>1<\/span>)<\/span>;<\/span>
    \n else<\/span> if<\/span> (<\/span>diff ><\/span> 0.0f<\/span>)<\/span> sign.<\/span>push_back<\/span>(<\/span>1<\/span>)<\/span>;<\/span>
    \n else<\/span> sign.<\/span>push_back<\/span>(<\/span>0<\/span>)<\/span>;<\/span>
    \n }<\/span><\/p>\n

    for<\/span> (<\/span>int<\/span> j =<\/span> 1<\/span>;<\/span> j <<\/span> sign.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> j++<\/span>)<\/span> {<\/span>
    \n int<\/span> diff =<\/span> sign[<\/span>j]<\/span> –<\/span> sign[<\/span>j–<\/span>1<\/span>]<\/span>;<\/span>
    \n if<\/span> (<\/span>diff !=<\/span> 0<\/span> &&<\/span> abs<\/span>(<\/span>data[<\/span>j]<\/span>)<\/span> ><\/span> threshold)<\/span> {<\/span>
    \n peaks.<\/span>push_back<\/span>(<\/span>j)<\/span>;<\/span>
    \n }<\/span>
    \n }<\/span>
    \n}<\/span><\/p>\n

    5.3 \u4e9a\u50cf\u7d20\u5b9a\u4f4d<\/h4>\n

    \u7528\u5cf0\u503c\u70b9\u53ca\u5176\u5de6\u53f3\u90bb\u70b9\u4e09\u70b9\u62df\u5408\u629b\u7269\u7ebf y = Ax\u00b2 + Bx + C，\u9876\u70b9\u5728 x = -B\/(2A)，\u5316\u7b80\u540e\u5c31\u662f u = 0.5 \u00d7 (a – c) \/ (a – 2b + c)，\u7cbe\u5ea6\u80fd\u5230 0.01 \u50cf\u7d20\u7ea7\u3002<\/p>\n

    \n

    6. \u6027\u80fd<\/h3>\n

    \u91c7\u6837\u6570\u7ec4\u6539\u7528 std::vector（\u5206\u914d\u6b21\u6570\u51cf\u5c11\u7ea6 95%），RAII \u81ea\u52a8\u7ba1\u7406\u751f\u547d\u5468\u671f\u6d88\u9664\u6cc4\u6f0f\u98ce\u9669，\u5bb9\u5668\u7528 reserve() \u9884\u5206\u914d\u51cf\u5c11\u6269\u5bb9\u5f00\u9500\u3002<\/p>\n

    \n

    7. \u9002\u7528\u4e0e\u5c40\u9650<\/h3>\n

    \u7cbe\u5ea6\u5230\u4e9a\u50cf\u7d20\u7ea7，\u6295\u5f71\u5e73\u5747\u5929\u7136\u6297\u566a，\u5cf0\u503c\u9009\u62e9\u6a21\u5f0f\u53ef\u6269\u5c55\u3002\u4ee3\u4ef7\u662f\u8ba1\u7b97\u91cf\u4e0e\u5361\u5c3a\u6570\u91cf\u6210\u6b63\u6bd4，\u5bf9\u56fe\u50cf\u8d28\u91cf\u6709\u4e00\u5b9a\u8981\u6c42，\u53c2\u6570（\u5bbd\u5ea6\u3001\u9ad8\u5ea6\u3001\u6570\u91cf\u3001\u9608\u503c）\u5f97\u6309\u573a\u666f\u8c03\u3002<\/p>\n

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