{"id":86067,"date":"2026-07-28T04:08:22","date_gmt":"2026-07-27T20:08:22","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/86067.html"},"modified":"2026-07-28T04:08:22","modified_gmt":"2026-07-27T20:08:22","slug":"mcu%e5%b9%b3%e5%8f%b0qr%e7%a0%81%e8%a7%a3%e7%a0%81%e5%bc%95%e6%93%8e%e5%ae%9e%e7%8e%b0%e5%88%86%e6%9e%90%ef%bc%9a%e4%bb%8e%e5%9b%be%e5%83%8f%e4%ba%8c%e5%80%bc%e5%8c%96%e5%88%b0reed-solomon%e7%ba%a0","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/86067.html","title":{"rendered":"MCU\u5e73\u53f0QR\u7801\u89e3\u7801\u5f15\u64ce\u5b9e\u73b0\u5206\u6790\uff1a\u4ece\u56fe\u50cf\u4e8c\u503c\u5316\u5230Reed-Solomon\u7ea0\u9519\u7684\u7eafC\u65b9\u6848\u8be6\u89e3"},"content":{"rendered":"<h2>MCU\u5e73\u53f0QR\u7801\u89e3\u7801\u5f15\u64ce\u5b9e\u73b0\u5206\u6790&#xff1a;\u4ece\u56fe\u50cf\u4e8c\u503c\u5316\u5230Reed-Solomon\u7ea0\u9519\u7684\u7eafC\u65b9\u6848\u8be6\u89e3<\/h2>\n<h3>\u4e00\u3001QR\u7801\u89e3\u7801\u6d41\u7a0b\u603b\u89c8\u4e0eMCU\u7ea6\u675f<\/h3>\n<p>QR\u7801\u89e3\u7801\u662f\u4e00\u4e2a\u591a\u9636\u6bb5\u4fe1\u53f7\u5904\u7406\u6d41\u7a0b&#xff0c;\u5305\u542b\u56fe\u50cf\u91c7\u96c6\u3001\u5b9a\u4f4d\u3001\u4e8c\u503c\u5316\u3001\u91c7\u6837\u3001\u7ea0\u9519\u4e0e\u6570\u636e\u6062\u590d\u516d\u4e2a\u73af\u8282\u3002\u5728Cortex-M4&#xff08;168MHz\u3001128KB RAM&#xff09;\u5e73\u53f0\u4e0a\u5b9e\u73b0\u5b8c\u6574\u89e3\u7801&#xff0c;\u9700\u5728\u6bcf\u4e2a\u73af\u8282\u4e25\u683c\u63a7\u5236\u5185\u5b58\u4e0e\u8ba1\u7b97\u5f00\u9500\u3002<\/p>\n<p>\u5168\u6d41\u7a0b\u6570\u636e\u7279\u5f81&#xff1a;<\/p>\n<table>\n<tr>\u73af\u8282\u8f84\u5165\u8f84\u51fa\u5185\u5b58\u5cf0\u503c\u8ba1\u7b97\u7279\u5f81<\/tr>\n<tbody>\n<tr>\n<td>\u56fe\u50cf\u91c7\u96c6<\/td>\n<td>CMOS\u539f\u59cb\u5e27<\/td>\n<td>\u7070\u5ea6\u77e9\u9635<\/td>\n<td>40KB(160\u00d7160)<\/td>\n<td>DMA\u642c\u8fd0<\/td>\n<\/tr>\n<tr>\n<td>\u5b9a\u4f4d<\/td>\n<td>\u7070\u5ea6\u77e9\u9635<\/td>\n<td>\u4e09\u4e2aFinder\u4e2d\u5fc3<\/td>\n<td>40KB<\/td>\n<td>\u884c\u626b\u63cf&#043;\u4ea4\u53c9\u6bd4<\/td>\n<\/tr>\n<tr>\n<td>\u4e8c\u503c\u5316<\/td>\n<td>\u7070\u5ea6\u77e9\u9635<\/td>\n<td>1-bit\u4f4d\u56fe<\/td>\n<td>3.2KB<\/td>\n<td>\u5c40\u90e8\u9608\u503c<\/td>\n<\/tr>\n<tr>\n<td>\u91c7\u6837<\/td>\n<td>\u4f4d\u56fe&#043;\u5b9a\u4f4d\u53c2\u6570<\/td>\n<td>\u6a21\u5757\u77e9\u9635<\/td>\n<td>2KB(max V40)<\/td>\n<td>\u900f\u89c6\u53d8\u6362<\/td>\n<\/tr>\n<tr>\n<td>\u7ea0\u9519<\/td>\n<td>\u6a21\u5757\u77e9\u9635<\/td>\n<td>\u7ea0\u9519\u540e\u6570\u636e<\/td>\n<td>8KB<\/td>\n<td>RS\u591a\u9879\u5f0f<\/td>\n<\/tr>\n<tr>\n<td>\u6570\u636e\u6062\u590d<\/td>\n<td>\u7ea0\u9519\u6570\u636e<\/td>\n<td>\u89e3\u7801\u5b57\u7b26\u4e32<\/td>\n<td>2KB<\/td>\n<td>\u6a21\u5f0f\u89e3\u6790<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u6838\u5fc3\u7ea6\u675f&#xff1a;128KB RAM\u9700\u5bb9\u7eb3\u7070\u5ea6\u5e27\u3001\u4e2d\u95f4\u7f13\u51b2\u4e0e\u7ea0\u9519\u5de5\u4f5c\u533a&#xff0c;\u5b9e\u9645\u53ef\u5206\u914d\u7ed9\u89e3\u7801\u5f15\u64ce\u7684\u8fde\u7eedRAM\u4e0d\u8d85\u8fc760KB\u3002\u56e0\u6b64\u7070\u5ea6\u5e27\u91c7\u7528160\u00d7160\u5206\u8fa8\u7387\u91c7\u96c6&#xff08;\u8986\u76d6V10\u7248\u672cQR\u7801&#xff09;&#xff0c;\u5bf9\u66f4\u9ad8\u7248\u672c\u9700\u5206\u5757\u5904\u7406\u3002<\/p>\n<h3>\u4e8c\u3001Finder Pattern\u5b9a\u4f4d\u4e0e\u4e8c\u503c\u5316\u7b97\u6cd5<\/h3>\n<p>Finder Pattern\u75311:1:3:1:1\u6bd4\u4f8b\u7684\u9ed1\u767d\u6a21\u5757\u7ec4\u6210&#xff0c;\u662fQR\u7801\u5b9a\u4f4d\u7684\u8d77\u70b9\u3002\u5b9a\u4f4d\u7b97\u6cd5\u91c7\u7528\u884c\u626b\u63cf\u7b56\u7565&#xff1a;<\/p>\n<li>\u5bf9\u7070\u5ea6\u56fe\u9010\u884c\u626b\u63cf&#xff0c;\u7edf\u8ba1\u8fde\u7eed\u9ed1\u767d\u50cf\u7d20\u6bb5\u957f\u5ea6<\/li>\n<li>\u8ba1\u7b97\u76f8\u90bb5\u6bb5\u7684\u6bd4\u4f8b&#xff0c;\u5224\u5b9a\u662f\u5426\u63a5\u8fd11:1:3:1:1<\/li>\n<li>\u5bf9\u5019\u9009\u884c\u505a\u4ea4\u53c9\u9a8c\u8bc1&#xff08;\u7eb5\u5411\u626b\u63cf\u540c\u6bd4\u4f8b&#xff09;<\/li>\n<p>\/\/ Finder Pattern\u884c\u626b\u63cf\u68c0\u6d4b\u6838\u5fc3\u4ee3\u7801<br \/>\n#define FINDER_RATIO_TOL  0.3f   \/\/ \u6bd4\u4f8b\u5bb9\u5dee30%<\/p>\n<p>typedef struct {<br \/>\n    int cx, cy;      \/\/ Finder\u4e2d\u5fc3\u5750\u6807<br \/>\n    int size;        \/\/ \u6a21\u5757\u4f30\u8ba1\u5c3a\u5bf8(\u50cf\u7d20)<br \/>\n} finder_t;<\/p>\n<p>static int check_finder_ratio(const int segs[5])<br \/>\n{<br \/>\n    \/\/ \u6bd4\u4f8b\u5e94\u4e3a 1:1:3:1:1&#xff0c;\u4ee5\u7b2c3\u6bb5(\u9ed1)\u4e3a\u57fa\u51c6<br \/>\n    int ref &#061; segs[2];<br \/>\n    if (ref &#061;&#061; 0) return 0;<\/p>\n<p>    float ratios[5];<br \/>\n    for (int i &#061; 0; i &lt; 5; i&#043;&#043;) {<br \/>\n        ratios[i] &#061; (float)segs[i] \/ ref;<br \/>\n    }<\/p>\n<p>    \/\/ \u6807\u51c6\u6bd4\u4f8b: [0.33, 0.33, 1.0, 0.33, 0.33]<br \/>\n    float target[5] &#061; {1.0f\/3, 1.0f\/3, 1.0f, 1.0f\/3, 1.0f\/3};<br \/>\n    for (int i &#061; 0; i &lt; 5; i&#043;&#043;) {<br \/>\n        if (fabsf(ratios[i] &#8211; target[i]) &gt; FINDER_RATIO_TOL * target[i]) {<br \/>\n            return 0;<br \/>\n        }<br \/>\n    }<br \/>\n    return 1;<br \/>\n}<\/p>\n<p>int finder_scan_row(const uint8_t *gray, int width, int y,<br \/>\n                    finder_t *finders, int max_finders)<br \/>\n{<br \/>\n    if (gray &#061;&#061; NULL || finders &#061;&#061; NULL) return -1;<\/p>\n<p>    int segs[5] &#061; {0};    \/\/ \u8fde\u7eed5\u6bb5\u9ed1\u767d\u50cf\u7d20\u8ba1\u6570<br \/>\n    int seg_idx &#061; 0;<br \/>\n    int count &#061; 0;<br \/>\n    int found &#061; 0;<br \/>\n    uint8_t prev &#061; 255;   \/\/ \u8d77\u59cb\u5047\u8bbe\u4e3a\u767d\u8272<\/p>\n<p>    for (int x &#061; 0; x &lt; width; x&#043;&#043;) {<br \/>\n        uint8_t val &#061; gray[y * width &#043; x];<br \/>\n        uint8_t cur &#061; (val &gt; 128) ? 1 : 0;  \/\/ \u7b80\u5355\u9608\u503c\u9884\u5224<\/p>\n<p>        if (cur &#061;&#061; prev) {<br \/>\n            count&#043;&#043;;<br \/>\n        } else {<br \/>\n            if (seg_idx &lt; 5) {<br \/>\n                segs[seg_idx&#043;&#043;] &#061; count;<br \/>\n            } else {<br \/>\n                \/\/ 5\u6bb5\u5df2\u6ee1&#xff0c;\u68c0\u67e5\u6bd4\u4f8b<br \/>\n                if (check_finder_ratio(segs)) {<br \/>\n                    int center_x &#061; x &#8211; segs[4] &#8211; segs[3] &#8211; segs[2]\/2;<br \/>\n                    finders[found].cx &#061; center_x;<br \/>\n                    finders[found].cy &#061; y;<br \/>\n                    finders[found].size &#061; segs[2] \/ 3;<br \/>\n                    found&#043;&#043;;<br \/>\n                    if (found &gt;&#061; max_finders) return found;<br \/>\n                }<br \/>\n                \/\/ \u6ed1\u52a8\u7a97\u53e3: \u540e\u79fb2\u6bb5<br \/>\n                segs[0] &#061; segs[2]; segs[1] &#061; segs[3]; segs[2] &#061; segs[4];<br \/>\n                segs[3] &#061; count; seg_idx &#061; 4;<br \/>\n            }<br \/>\n            count &#061; 1;<br \/>\n            prev &#061; cur;<br \/>\n        }<br \/>\n    }<br \/>\n    return found;<br \/>\n}<\/p>\n<p>\u4e8c\u503c\u5316\u91c7\u7528\u5c40\u90e8\u81ea\u9002\u5e94\u9608\u503c&#xff08;Sauvola\u65b9\u6cd5\u7b80\u5316\u7248&#xff09;&#xff0c;\u7a97\u53e3\u5c3a\u5bf8\u53d6\u6a21\u5757\u4f30\u8ba1\u5c3a\u5bf8\u76844\u500d&#xff1a;<\/p>\n<p>\/\/ Sauvola\u7b80\u5316\u5c40\u90e8\u4e8c\u503c\u5316<br \/>\nstatic uint8_t sauvola_threshold(const uint8_t *gray, int w, int h,<br \/>\n                                  int cx, int cy, int win)<br \/>\n{<br \/>\n    int sum &#061; 0, count &#061; 0;<br \/>\n    for (int dy &#061; -win\/2; dy &lt;&#061; win\/2; dy&#043;&#043;) {<br \/>\n        for (int dx &#061; -win\/2; dx &lt;&#061; win\/2; dx&#043;&#043;) {<br \/>\n            int x &#061; cx &#043; dx, y &#061; cy &#043; dy;<br \/>\n            if (x &lt; 0 || x &gt;&#061; w || y &lt; 0 || y &gt;&#061; h) continue;<br \/>\n            sum &#043;&#061; gray[y * w &#043; x];<br \/>\n            count&#043;&#043;;<br \/>\n        }<br \/>\n    }<br \/>\n    if (count &#061;&#061; 0) return 128;<br \/>\n    int mean &#061; sum \/ count;<br \/>\n    \/\/ Sauvola\u9608\u503c: T &#061; mean * (1 &#8211; k * (1 &#8211; stddev\/128))<br \/>\n    \/\/ \u7b80\u5316\u4e3a: T &#061; mean * 0.85 (k&#061;0.15\u8fd1\u4f3c)<br \/>\n    return (uint8_t)(mean * 0.85f);<br \/>\n}<\/p>\n<h3>\u4e09\u3001\u900f\u89c6\u53d8\u6362\u91c7\u6837\u4e0eReed-Solomon\u7ea0\u9519<\/h3>\n<p>Finder Pattern\u786e\u5b9a\u4e09\u4e2a\u89d2\u70b9\u540e&#xff0c;\u901a\u8fc7\u900f\u89c6\u53d8\u6362\u5c06QR\u7801\u6a21\u5757\u6620\u5c04\u81f3\u6b63\u65b9\u5f62\u91c7\u6837\u7f51\u683c\u3002\u900f\u89c6\u53d8\u6362\u77e9\u96354\u00d74\u53c2\u6570\u7531\u4e09\u4e2aFinder\u4e2d\u5fc3&#043;Alignment Pattern\u8ba1\u7b97\u5f97\u51fa\u3002<\/p>\n<p>Reed-Solomon\u7ea0\u9519\u662fQR\u89e3\u7801\u4e2d\u8ba1\u7b97\u91cf\u6700\u5927\u7684\u73af\u8282\u3002QR\u7801\u91c7\u7528GF(2^8)\u57df\u4e0a\u7684RS(n,k)\u7801&#xff0c;\u7ea0\u9519\u80fd\u529b\u4e3a(n-k)\/2\u4e2a\u9519\u8bef\u7b26\u53f7\u3002V1-M\u7248\u672c&#xff1a;RS(26,19)&#xff0c;\u53ef\u7ea0\u6b633\u4e2a\u9519\u8bef\u3002<\/p>\n<p>RS\u89e3\u7801\u6838\u5fc3\u6b65\u9aa4&#xff1a;<\/p>\n<li>\u7531\u63a5\u6536\u7801\u5b57\u8ba1\u7b97syndrome\u591a\u9879\u5f0f<\/li>\n<li>Berlekamp-Massey\u7b97\u6cd5\u6c42\u89e3\u9519\u8bef\u5b9a\u4f4d\u591a\u9879\u5f0f<\/li>\n<li>Chien\u641c\u7d22\u5b9a\u4f4d\u9519\u8bef\u4f4d\u7f6e<\/li>\n<li>Forney\u7b97\u6cd5\u8ba1\u7b97\u9519\u8bef\u5e45\u503c<\/li>\n<p>\/\/ GF(2^8)\u57df\u4e58\u6cd5&#xff08;\u67e5\u8868\u6cd5&#xff0c;\u907f\u514d\u5b9e\u65f6\u8ba1\u7b97&#xff09;<br \/>\nstatic const uint8_t gf_exp[256] &#061; { \/* \u9884\u8ba1\u7b97\u6307\u6570\u8868 *\/ };<br \/>\nstatic const uint8_t gf_log[256]  &#061; { \/* \u9884\u8ba1\u7b97\u5bf9\u6570\u8868 *\/ };<\/p>\n<p>static uint8_t gf_mul(uint8_t a, uint8_t b)<br \/>\n{<br \/>\n    if (a &#061;&#061; 0 || b &#061;&#061; 0) return 0;<br \/>\n    return gf_exp[(gf_log[a] &#043; gf_log[b]) % 255];<br \/>\n}<\/p>\n<p>\/\/ Berlekamp-Massey\u7b97\u6cd5\u6838\u5fc3\u5b9e\u73b0<br \/>\nint rs_berlekamp_massey(const uint8_t *syndrome, int nsym,<br \/>\n                         uint8_t *err_loc, int *err_loc_len)<br \/>\n{<br \/>\n    if (syndrome &#061;&#061; NULL || err_loc &#061;&#061; NULL) return -1;<\/p>\n<p>    uint8_t C[64] &#061; {0}, B[64] &#061; {0};<br \/>\n    C[0] &#061; 1; B[0] &#061; 1;<br \/>\n    int L &#061; 0, m &#061; 1, b &#061; 1;<\/p>\n<p>    for (int n &#061; 0; n &lt; nsym; n&#043;&#043;) {<br \/>\n        uint8_t delta &#061; syndrome[n];<br \/>\n        for (int i &#061; 1; i &lt;&#061; L; i&#043;&#043;) {<br \/>\n            delta &#061; gf_sub(delta, gf_mul(C[i], syndrome[n &#8211; i]));<br \/>\n        }<\/p>\n<p>        if (delta &#061;&#061; 0) { m&#043;&#043;; continue; }<\/p>\n<p>        uint8_t T[64] &#061; {0};<br \/>\n        for (int i &#061; 0; i &lt; 64; i&#043;&#043;) T[i] &#061; C[i];<\/p>\n<p>        \/\/ C &#061; C &#8211; delta * B * x^m<br \/>\n        uint8_t scale &#061; gf_mul(delta, gf_inv(b));<br \/>\n        for (int i &#061; 0; i &#043; m &lt; 64; i&#043;&#043;) {<br \/>\n            C[i &#043; m] &#061; gf_sub(C[i &#043; m], gf_mul(scale, B[i]));<br \/>\n        }<\/p>\n<p>        if (2 * L &lt;&#061; n) {<br \/>\n            L &#061; n &#043; 1 &#8211; L;<br \/>\n            for (int i &#061; 0; i &lt; 64; i&#043;&#043;) B[i] &#061; T[i];<br \/>\n            b &#061; delta;<br \/>\n            m &#061; 1;<br \/>\n        } else {<br \/>\n            m&#043;&#043;;<br \/>\n        }<br \/>\n    }<\/p>\n<p>    *err_loc_len &#061; L;<br \/>\n    for (int i &#061; 0; i &lt;&#061; L; i&#043;&#043;) err_loc[i] &#061; C[i];<br \/>\n    return 0;<br \/>\n}<\/p>\n<p>GF\u6307\u6570\/\u5bf9\u6570\u8868\u5404256\u5b57\u8282&#xff0c;\u5408\u8ba1512\u5b57\u8282ROM\u5360\u7528&#xff0c;\u66ff\u4ee3\u5b9e\u65f6\u4e58\u6cd5\u8ba1\u7b97\u540e\u5355\u6b21RS\u89e3\u7801\u8017\u65f6\u7ea612ms&#xff08;Cortex-M4&#064;168MHz&#xff09;\u3002<\/p>\n<h3>\u56db\u3001\u6570\u636e\u6a21\u5f0f\u89e3\u6790\u4e0e\u5185\u5b58\u4f18\u5316<\/h3>\n<p>QR\u7801\u6570\u636e\u533a\u7ecf\u7ea0\u9519\u6062\u590d\u540e&#xff0c;\u6309\u6a21\u5f0f\u6307\u793a\u7b26\u9010\u6bb5\u89e3\u6790\u3002\u56db\u79cd\u6a21\u5f0f&#xff1a;Numeric(0001)\u3001Alphanumeric(0010)\u3001Byte(0100)\u3001Kanji(1000)\u3002<\/p>\n<p>\/\/ \u6570\u636e\u6a21\u5f0f\u89e3\u6790\u4e3b\u5faa\u73af<br \/>\nint qr_decode_data(const uint8_t *modules, int version,<br \/>\n                   char *output, int max_len)<br \/>\n{<br \/>\n    if (modules &#061;&#061; NULL || output &#061;&#061; NULL) return -1;<\/p>\n<p>    qr_bitstream_t bs;<br \/>\n    bs_init(&amp;bs, modules, version);<\/p>\n<p>    int out_pos &#061; 0;<br \/>\n    while (bs_has_bits(&amp;bs, 4)) {<br \/>\n        uint8_t mode &#061; bs_read(&amp;bs, 4);<\/p>\n<p>        switch (mode) {<br \/>\n        case QR_MODE_NUMERIC:<br \/>\n            out_pos &#043;&#061; decode_numeric(&amp;bs, output &#043; out_pos, max_len &#8211; out_pos);<br \/>\n            break;<br \/>\n        case QR_MODE_ALPHANUM:<br \/>\n            out_pos &#043;&#061; decode_alphanum(&amp;bs, output &#043; out_pos, max_len &#8211; out_pos);<br \/>\n            break;<br \/>\n        case QR_MODE_BYTE:<br \/>\n            out_pos &#043;&#061; decode_byte(&amp;bs, output &#043; out_pos, max_len &#8211; out_pos);<br \/>\n            break;<br \/>\n        default:<br \/>\n            fprintf(stderr, &#034; \u4e0d\u652f\u6301\u7684\u6a21\u5f0f: 0x%X\\\\n&#034;, mode);<br \/>\n            return ERR_UNSUPPORTED_MODE;<br \/>\n        }<br \/>\n        if (out_pos &gt;&#061; max_len) {<br \/>\n            fprintf(stderr, &#034; \u8f93\u51fa\u7f13\u51b2\u6ea2\u51fa\\\\n&#034;);<br \/>\n            return ERR_BUFFER_OVERFLOW;<br \/>\n        }<br \/>\n    }<br \/>\n    return out_pos;<br 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