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B题碎纸片的拼接复原摘要破碎文件的拼接在实际生活中有着重要的应用。当文件的碎片形状相同时，我们需要基于文字特征，对文档进行拼接。

首先，我们建立了关于“相似度”的数学模型。通过 matlab 中的 imread 函数，将每个碎片均转化成灰度值矩阵，通过比较矩阵边界向量的相似度来确定两碎片是否相邻。通常情况下，如果两块碎片边界的灰度值向量相似度极高，那么这两块碎片相邻的可能性非常大。通过这个模型，我们成功拼接了附件 1 与附件 2。其序列分别为：

附件 1 8 14 12 15 3 10 2 16 1 4 5 9 13 18 11 7 17 0 6 附件 2 3 6 2 7 15 18 11 0 5 1 9 13 10 8 12 14 17 16 4 然而，在拼接附件 3 与附件 4 时，我们发现上述模型并不适用，因为附件 3 被分割成了 19×11=209 块，碎块数量较多。我们另辟蹊径，发现同一行中的碎片上方（或下方）空白部分的宽度相等。以此为基础，我们建立了“留白模型” 。用来将 209 块碎片分成 11 组，每组中的元素均在同一行。至此，我们将 209 块碎片的拼接问题转化成了 19 块碎片的拼接问题。将 11 组碎片分别拼接完毕后，我们得到了 11 块较大的碎片，其中每块代表一行，进而利用“相似度”的数学模型，找到这 11 行的顺序，我们就可以完成破碎文件的拼接。

由于附件 5 的碎纸片包含正反两面，所以附件 5 的拼接难度大大高于前四个附件。

我们需要在编程筛选的基础上，加入人工干预（即通过 excel 手动筛选），最终将附件 5 的拼接问题化简，最后采用附件 3 的拼接方式，完成附件 5 的拼接。

最后，验证模型的正确性，总结模型的优缺点。关键词：拼接；灰度值；相似度；留白；文字特征 1 1. 问题的重述破碎文件的拼接在司法物证复原、历史文献修复以及军事情报获取等领域都有着重要的应用。传统上，拼接复原工作需由人工完成，准确率较高，但效率很低。特别是当碎片数量巨大，人工拼接很难在短时间内完成任务。随着计算机技术的发展，人们试图开发碎纸片的自动拼接技术，以提高拼接复原效率。请讨论以下问题：

1. 对于给定的来自同一页印刷文字文件的碎纸机破碎纸片（仅纵切），建立碎纸片拼接复原模型和算法，并针对附件 1、附件 2 给出的中、英文各一页文件的碎片数据进行拼接复原。如果复原过程需要人工干预，请写出干预方式及干预的时间节点。复原结果以图片形式及表格形式表达（见【结果表达格式说明】）。

2. 对于碎纸机既纵切又横切的情形，请设计碎纸片拼接复原模型和算法，并针对附件 3、附件 4 给出的中、英文各一页文件的碎片数据进行拼接复原。如果复原过程需要人工干预，请写出干预方式及干预的时间节点。复原结果表达要求同上。

3. 上述所给碎片数据均为单面打印文件，从现实情形出发，还可能有双面打印文件的碎纸片拼接复原问题需要解决。

附件 5 给出的是一页英文印刷文字双面打印文件的碎片数据。请尝试设计相应的碎纸片拼接复原模型与算法，并就附件 5 的碎片数据给出拼接复原结果，结果表达要求同上。 2. 问题的分析常规文档碎纸片计算机拼接方法一般利用碎片边缘的尖点特征、尖角特征、面积特征等几何特征，搜索与之匹配的相邻碎纸片并进行拼接, 这种基于边界几何特征的拼接方法并不适用于边缘形状相似的碎纸片。但是人手撕裂碎纸片时，为节省时间习惯上总是先将碎纸片重叠在一起，然后撕裂，再将碎纸片重叠起来，再继续撕裂，这样反复下去，直到得到满意大小的碎纸片为止。

这种撕裂过程会产生很多形状非常相似的碎纸片，拼接时如果只利用碎片的边界特征，拼接效果并不理想。进一步说，如果碎片的大小形状完全相同，那么传统的拼接方法将完全失效。

对这类边缘相似的碎纸片的拼接，理想的计算机拼接过程应与人工拼接过程类似，即拼接时不但要考虑待拼接碎纸片边缘是否匹配，还要判断碎片内的字迹断线或碎片内的文字内容是否匹配，然而由于理论和技术的限制，让计算机具备类似人那种识别碎片边缘的字迹断线、以及理解碎片内文字图像含义的智能几乎不太可能。但是利用现有的技术，完全可以获取碎片文字所在行的几何特征信息，比如文字行的行高、文字的行距等信息，拼接碎片时如利用这些信息进行拼接，其拼接效率无疑比单纯利用边界几何特征方法要好些。本题中需要基于文字特征对文档碎纸片进行拼接。 3. 模型的假设（1）纸张为矩形，切割时保证碎片的方向与纸张边缘平行。

（2）附件 1、附件 2 为纵切碎片数据，每页纸被切为 19 条碎片，每个碎片的像素均为 72*1980（在图片文件的“属性”中可以找到其像素值）。

（3）附件 3、附件 4 为纵横切碎片数据，每页纸被切为 11×19 个碎片。每个碎片的像素为 72*180。 2 （4）除字体覆盖部分外，纸张其余的区域均为白色，灰度值为 255。

（即认为纸张本身无颜色深浅的变化，无脏污部分。

） 4. 定义 4.1 向量的相似度语言描述：两个 n 维向量中相等的对应元素的对数与向量长度的比值为两向量的相似度。

程序语言表述：设 a,b 均为 n 维向量，且 a=（ a1 , a2 ,?, an ）,b=( b1 , b2 ,?, bn ). 在 matlab 中执行下列语句：

for i=1:n if ( ai == bi ) s=s+1;

end end S=s/n 定义 S 为向量 a 与向量 b 的相似度。

4.2 图片的“上留白” ， “下留白” ， “左留白” ， “右留白” 设单位像素的高为 1，宽为 1。

上留白，指的是图片中的文字的上边缘与图片上边缘之间的距离。

下留白，指的是图片中的文字的下边缘与图片下边缘之间的距离。

左留白，指的是图片中的文字的左边缘与图片左边缘之间的距离。

右留白，指的是图片中的文字的右边缘与图片右边缘之间的距离。 5. 符号说明 a000 a001 a002 ?? a018 a00i (:, j ) 轾 a11 犏犏 a21 M P2 = 犏犏犏犏 an1 臌附件 1 中碎片 000.bmp 所对应的灰度值矩阵附件 1 中碎片 001.bmp 所对应的灰度值矩阵附件 1 中碎片 002.bmp 所对应的灰度值矩阵附件 1 中碎片 018.bmp 所对应的灰度值矩阵矩阵 a00i 的第 j 列表示的列向量 a12 a22 an 2 鬃 a1n 鬃 a2 n ann 3 图 2 对应的灰度值矩阵轾 b11 b12 鬃 b1n 犏犏 b21 b22 鬃 b2 n M P3 = 犏犏犏犏 bn1 bn 2 bnn 臌轾 c11 c12 鬃 c1n 犏犏 c21 c22 鬃 c2 n M P4 = 犏犏犏犏 cn1 cn 2 cnn 臌图 3 对应的灰度值矩阵图 4 对应的灰度值矩阵 S order1 order2 两向量的相似度附件 1 中碎片的顺序附件 2 中碎片的顺序 6. 模型的建立与求解 6.1 问题 1 针对附件 1、附件 2 给出的中、英文各一页文件的碎片数据进行拼接复原。

6.1.1 复原附件 1 中的文件碎片 6.1.1.1 问题的分析（1）观察首先，观察附件 1 中的 19 块碎片，发现附件 1 “ 008.bmp” 的左侧与附件 1 “ 006.bmp” 的右侧均有很宽的空白，而其余的部分左右无空白。

因为这是一页文件裁剪下来的碎片，所以很容易得知附件 1 的“008.bmp”为该文件的左边界；附件 1 的“006.bmp”为该文件的右边界。附件 1 008.bmp 附件 1 006.bmp （注：由于原图过大，为了节约空间，只截取两图中的一部分。

）（2）将碎片转化为数据附件一中每一块碎片的像素均为 72*1980，每一个像素均对应着一个灰度值。

（灰度值为 0 时，像素为黑色，灰度值越大，像素的颜色越浅。

灰度值为 255 时，像素为白色。

） 4 通过 matlab 中的“imread”函数，可以将图片转化成一个 1980×72 的灰度值矩阵。

（矩阵中元素的值介于 0 到 255 之间。

）由此，我们得到了一系列 1980×72 的矩阵 a000 ，a001 ， a002 ，??， a018 。

（3）分析相邻碎片之间的关系。

将图片分割时，其中的文字也同时被分割。如图 1，2，3 所示， “同”字被分成了两半，在笔画被截断的部分，左右两侧像素的灰度值应相等或近似。因此，我们可以得知轾轾 a11 a12 鬃 a1n a1n 犏犏犏犏 a21 a22 鬃 a2 n a2 n 犏 “图 2”对应的灰度值矩阵 M P 2 = 犏最右侧的列向量犏犏，应与“图 3” 犏犏犏犏 a a a ann n1 n2 nn 臌臌轾轾 b11 b12 鬃 b1n b11 犏犏犏犏 b21 b22 鬃 b2 n b21 犏对应的灰度值矩阵 M P 3 = 犏最左侧的列向量（此处先犏犏的相似度很高。

犏犏犏犏 b b b bn1 n1 n2 nn 臌臌做定性的说明，在 6.1.1.2 中我们将通过计算机对其进行定量处理。

）（图 1）（图 2）图（3）如果拼图时左右两端不匹配，如 “图 2” “图 4” ，此时“图 2”对应的灰度值矩阵 M P 2 轾轾 c11 c12 鬃 c1n a1n 犏犏犏犏 c21 c22 鬃 c2 n a2 n 犏 M = 最右侧的列向量犏，与图 4 对应的灰度值矩阵最左侧的列向 P 4 犏犏犏犏犏犏 cn1 cn 2 cnn a nn 臌臌轾 c11 犏犏 c21 量犏犏之间的相似度很低。

犏犏 cn1 臌 5 （图 2）（图 4） 6.1.1.2 模型的建立我们需要将附件 1 中的十九块碎片转化为矩阵，通过 matlab 模拟矩阵之间的关系，进而得到碎片之间的关系。

附件 1 中每一块碎片的像素均为 72*1980，则通过 matlab 中的 imread 函数，可以将其转化成 1980×72 的灰度值矩阵，每个矩阵有 72 个列向量，每个列向量中有 1980 个元素。

建立“相似度”模型，将这些碎片抽象成矩阵，其中首列向量、末列向量分别构成构成 1980×19 的矩阵 A,B。

A 的列向量记为 A(:,i),B 的列向量记为 B(:,j) （ 1 ＃i, j 19 ）。

假设 Si , j 为 A(:,i)与 B(:,j)之间的相似度，固定 i，对所有的 1 ＃ j 19 ，求最大的 Si , j ，这样的 i 与 j 所对应的碎片是相邻的。通过 matlab，我们可以直观的表示出：

a008 (:,72) 与 a000 (:,1) 的相似度， a008 (:,72) 与 a001 (:,1) 的相似度， a008 (:,72) 与 a002 (:,1) 的相似度，??， a008 (:,72) 与 a018 (:,1) 的相似度。

运行附录中的“program0”即可输出其相似度: 0 0.7015 10 0.6722 1 0.6707 11 0.7258 2 0.6854 12 0.7177 3 0.6429 13 0.6545 4 0.6869 14 0.85 5 0.7485 15 0.754 6 0.6722 16 0.6798 7 0.7056 17 0.6677 8 0.8273 18 0.7343 9 0.6798 显然 a008 (:,72) 与 a014 (:,1) 的相似度最高，为 0.85。

运行附录中的“program1” 。可以从图像直观的呈现其相似度。其结果如“图 5（0），图 5（1），图 5（2）??图 5（18） ”所示。其中横轴表示列向量 a008 (:,72) 中元素的灰度值，纵轴分别表示列向量 a000 (:,1) ， a001 (:,1) ， a002 (:,1) ，??， a018 (:,1) 中元素的灰度值。

观察图 5（14），我们发现图中的元素集中在对角线上，而其他图中元素都很分散。

由此我们得到，a008 (:,72) 与 a014 (:,1) 中的对应元素相似度最高。

说明附件 1 的 “008.bmp” 与附件 1 的“014.bmp”相邻，手动拼接，发现两者恰好匹配。用同样的方法循环 18 次后，即可得到完整的图。 6 图 5（0）图 5（1） 7 图 5（2）图 5（3） 8 图 5（4）图 5（5） 9 图 5（6）图 5（7）图 5（8） 10 图 5（9）图 5（10） 11 图 5（11）图 5（12） 12 图 5（13）图 5（14） 13 图 5（15）图 5（16） 14 图 5（17）图 5（18） 6.1.1.3 程序的设计与模型的求解 15 （1）程序的设计我们通过观察得知“附件 1 的 008.bmp”为该文件的左边界，其灰度值矩阵为 a008 。

通过循环语句，我们可以依次求出 a008 (:,72) 与 a000 (:,1) 的相似度 S0 ，a008 (:,72) 与 a001 (:,1) 的相似度 S1 ， a008 (:,72) 与 a002 (:,1) 的相似度 S2 ,??, a008 (:,72) 与 a018 (:,1) 的相似度 S18 。

然后求出 S0 ， S1 ， S2 ，??， S18 的最大值。经过 6.1.1.1 的分析，我们得知，相邻列向量的相似度最高，所以，该相似度对应着“008.bmp”和与“008.bmp”右临的碎片。

找到该碎片后，重复上边的循环，得到下一个碎片，以此类推，最终得到整个拼接序列。

（2）程序的编写与运行利用 6.1.1.3（1）中介绍的思路进行编程，得到“program2” （见附录）。运行 “program2” ，输出以下结果： order1= 8 18 11 7 14 17 12 0 15 6 3 10 2 16 1 4 5 9 13 则附件 1 中碎片的排序为 8 14 12 15 3 10 2 16 1 4 表2 5 9 13 18 11 7 17 0 6 运行附件中的“program3” ，得到拼接完成的图片。

（此为示意图，清晰的图在附录中）图6 6.1.2 复原附件 2 中的文件碎片拼接附件 2 的整体思路与拼接附件 1 的相同。要注意的是在编写拼接附件 2 的 “ program4 ”时，程序循环的方向和起始点均与“ program2 ”不同（ “ program2 ”从 16 “008.bmp”开始，从左向右循环。

“program4”从“011.bmp“开始，从右向左循环）。

首先通过观察得知：附件 2 中的“003.bmp”为该文件的左边界，附件 2 中的“004.bmp” 为该文件的右边界。

运行附录中的“program4” ，输出以下结果： order2 = 0 2 0 3 3 7 15 5 6 1 2 5 18 9 7 1 11 13 15 10 18 8 11 12 14 17 16 4 9 13 10 8 12 14 17 16 43 6 注意到附件 2 的“003.bmp”为左边界。

“004.bmp”为右边界。将 order2 中 3 与 4 分开。得到：由此易得附件 2 中碎片的顺序为：

6 2 7 15 18 11 0 5 1 9 表2 13 10 8 12 14 17 16 4 运行“program5” 得到拼接完成的图片。

（此为示意图，清晰的图在附录中）图7 6.2 问题 2 针对附件 3、附件 4 给出的中、英文各一页文件的碎片数据进行拼接复原。

6.2.1 复原附件 3 中的文件碎片 6.2.1.1 问题的分析本题中的文件被分成 11 行、19 列共 209 块碎片，每块的像素为 180×72。由于碎片的数量多、尺寸小，所以拼接附件 1、2 的方法并不完全适用于附件 3。因此我们要寻找其他的出路。 17 6.2.1.2 模型的建立（1）将 209 块碎片分成 11 组由于切割的方向与纸张的边界平行，所以同一行的 19 块碎片的“上留白” （或“下留白” ）相差很小。不同行碎片的“上留白” （或“下留白” ）相差很大。我们可以通过编程，计算出 209 块碎片的“上留白”和“下留白” 。再通过程序将留白近似的碎片份批次筛选出来，最终筛选出 11 组，每组 19 块碎片。

因为留白近似相等，所以同一组的十九块碎片必然属于同一行。这样我们一次只需拼接 19 块碎片，重复拼接 11 组。将每组的 19 块碎片拼接完毕后，最终得到 11 块较大的碎片。

（2）寻找 11 块大碎片之间的顺序 209 块小碎片要拼接成 11 行，19 列的文件。其中，左边缘的那一列小碎片（共 11 个）分别为 11 块大碎片的最左端。因此，左边缘 11 块小碎片之间的顺序即为 11 块大碎片的顺序。只要我们通过编写程序，筛选出左边缘的 11 块小碎片，并确定他们之间的顺序，就可以在同一时间得到 11 块大碎片的顺序，进而拼接出整个文件。

（3）筛选出左边缘的小碎块因为文件都是左对齐的，因此左边缘的 11 块小碎片的“左留白”近似相等。这样，我们就可以通过程序，将这 11 块小碎片筛选出来。

筛选出 11 块小碎片后，我们可以通过拼接附件 1 的方法，来确定这 11 块小碎片的顺序，从而得到了拼接好的文件。

6.2.1.3 程序的设计与模型的求解（1）筛选出 11 组数据按照 6.2.1.2（1）介绍的思路设计程序，运行附录中的“program6” ，输出 11 组数据，每组 19 个。如下表所示：

次序 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 13 16 21 66 106 109 110 125 139 145 150 2 1 18 23 26 30 41 50 62 76 86 87 3 3 12 14 31 39 51 73 82 107 115 128 4 2 11 22 28 49 54 57 65 91 95 118 5 15 17 27 33 60 71 80 83 85 132 133 6 6 19 20 36 52 61 63 67 69 72 78 7 0 7 32 45 53 56 68 70 93 126 137 8 34 42 43 47 58 77 84 90 94 97 112 9 8 9 24 25 35 38 46 74 81 88 103 10 4 40 89 101 102 108 113 114 117 119 123 11 5 10 29 37 44 48 55 59 64 75 92 表3 157 100 134 129 152 79 138 121 105 140 98 173 120 135 141 156 96 153 124 122 146 104 181 142 159 143 165 99 158 127 130 151 111 182 147 160 178 170 116 166 136 148 154 171 184 168 169 186 198 131 174 144 161 155 172 187 179 176 188 200 162 175 149 167 185 180 197 191 199 190 202 163 196 164 189 194 201 204 195 203 192 205 177 208 183 193 207 206 （2）筛选出左边缘的 11 个小碎块，并将其排序。 18 根据 6.2.1.2（3）中介绍的思路，设计程序。运行“program7” ：输出： column1 = 7 7 14 29 14 38 29 38 49 49 61 61 71 表4 71 89 89 94 94 125 125 168 168 左边缘的 11 块小碎块的拼接方法，与拼接附件 1 的方法类似。

不过要重复运行程序。

运行“program8” ，输入 0；运行“program8” ，输入 1；运行“program8” ，输入 2；运行“program8” ，输入 3；运行“program8” ，输入 4；运行“program8” ，输入 5；运行“program8” ，输入 6；运行“program8” ，输入 7；运行“program8” ，输入 8；运行“program8” ，输入 9；运行“program8” ，输入 10；分析结果，只能得到 14 与 94 相邻，49 与 61 相邻，125、29、7 相邻，168 与 38 相邻， 89、71 无法确定。

此时通过人为干预，得出正确的序列： 49 61 168 38 71 14 94 表5 125 29 7 89 （3）将表 3 中的 11 组碎块分别排序第一组的排序对于第一行的数据 13 16 21 66 106 109 110 125 139 145 150 157 173 181 182 184 187 197 204 运行“program9” ，输入“15”,输出： order= 15 7 0 7 6 0 16 7 3 0 4 10 2 12 11 13 18 7 0 运行“program10” ，输入 15，输出： order= 18 8 9 4 10 2 12 11 13 18 8 9 7 0 14 5 17 1 15 注意到 7 是开头，观察两组向量中加粗的斜体字。易知表 4 中第一行的序列为： 125 13 182 109 197 16 184 110 187 66 106 150 21 173 157 181 204 139 145 表6 由表 5 知，125 为第 8 行的开头，所以其图像为： 19 图 8（1）同理可得：

第二组的排序 168 100 76 62 142 30 41 23 147 191 50 179 120 86 195 26 1 87 18 图 8（2）第三组的排序 14 128 3 159 82 199 135 12 73 160 203 169 134 39 31 51 107 115 176 图 8（3）第四组的排序 49 54 65 143 186 2 57 192 178 118 190 95 11 22 129 28 91 188 141 20 图 8（4）第五组的排序 71 156 83 132 200 17 80 33 202 198 15 133 170 205 85 152 165 27 60 图 8（5）第六组的排序 61 19 78 67 69 99 162 96 131 79 63 116 163 72 6 177 20 52 36 图 8（6）第七组的排序 7 208 138 158 126 68 175 45 174 0 137 53 56 93 153 70 166 32 196 21 图 8（7）第八组的排序 94 34 84 183 90 47 121 42 124 144 77 112 149 97 136 164 127 58 43 图 8（8）第九组的排序 38 148 46 161 24 35 81 189 122 103 130 193 88 167 25 8 9 105 74 图 8（9）第十组的排序 89 146 102 154 114 40 151 207 155 140 185 108 117 4 101 113 194 119 123 22 图 8（10）第十一组的排序 29 64 111 201 5 92 180 48 37 75 55 44 206 10 104 98 172 171 59 图 8（11）综上，附件三中碎片的顺序为： 49 61 168 38 71 14 94 125 29 7 89 54 19 100 148 156 128 34 13 64 208 146 65 78 76 46 83 3 84 182 111 138 102 143 67 62 161 132 159 183 109 201 158 154 186 2 57 192 178 118 190 69 99 162 96 131 79 63 142 30 41 23 147 191 50 24 35 81 189 122 103 130 200 17 80 33 202 198 15 82 199 135 12 73 160 203 90 47 121 42 124 144 77 197 16 184 110 187 66 106 5 92 180 48 37 75 55 126 68 175 45 174 0 137 114 40 151 207 155 140 185 表7 95 116 179 193 133 169 112 150 44 53 108 11 22 129 28 91 188 163 72 6 177 20 52 120 86 195 26 1 87 88 167 25 8 9 105 170 205 85 152 165 27 134 39 31 51 107 115 149 97 136 164 127 58 21 173 157 181 204 139 206 10 104 98 172 171 56 93 153 70 166 32 117 4 101 113 194 119 141 36 18 74 60 176 43 145 59 196 123 （4）根据上述结果，编写程序，输出完整的图片。

运行附录中的“program11” ，输出：

（此为示意图，清晰的图在附录中） 23 图9 6.2.2 复原附件 4 中的文件碎片。

6.2.2.1 问题的分析附件 4 同附件 3 相同，均被分割成 11×19 块小碎片。故拼接附件 4 的方法与附件 3 相同。

6.2.2.2 模型的建立与求解（1）将 209 块小碎片分组首先运行 program12，program13，求出每一块小碎片的“上留白”和“下留白” ，因为同一行的小碎片“上留白” （或“下留白” ）近似相等，所以对小碎片进行筛选。

上留白为构成一个长度为 209 的向量 blank： blank = Columns 1 through 12 17 30 31 0 39 0 0 0 115 9 0 0 0 21 0 12 0 0 8 0 9 12 37 52 Columns 13 through 24 Columns 25 through 36????????（后边的省略）下留白构成一个长度为 209 的向量 blankx blankx = Columns 1 through 12 48 61 0 18 0 27 17 0 0 8 5 0 0 0 0 9 0 51 8 0 8 9 0 27 Columns 13 through 24 Columns 25 through 36????????（后边的省略） 24 因为英文字母尺寸较小，空白位置较大，靠近边界的字母的留白时常发生大规模的波动，所以必须用 excel 进行人工筛选，筛选的结果为：序号 12 26 35 4 19 51 6 15 77 88 93 10 9 11 0 1 4 17 24 22 31 20 21 14 13 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 11 32 39 64 65 67 75 104 106 147 149 154 180 184 190 191 204 26 29 57 38 36 33 23 25 28 30 71 50 41 49 47 27 78 37 82 53 43 54 60 34 80 40 88 63 45 61 68 69 91 46 93 85 73 62 70 95 94 51 105 97 76 112 84 110 100 58 114 120 79 118 90 111 101 59 121 123 108 119 96 130 103 86 126 129 116 133 99 132 113 92 141 138 135 142 109 144 146 98 151 139 136 162 122 163 148 107 155 153 143 168 137 166 164 117 165 159 161 169 156 167 170 127 176 160 173 189 172 178 196 150 182 175 179 192 174 181 198 158 194 187 199 197 185 188 201 186 202 203 207 208 195 206 10 16 18 35 42 44 55 56 66 74 83 134 145 152 157 171 183 205 12 48 52 72 77 81 87 89 102 115 124 125 128 131 140 177 193 200 表8 （2）筛选出左边缘的 11 块小碎片根据左边缘的碎块“左留白”近似相等的原理，编写程序。

运行“program14” ，输出： Column1=19 20 70 81 86 132 159 171 191 201 208 132 159 表9 171 191 201 208 则附件 4 的左边缘为： 19 20 70 81 86 根据 6.2.1.3（2）提供的方法，对表 9 中的碎块进行拼接。结果为： 191 201 86 19 159 20 208 表 10 70 132 171 81 （3）分别拼接表 8 中的 11 组碎块，方法同 6.2.1.3（3），在此不赘述，结果为： 191 75 11 154 190 184 2 104 180 64 106 4 201 148 170 196 198 94 113 164 78 103 91 80 86 19 159 20 208 70 132 171 81 51 194 139 41 21 84 181 42 77 107 93 1 108 7 60 95 66 128 29 141 129 116 49 14 69 205 200 40 88 63 136 61 68 167 10 131 158 121 138 73 119 174 163 157 52 186 126 153 36 33 137 166 74 125 98 105 53 207 142 195 188 145 140 24 155 38 135 168 8 111 83 193 117 114 123 15 62 47 144 134 87 150 5 176 182 120 175 76 43 169 54 172 156 206 3 55 18 89 48 表 11 149 32 101 26 59 151 85 199 192 96 130 56 72 58 22 50 45 133 23 34 35 12 204 65 100 6 92 57 160 173 118 99 13 16 177 30 202 187 79 189 122 110 9 124 39 17 37 71 97 161 162 90 25 183 0 67 28 46 165 203 179 197 185 27 152 102 147 146 127 82 31 143 112 109 178 44 115 （4）根据上述结果，编辑程序，输出完整的图片 25 运行“program15” ，输出：图 10 6.3 问题 3 针对附件 5 给出的英文文件的碎片数据进行拼接复原。

6.3.1 问题的分析本题中被切碎的文件虽然是正反面，碎片数量扩大了一倍，但是拼接附件 3 的方法仍然适用。只要我们拼出了一面，就可以根据这一面的数据，迅速推出另一面的数据。

6.3.2 模型的建立和求解 (1)求出附件 5 中 418 块碎片的“上留白”与“下留白” 。然后进行人工筛选。由于留白近似的碎片均在同一行，因此可将 418 块碎片分成 11 组，每组 19×2 块碎片（一块碎片的正面和反面必须在同一组内）。

运行 program16，得到两个长度均为 418 的向量 blank1，blank2（由于内容过长，故不在文本中显示。

）。其中 blank1 为 418 块碎片的“上留白” ，blank2 为 418 块最片的 “下留白” 。用 excel 进行筛选得到； 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 序号 1 111a 108b 110b 18a 20b 189a 47b 155b 174a 66b 183a 125b 150b 81a 136a 164a 140b 29b 78a 2 10a 120a 124a 144b 147b 14b 152b 178b 192b 22b 25a 36b 44b 59b 5b 60a 76a 79b 89b 3 153b 137a 94a 45b 86a 56a 200a 30b 98b 61a 121b 84a 38b 131a 143a 187a 42a 138b 186a 4 11a 198a 34b 87b 97b 93b 39a 194a 156b 181a 206a 161b 173a 72a 83b 175b 169a 132a 199a 5 107b 151a 166a 170a 162a 70a 203a 37a 115a 1a 65a 149a 191b 139a 90b 2b 180b 41b 88a 6 184a 12b 154a 17a 57b 64a 24b 207b 197b 28a 158b 179a 58b 208b 13b 142b 116a 102a 114b 7 171a 53a 16a 202b 73a 130b 159b 50b 19a 177a 92a 31b 190a 163b 35b 193a 201b 21a 146b 8 195b 117a 75a 8a 182a 188b 122b 168b 63a 167b 67b 128b 46b 127b 172b 40b 157b 68a 165a 9 7a 176b 74a 185b 141b 80a 204a 77b 32b 126a 69b 85a 4b 27b 105b 135a 148a 0a 3a 10 133b 62b 71a 129a 82a 101b 145b 95b 33a 52b 119b 48b 160a 15a 9a 205b 51a 118a 23a 11 43b 49a 113b 91b 112b 100a 196a 123b 134b 26a 104b 96a 6b 55a 54a 103b 109b 106a 99b 序号 20 21 22 23 24 25 26 27 28 26 29 30 31 32 33 34 35 36 37 38 1 108a 110a 111b 125a 136b 140a 150a 155a 164b 174b 183b 189b 18b 20a 29a 47a 66a 78b 81b 2 120b 124b 10b 36a 5a 76b 44a 178a 60b 192a 25b 14a 144a 147a 79a 152a 22a 89a 59a 3 137b 94b 153a 84b 143b 42b 38a 30a 187b 98a 121a 56b 45a 86b 138a 200b 61b 186b 131b 4 198b 34a 11b 161a 83a 169b 173b 194b 175a 156a 206b 93a 87a 97a 132b 39b 181b 199b 72b 5 151b 166b 107a 149b 90a 180a 191a 37b 2a 115b 65b 70b 170b 162b 41a 203b 1b 88b 139b 6 12a 154b 184b 179b 13a 116b 58a 207a 142a 197a 158a 64b 17b 57a 102b 24a 28b 114a 208a 7 53b 16b 171b 31a 35a 201a 190b 50a 193b 19b 92b 130a 202a 73b 21b 159a 177b 146a 163a 8 117b 75b 195a 128a 172a 157a 46a 168a 40a 63b 67a 188a 8b 182b 68b 122a 167a 165b 127a 9 176a 74b 7b 85b 105a 148b 4a 77a 135b 32a 69a 80b 185a 141a 0b 204b 126b 3b 27a 10 62a 71b 133a 48a 9b 51b 160b 95a 205a 33b 119a 101a 129b 82b 118b 145a 52a 23b 15b 11 49b 113a 43a 96b 54b 109a 6a 123a 103a 134a 104a 100b 91a 112a 106b 196b 26b 99a 55b 表 12 （2）利用 6.2.1.3（2）中的方法，筛选出附件 5 左边缘的 11 块碎片（这些碎片的反面同样代表文件背面右边缘，在此只考虑左边缘即可）。

运行“program17” ，输出： column1a = 9 54 136 143 column1b = 0 0 0 0 5 13 35 83 90 105 172 则“009a.bmp” ， “054a.bmp” ， “136a.bmp” ， “143a.bmp” “005b.bmp” ， “013b.bmp” ， “035b.bmp” ， “083b.bmp” ， “090b.bmp” ， “105b.bmp” ， “172b.bmp” ，这 11 块碎片构成该文件其中一面的左边缘。

与拼接附件 4 的左边类似。

通过程序，仅仅能够确定：35b、 172b、105b 相邻，136a、 5b 相邻，90b、13b 相邻。通过人为干预，我们得知其正确的顺序为： 136a 5b 143a 83b 90b 13b 35b 表 13 172b 105b 9a 54a （3）利用 6.2.1.3（3）中的方法，将表 12 中的 11 组碎片分别排序，方法与拼接附件 3 时完全相同。再将其与表 13 结合，得出拼接结果。 136a 47b 20b 164a 81a 189a 29b 18a 108b 66b 110b 174a 183a 150b 155b 140b 125b 111a 78a 5b 152b 147b 60a 59b 14b 79b 144b 120a 22b 124a 192b 25a 44b 178b 76a 36b 10a 89b 143a 200a 86a 187a 131a 56a 138b 45b 137a 61a 94a 98b 121b 38b 30b 42a 84a 153b 186a 83b 39a 97b 175b 72a 93b 132a 87b 198a 181a 34b 156b 206a 173a 194a 169a 161b 11a 199a 90b 203a 162a 2b 139a 70a 41b 170a 151a 1a 166a 115a 65a 191b 37a 180b 149a 107b 88a 13b 24b 57b 142b 208b 64a 102a 17a 12b 28a 154a 197b 158b 58b 207b 116a 179a 184a 114b 35b 159b 73a 193a 163b 130b 21a 202b 53a 177a 16a 19a 92a 190a 50b 201b 31b 171a 146b 172b 122b 182a 40b 127b 188b 68a 8a 117a 167b 75a 63a 67b 46b 168b 157b 128b 195b 165a 105b 204a 141b 135a 27b 80a 0a 185b 176b 126a 74a 32b 69b 4b 77b 148a 85a 7a 3a 9a 145b 82a 205b 15a 101b 118a 129a 62b 52b 71a 33a 119b 160a 95b 51a 48b 133b 23a 54a 196a 112b 103b 55a 100a 106a 91b 49a 26a 113b 134b 104b 6b 123b 109b 96a 43b 99b 表 14（附件 5 的正面） 27 78b 111b 125a 140a 155a 150a 183b 174b 110a 66a 108a 18b 29a 189b 81b 164b 20a 47a 136b 89a 10b 36a 76b 178a 44a 25b 192a 124b 22a 120b 144a 79a 14a 59a 60b 147a 152a 5a 186b 153a 84b 42b 30a 38a 121a 98a 94b 61b 137b 45a 138a 56b 131b 187b 86b 200b 143b 199b 11b 161a 169b 194b 173b 206b 156a 34a 181b 198b 87a 132b 93a 72b 175a 97a 39b 83a 88b 107a 149b 180a 37b 191a 65b 115b 166b 1b 151b 170b 41a 70b 139b 2a 162b 203b 90a 114a 184b 179b 116b 207a 58a 158a 197a 154b 28b 12a 17b 102b 64b 208a 142a 57a 24a 13a 146a 171b 31a 201a 50a 190b 92b 19b 16b 177b 53b 202a 21b 130a 163a 193b 73b 159a 35a 165b 195a 128a 157a 168a 46a 67a 63b 75b 167a 117b 8b 68b 188a 127a 40a 182b 122a 172a 3b 7b 85b 148b 77a 4a 69a 32a 74b 126b 176a 185a 0b 80b 27a 135b 141a 204b 105a 23b 133a 48a 51b 95a 160b 119a 33b 71b 52a 62a 129b 118b 101a 15b 205a 82b 145a 9b 99a 43a 96b 109a 123a 6a 104a 134a 113a 26b 49b 91a 106b 100b 55b 103a 112a 196b 54b 表 15（附件 5 的反面）（4）根据上述结果，编辑程序，输出完整的图片运行“program18” ，输出：图 11 28 图 12 经过模型的建立与计算机模拟，我们得到了图 7、9、10、11、12 五幅图，经观察，这五幅图拼接状况良好，衔接自然，文字连贯。说明拼接结果正确。 7. 模型的分析模型优点：

（1）常规文档的碎纸片拼接方式，需要利用碎片边缘的尖点特征，几何特征，尖角特征，面积特征等几何特征。不适用于碎片完全相同的情形。而本模型很好地弥补了这一点。

（2）本模型的应用范围广泛，不只适用于矩形碎片的拼接。对于可镶嵌的多边形碎片，均可使用本模型来拼接。

模型缺点：

建模方法较单一，对于同一个问题没有建立多个模型，无法进行多种方法的分析比较。 8. 参考文献 [1] 罗智中《基于文字特征的文档碎纸片半自动拼接》华东交通大学机电工程学院，南昌 330013 文章编号：1002．833l(2012)05．0207．04 [2] 姜启源，谢金星，叶俊《数学模型（第三版）》高等教育出版社出版时间：

2003-8-1 [3] 张立科《matlab 7.0 从入门到精通》人民邮电出版社出版时间：2006-3 9. 附录 29 9.1 附件的碎片序号与复原图附件 1 8 14 12 15 3 10 2 16 1 4 5 9 13 18 11 7 17 0 6 附件 2 3 6 2 7 15 18 11 0 5 1 9 13 10 8 12 14 17 16 4 30 附件 3 49 61 168 38 71 14 94 125 29 7 54 65 143 186 2 57 192 178 19 78 67 69 99 162 96 131 100 76 62 142 30 41 23 147 148 46 161 24 35 81 189 122 156 83 132 200 17 80 33 202 128 3 159 82 199 135 12 73 34 84 183 90 47 121 42 124 13 182 109 197 16 184 110 187 64 111 201 5 92 180 48 37 208 138 158 126 68 175 45 174 118 79 191 103 198 160 144 66 75 0 190 63 50 130 15 203 77 106 55 137 31 95 116 179 193 133 169 112 150 44 53 11 22 129 28 91 163 72 6 177 20 120 86 195 26 1 88 167 25 8 9 170 205 85 152 165 134 39 31 51 107 149 97 136 164 127 21 173 157 181 204 206 10 104 98 172 56 93 153 70 166 188 52 87 105 27 115 58 139 171 32 141 36 18 74 60 176 43 145 59 196 89 146 102 154 114 40 151 207 155 140 185 108 117 4 101 113 194 119 123 附件 4 191 201 86 19 159 20 75 148 51 194 139 41 11 170 107 93 1 108 154 196 29 141 129 116 190 198 40 88 63 136 184 94 158 121 138 73 2 113 186 126 153 36 104 164 98 105 53 207 180 78 24 155 38 135 64 103 117 114 123 15 106 91 150 176 120 76 32 4 80 5 182 175 43 149 101 59 151 85 199 32 26 58 22 50 45 204 100 92 57 160 173 65 6 30 202 187 79 39 17 37 71 97 161 67 28 46 165 203 179 147 146 127 82 31 143 208 21 70 132 171 81 84 181 42 77 7 60 95 66 128 49 14 69 205 200 61 68 167 10 131 119 33 174 163 157 52 137 166 74 125 142 168 62 195 188 145 140 8 111 83 193 47 144 134 87 169 54 172 206 55 89 156 3 18 48 192 133 118 189 162 197 112 96 130 56 72 23 34 35 12 99 13 16 177 122 110 9 124 90 25 183 0 185 27 152 102 109 178 44 115 附件 5 136a 47b 20b 164a 81a 189a 29b 18a 108b 66b 110b 174a 183a 150b 155b 140b 125b 111a 78a 33 5b 152b 147b 60a 59b 14b 79b 144b 120a 22b 124a 192b 25a 44b 178b 76a 36b 10a 89b 143a 200a 86a 187a 131a 56a 138b 45b 137a 61a 94a 98b 121b 38b 30b 42a 84a 153b 186a 83b 39a 97b 175b 72a 93b 132a 87b 198a 181a 34b 156b 206a 173a 194a 169a 161b 11a 199a 90b 203a 162a 2b 139a 70a 41b 170a 151a 1a 166a 115a 65a 191b 37a 180b 149a 107b 88a 13b 24b 57b 142b 208b 64a 102a 17a 12b 28a 154a 197b 158b 58b 207b 116a 179a 184a 114b 35b 159b 73a 193a 163b 130b 21a 202b 53a 177a 16a 19a 92a 190a 50b 201b 31b 171a 146b 172b 122b 182a 40b 127b 188b 68a 8a 117a 167b 75a 63a 67b 46b 168b 157b 128b 195b 165a 105b 204a 141b 135a 27b 80a 0a 185b 176b 126a 74a 32b 69b 4b 77b 148a 85a 7a 3a 9a 145b 82a 205b 15a 101b 118a 129a 62b 52b 71a 33a 119b 160a 95b 51a 48b 133b 23a 54a 196a 112b 103b 55a 100a 106a 91b 49a 26a 113b 134b 104b 6b 123b 109b 96a 43b 99b 表 14（附件 5 的正面） 34 78b 111b 125a 140a 155a 150a 183b 174b 110a 66a 108a 18b 29a 189b 81b 164b 20a 47a 136b 89a 10b 36a 76b 178a 44a 25b 192a 124b 22a 120b 144a 79a 14a 59a 60b 147a 152a 5a 186b 153a 84b 42b 30a 38a 121a 98a 94b 61b 137b 45a 138a 56b 131b 187b 86b 200b 143b 199b 11b 161a 169b 194b 173b 206b 156a 34a 181b 198b 87a 132b 93a 72b 175a 97a 39b 83a 88b 107a 149b 180a 37b 191a 65b 115b 166b 1b 151b 170b 41a 70b 139b 2a 162b 203b 90a 114a 184b 179b 116b 207a 58a 158a 197a 154b 28b 12a 17b 102b 64b 208a 142a 57a 24a 13a 146a 171b 31a 201a 50a 190b 92b 19b 16b 177b 53b 202a 21b 130a 163a 193b 73b 159a 35a 165b 195a 128a 157a 168a 46a 67a 63b 75b 167a 117b 8b 68b 188a 127a 40a 182b 122a 172a 3b 7b 85b 148b 77a 4a 69a 32a 74b 126b 176a 185a 0b 80b 27a 135b 141a 204b 105a 23b 133a 48a 51b 95a 160b 119a 33b 71b 52a 62a 129b 118b 101a 15b 205a 82b 145a 9b 99a 43a 96b 109a 123a 6a 104a 134a 113a 26b 49b 91a 106b 100b 55b 103a 112a 196b 54b 表 15（附件 5 的反面） 35 9.2 使用的程序为 matlab 7.10.0.499 excel2003 word PS CS 9.3 以下为 matlab 源代码 program0: 36 a0=imread('000.bmp');a1=imread('001.bmp');a2=imread('002.bmp');a3=imread('0 03.bmp');a4=imread('004.bmp');a5=imread('005.bmp');a6=imread('006.bmp');a7= imread('007.bmp');a8=imread('008.bmp');a9=imread('009.bmp');a10=imread('010 .bmp');a11=imread('011.bmp');a12=imread('012.bmp');a13=imread('013.bmp');a1 4=imread('014.bmp');a15=imread('015.bmp');a16=imread('016.bmp');a17=imread( '017.bmp');a18=imread('018.bmp');

left0=a0(:,1);left1=a1(:,1);left2=a2(:,1);left3=a3(:,1);left4=a4(:,1);left5 =a5(:,1);left6=a6(:,1);left7=a7(:,1);left8=a8(:,1);left9=a9(:,1);left10=a10 (:,1);left11=a11(:,1);left12=a12(:,1);left13=a13(:,1);left14=a14(:,1);left1 5=a15(:,1);left16=a16(:,1);left17=a17(:,1);

left18=a18(:,1);right0=a0(:,end);right1=a1(:,end);right2=a2(:,end);right3=a 3(:,end);right4=a4(:,end);right5=a5(:,end);right6=a6(:,end);right7=a7(:,end );right8=a8(:,end);right9=a9(:,end);right10=a10(:,end);right11=a11(:,end);r ight12=a12(:,end);right13=a13(:,end);right14=a14(:,end);right15=a15(:,end);

right16=a16(:,end);right17=a17(:,end);right18=a18(:,end); A=[left0,left1,left2,left3,left4,left5,left6,left7,left8,left9,left10,left1 1,left12,left13,left14,left15,left16,left17,left18];

B=[right0,right1,right2,right3,right4,right5,right6,right7,right8,right9,ri ght10,right11,right12,right13,right14,right15,right16,right17,right18];

S=zeros(1,19);

for i=1:19 for j=1:1980 if (B(j,9)==A(j,i)) S(i)=S(i)+1;

end end end S=S/1980;

S program1：

a0=imread('000.bmp');a1=imread('001.bmp');a2=imread('002.bmp');a3=imread('0 03.bmp');a4=imread('004.bmp');a5=imread('005.bmp');a6=imread('006.bmp');a7= imread('007.bmp');a8=imread('008.bmp');a9=imread('009.bmp');a10=imread('010 .bmp');a11=imread('011.bmp');a12=imread('012.bmp');a13=imread('013.bmp');a1 4=imread('014.bmp');a15=imread('015.bmp');a16=imread('016.bmp');a17=imread( '017.bmp');a18=imread('018.bmp');

plot(a8(:,72),a0(:,1));

figure() plot(a8(:,72),a1(:,1));

figure() 37 plot(a8(:,72),a2(:,1));

figure() plot(a8(:,72),a3(:,1));

figure() plot(a8(:,72),a4(:,1));

figure() plot(a8(:,72),a5(:,1));

figure() plot(a8(:,72),a6(:,1));

figure() plot(a8(:,72),a7(:,1));

figure() plot(a8(:,72),a8(:,1));

figure() plot(a8(:,72),a9(:,1));

figure() plot(a8(:,72),a10(:,1));

figure() plot(a8(:,72),a11(:,1));

figure() plot(a8(:,72),a12(:,1));

figure() plot(a8(:,72),a13(:,1));

figure() plot(a8(:,72),a14(:,1));

figure() plot(a8(:,72),a15(:,1));

figure() plot(a8(:,72),a16(:,1)); 38 figure() plot(a8(:,72),a17(:,1));

figure() plot(a8(:,72),a18(:,1));

program2：

right16=a16(:,end);right17=a17(:,end);right18=a18(:,end);

A=[left0,left1,left2,left3,left4,left5,left6,left7,left8,left9,left10,left1 1,left12,left13,left14,left15,left16,left17,left18];

B=[right0,right1,right2,right3,right4,right5,right6,right7,right8,right9,ri ght10,right11,right12,right13,right14,right15,right16,right17,right18];

d=size(a0);

x=zeros(18,19);

y=zeros(18,2);

num=zeros(19,1);

order1=zeros(19,1);

order1(1,1)=8;

for k=1:18 for i=0:18 for j=1:d(1) if (B(j,order1(k,1)+1)==A(j,i+1)) x(k,i+1)=x(k,i+1)+1;

end end end [num(k+1,1),z]=max(x(k,:));

order1(k+1,1)=z-1; 39 end order1 program3: a0=imread('000.bmp');a1=imread('001.bmp');a2=imread('002.bmp');a3=imread('0 03.bmp');a4=imread('004.bmp');a5=imread('005.bmp');a6=imread('006.bmp');a7= imread('007.bmp');a8=imread('008.bmp');a9=imread('009.bmp');a10=imread('010 .bmp');a11=imread('011.bmp');a12=imread('012.bmp');a13=imread('013.bmp');a1 4=imread('014.bmp');a15=imread('015.bmp');a16=imread('016.bmp');a17=imread( '017.bmp');a18=imread('018.bmp');

A=[a8,a14,a12,a15,a3,a10,a2,a16,a1,a4,a5,a9,a13,a18,a11,a7,a17,a0,a6];

imshow(A,[]);

program4：

right16=a16(:,end);right17=a17(:,end);right18=a18(:,end);

A=[left0,left1,left2,left3,left4,left5,left6,left7,left8,left9,left10,left1 1,left12,left13,left14,left15,left16,left17,left18];

B=[right0,right1,right2,right3,right4,right5,right6,right7,right8,right9,ri ght10,right11,right12,right13,right14,right15,right16,right17,right18];

d=size(a0);

x=zeros(18,19);

y=zeros(18,2);

num=zeros(19,1);

order=zeros(19,1);

order(1,1)=11;

for k=1:18 for i=0:18 for j=1:d(1) 40 if (A(j,order(k,1)+1)==B(j,i+1)) x(k,i+1)=x(k,i+1)+1;

end end end [num(k+1,1),z]=max(x(k,:));

order(k+1,1)=z-1;

end for i=1:19 order2(i)=order(20-i);

end order2 program5：

A=[a3,a6,a2,a7,a15,a18,a11,a0,a5,a1,a9,a13,a10,a8,a12,a14,a17,a16,a4];

imshow(A,[]);

program6：

);a21=imread('021.bmp');a22=imread('022.bmp');a23=imread('023.bmp');a24=imr ead('024.bmp');a25=imread('025.bmp');a26=imread('026.bmp');a27=imread('027. bmp');a28=imread('028.bmp');a29=imread('029.bmp');a30=imread('030.bmp');a31 =imread('031.bmp');a32=imread('032.bmp');a33=imread('033.bmp');a34=imread('

034.bmp');a35=imread('035.bmp');a36=imread('036.bmp');a37=imread('037.bmp') ;a38=imread('038.bmp');a39=imread('039.bmp');a40=imread('040.bmp');a41=imre ad('041.bmp');a42=imread('042.bmp');a43=imread('043.bmp');a44=imread('044.b mp');a45=imread('045.bmp');a46=imread('046.bmp');a47=imread('047.bmp');a48= imread('048.bmp');a49=imread('049.bmp');a50=imread('050.bmp');a51=imread('0 51.bmp');a52=imread('052.bmp');a53=imread('053.bmp');a54=imread('054.bmp');

a55=imread('055.bmp');a56=imread('056.bmp');a57=imread('057.bmp');a58=imrea d('058.bmp');a59=imread('059.bmp');a60=imread('060.bmp');a61=imread('061.bm p');a62=imread('062.bmp');a63=imread('063.bmp');a64=imread('064.bmp');a65=i 41 mread('065.bmp');a66=imread('066.bmp');a67=imread('067.bmp');a68=imread('06 8.bmp');a69=imread('069.bmp');a70=imread('070.bmp');a71=imread('071.bmp');a 72=imread('072.bmp');a73=imread('073.bmp');a74=imread('074.bmp');a75=imread ('075.bmp');a76=imread('076.bmp');a77=imread('077.bmp');a78=imread('078.bmp ');a79=imread('079.bmp');a80=imread('080.bmp');a81=imread('081.bmp');a82=im read('082.bmp');a83=imread('083.bmp');a84=imread('084.bmp');a85=imread('085 .bmp');a86=imread('086.bmp');a87=imread('087.bmp');a88=imread('088.bmp');a8 9=imread('089.bmp');a90=imread('090.bmp');a91=imread('091.bmp');a92=imread( '092.bmp');a93=imread('093.bmp');a94=imread('094.bmp');a95=imread('095.bmp'

);a96=imread('096.bmp');a97=imread('097.bmp');a98=imread('098.bmp');a99=imr ead('099.bmp');a100=imread('100.bmp');a101=imread('101.bmp');a102=imread('1 02.bmp');a103=imread('103.bmp');a104=imread('104.bmp');a105=imread('105.bmp ');a106=imread('106.bmp');a107=imread('107.bmp');a108=imread('108.bmp');a10 9=imread('109.bmp');a110=imread('110.bmp');a111=imread('111.bmp');a112=imre ad('112.bmp');a113=imread('113.bmp');a114=imread('114.bmp');a115=imread('11 5.bmp');a116=imread('116.bmp');a117=imread('117.bmp');a118=imread('118.bmp'

);a119=imread('119.bmp');a120=imread('120.bmp');a121=imread('121.bmp');a122 =imread('122.bmp');a123=imread('123.bmp');a124=imread('124.bmp');a125=imrea d('125.bmp');a126=imread('126.bmp');a127=imread('127.bmp');a128=imread('128 .bmp');a129=imread('129.bmp');a130=imread('130.bmp');a131=imread('131.bmp') ;a132=imread('132.bmp');a133=imread('133.bmp');a134=imread('134.bmp');a135= imread('135.bmp');a136=imread('136.bmp');a137=imread('137.bmp');a138=imread ('138.bmp');a139=imread('139.bmp');a140=imread('140.bmp');a141=imread('141. bmp');a142=imread('142.bmp');a143=imread('143.bmp');a144=imread('144.bmp');

a145=imread('145.bmp');a146=imread('146.bmp');a147=imread('147.bmp');a148=i mread('148.bmp');a149=imread('149.bmp');a150=imread('150.bmp');a151=imread( '151.bmp');a152=imread('152.bmp');a153=imread('153.bmp');a154=imread('154.b mp');a155=imread('155.bmp');a156=imread('156.bmp');a157=imread('157.bmp');a 158=imread('158.bmp');a159=imread('159.bmp');a160=imread('160.bmp');a161=im read('161.bmp');a162=imread('162.bmp');a163=imread('163.bmp');a164=imread('

164.bmp');a165=imread('165.bmp');a166=imread('166.bmp');a167=imread('167.bm p');a168=imread('168.bmp');a169=imread('169.bmp');a170=imread('170.bmp');a1 71=imread('171.bmp');a172=imread('172.bmp');a173=imread('173.bmp');a174=imr ead('174.bmp');a175=imread('175.bmp');a176=imread('176.bmp');a177=imread('1 77.bmp');a178=imread('178.bmp');a179=imread('179.bmp');a180=imread('180.bmp ');a181=imread('181.bmp');a182=imread('182.bmp');a183=imread('183.bmp');a18 4=imread('184.bmp');a185=imread('185.bmp');a186=imread('186.bmp');a187=imre ad('187.bmp');a188=imread('188.bmp');a189=imread('189.bmp');a190=imread('19 0.bmp');a191=imread('191.bmp');a192=imread('192.bmp');a193=imread('193.bmp'

);a194=imread('194.bmp');a195=imread('195.bmp');a196=imread('196.bmp');a197 =imread('197.bmp');a198=imread('198.bmp');a199=imread('199.bmp');a200=imrea d('200.bmp');a201=imread('201.bmp');a202=imread('202.bmp');a203=imread('203 .bmp');a204=imread('204.bmp');a205=imread('205.bmp');a206=imread('206.bmp') ;a207=imread('207.bmp');a208=imread('208.bmp'); 42 A=zeros(180,72,209);

A(:,:,1)=a0;A(:,:,2)=a1;A(:,:,3)=a2;A(:,:,4)=a3;A(:,:,5)=a4;A(:,:,6)=a5;A(: ,:,7)=a6;A(:,:,8)=a7;A(:,:,9)=a8;A(:,:,10)=a9;A(:,:,11)=a10;A(:,:,12)=a11;A (:,:,13)=a12;A(:,:,14)=a13;A(:,:,15)=a14;A(:,:,16)=a15;A(:,:,17)=a16;A(:,:, 18)=a17;A(:,:,19)=a18;A(:,:,20)=a19;A(:,:,21)=a20;A(:,:,22)=a21;A(:,:,23)=a 22;A(:,:,24)=a23;A(:,:,25)=a24;A(:,:,26)=a25;A(:,:,27)=a26;A(:,:,28)=a27;A( :,:,29)=a28;A(:,:,30)=a29;A(:,:,31)=a30;A(:,:,32)=a31;A(:,:,33)=a32;A(:,:,3 4)=a33;A(:,:,35)=a34;A(:,:,36)=a35;A(:,:,37)=a36;A(:,:,38)=a37;A(:,:,39)=a3 8;A(:,:,40)=a39;A(:,:,41)=a40;A(:,:,42)=a41;A(:,:,43)=a42;A(:,:,44)=a43;A(: ,:,45)=a44;A(:,:,46)=a45;A(:,:,47)=a46;A(:,:,48)=a47;A(:,:,49)=a48;A(:,:,50 )=a49;A(:,:,51)=a50;A(:,:,52)=a51;A(:,:,53)=a52;A(:,:,54)=a53;A(:,:,55)=a54 ;A(:,:,56)=a55;A(:,:,57)=a56;A(:,:,58)=a57;A(:,:,59)=a58;A(:,:,60)=a59;A(:, :,61)=a60;A(:,:,62)=a61;A(:,:,63)=a62;A(:,:,64)=a63;A(:,:,65)=a64;A(:,:,66) =a65;A(:,:,67)=a66;A(:,:,68)=a67;A(:,:,69)=a68;A(:,:,70)=a69;A(:,:,71)=a70;

A(:,:,72)=a71;A(:,:,73)=a72;A(:,:,74)=a73;A(:,:,75)=a74;A(:,:,76)=a75;A(:,: ,77)=a76;A(:,:,78)=a77;A(:,:,79)=a78;A(:,:,80)=a79;A(:,:,81)=a80;A(:,:,82)= a81;A(:,:,83)=a82;A(:,:,84)=a83;A(:,:,85)=a84;A(:,:,86)=a85;A(:,:,87)=a86;A (:,:,88)=a87;A(:,:,89)=a88;A(:,:,90)=a89;A(:,:,91)=a90;A(:,:,92)=a91;A(:,:, 93)=a92;A(:,:,94)=a93;A(:,:,95)=a94;A(:,:,96)=a95;A(:,:,97)=a96;A(:,:,98)=a 97;A(:,:,99)=a98;A(:,:,100)=a99;A(:,:,101)=a100;A(:,:,102)=a101;A(:,:,103)= a102;A(:,:,104)=a103;A(:,:,105)=a104;A(:,:,106)=a105;A(:,:,107)=a106;A(:,:, 108)=a107;A(:,:,109)=a108;A(:,:,110)=a109;A(:,:,111)=a110;A(:,:,112)=a111;A (:,:,113)=a112;A(:,:,114)=a113;A(:,:,115)=a114;A(:,:,116)=a115;A(:,:,117)=a 116;A(:,:,118)=a117;A(:,:,119)=a118;A(:,:,120)=a119;A(:,:,121)=a120;A(:,:,1 22)=a121;A(:,:,123)=a122;A(:,:,124)=a123;A(:,:,125)=a124;A(:,:,126)=a125;A( :,:,127)=a126;A(:,:,128)=a127;A(:,:,129)=a128;A(:,:,130)=a129;A(:,:,131)=a1 30;A(:,:,132)=a131;A(:,:,133)=a132;A(:,:,134)=a133;A(:,:,135)=a134;A(:,:,13 6)=a135;A(:,:,137)=a136;A(:,:,138)=a137;A(:,:,139)=a138;A(:,:,140)=a139;A(: ,:,141)=a140;A(:,:,142)=a141;A(:,:,143)=a142;A(:,:,144)=a143;A(:,:,145)=a14 4;A(:,:,146)=a145;A(:,:,147)=a146;A(:,:,148)=a147;A(:,:,149)=a148;A(:,:,150 )=a149;A(:,:,151)=a150;A(:,:,152)=a151;A(:,:,153)=a152;A(:,:,154)=a153;A(:, :,155)=a154;A(:,:,156)=a155;A(:,:,157)=a156;A(:,:,158)=a157;A(:,:,159)=a158 ;A(:,:,160)=a159;A(:,:,161)=a160;A(:,:,162)=a161;A(:,:,163)=a162;A(:,:,164) =a163;A(:,:,165)=a164;A(:,:,166)=a165;A(:,:,167)=a166;A(:,:,168)=a167;A(:,: ,169)=a168;A(:,:,170)=a169;A(:,:,171)=a170;A(:,:,172)=a171;A(:,:,173)=a172;

A(:,:,174)=a173;A(:,:,175)=a174;A(:,:,176)=a175;A(:,:,177)=a176;A(:,:,178)= a177;A(:,:,179)=a178;A(:,:,180)=a179;A(:,:,181)=a180;A(:,:,182)=a181;A(:,:, 183)=a182;A(:,:,184)=a183;A(:,:,185)=a184;A(:,:,186)=a185;A(:,:,187)=a186;A (:,:,188)=a187;A(:,:,189)=a188;A(:,:,190)=a189;A(:,:,191)=a190;A(:,:,192)=a 191;A(:,:,193)=a192;A(:,:,194)=a193;A(:,:,195)=a194;A(:,:,196)=a195;A(:,:,1 97)=a196;A(:,:,198)=a197;A(:,:,199)=a198;A(:,:,200)=a199;A(:,:,201)=a200;A( :,:,202)=a201;A(:,:,203)=a202;A(:,:,204)=a203;A(:,:,205)=a204;A(:,:,206)=a2 43 05;A(:,:,207)=a206;A(:,:,208)=a207;A(:,:,209)=a208;

blank1=zeros(1,209);

q1=zeros(209,180);

for i=1:209 for j=1:180 for k=1:72 q1(i,j)=q1(i,j)+A(j,k,i);

end if (q1(i,j)>18300) blank1(i)=blank1(i)+1;

else break;

end end end q2=zeros(209,180);

blank2=zeros(1,209);

for i=1:209 for j=1:180 for k=1:72 q2(i,181-j)=q2(i,181-j)+A(181-j,k,i);

end if (q2(i,181-j)>18300) blank2(i)=blank2(i)+1;

else break;

end end end blank2(82)=95;

blank2(106)=95;

blank2(123)=95;

blank2(30)=0;

blank1(30)=0;

blank1(29)=35;%?????×???? e=zeros(11,11);

F=zeros(11,19);

disp('8');

for i=1:11 for j=1:209 if (blank1(j)>5&blank1(j)<=10) 44 e(1,i)=e(1,i)+1;

r=e(1,i);

F(1,r)=j-1;

end end end F(1,:) disp('3');

for i=1:11 for j=1:209 if (blank1(j)>16&blank1(j)<=24) e(2,i)=e(2,i)+1;

r=e(2,i);

F(2,r)=j-1;

end end end F(2,:) disp('6');

for i=1:11 for j=1:209 if ((blank1(j)>24&blank1(j)<=30)|(blank1(j)>92)) e(3,i)=e(3,i)+1;

r=e(3,i);

F(3,r)=j-1;

end end end F(3,:) disp('1');

for i=1:11 for j=1:209 if (blank1(j)>32&blank1(j)<=45) e(4,i)=e(4,i)+1;

r=e(4,i);

F(4,r)=j-1;

end end end F(4,:) 45 disp('5');

for i=1:11 for j=1:209 if ((blank2(j)>0&blank2(j)<=5)|(blank2(j)>65&blank2(j)<=75)) e(5,i)=e(5,i)+1;

r=e(5,i);

F(5,r)=j-1;

end end end F(5,:) disp('2');

for i=1:11 for j=1:209 if (blank2(j)>5&blank2(j)<=10) e(6,i)=e(6,i)+1;

r=e(6,i);

F(6,r)=j-1;

end end end F(6,:) disp('10');

for i=1:11 for j=1:209 if ((blank2(j)>10&blank2(j)<=20)|(blank2(j)>80&blank2(j)<=90)) e(7,i)=e(7,i)+1;

r=e(7,i);

F(7,r)=j-1;

end end end F(7,:) disp('7');

for i=1:11 for j=1:209 if (blank2(j)>20&blank2(j)<=25) e(8,i)=e(8,i)+1;

r=e(8,i);

F(8,r)=j-1;

end 46 end end F(8,:) disp('4');

for i=1:11 for j=1:209 if ((blank2(j)>25&blank2(j)<=30)|blank2(j)>90) e(9,i)=e(9,i)+1;

r=e(9,i);

F(9,r)=j-1;

end end end F(9,:) disp('11');

for i=1:11 for j=1:209 if (blank2(j)>55&blank2(j)<=60) e(10,i)=e(10,i)+1;

r=e(10,i);

F(10,r)=j-1;

end end end F(10,:) disp('9');

for i=1:11 for j=1:209 if (blank1(j)==0&blank2(j)==0) e(11,i)=e(11,i)+1;

r=e(11,i);

F(11,r)=j-1;

end end end F(11,:) F program7：

a0=imread('000.bmp');a1=imread('001.bmp');a2=imread('002.bmp');a3=imread('0 47 03.bmp');a4=imread('004.bmp');a5=imread('005.bmp');a6=imread('006.bmp');a7= imread('007.bmp');a8=imread('008.bmp');a9=imread('009.bmp');a10=imread('010 .bmp');a11=imread('011.bmp');a12=imread('012.bmp');a13=imread('013.bmp');a1 4=imread('014.bmp');a15=imread('015.bmp');a16=imread('016.bmp');a17=imread( '017.bmp');a18=imread('018.bmp');a19=imread('019.bmp');a20=imread('020.bmp'

a55=imread('055.bmp');a56=imread('056.bmp');a57=imread('057.bmp');a58=imrea d('058.bmp');a59=imread('059.bmp');a60=imread('060.bmp');a61=imread('061.bm p');a62=imread('062.bmp');a63=imread('063.bmp');a64=imread('064.bmp');a65=i mread('065.bmp');a66=imread('066.bmp');a67=imread('067.bmp');a68=imread('06 8.bmp');a69=imread('069.bmp');a70=imread('070.bmp');a71=imread('071.bmp');a 72=imread('072.bmp');a73=imread('073.bmp');a74=imread('074.bmp');a75=imread ('075.bmp');a76=imread('076.bmp');a77=imread('077.bmp');a78=imread('078.bmp ');a79=imread('079.bmp');a80=imread('080.bmp');a81=imread('081.bmp');a82=im read('082.bmp');a83=imread('083.bmp');a84=imread('084.bmp');a85=imread('085 .bmp');a86=imread('086.bmp');a87=imread('087.bmp');a88=imread('088.bmp');a8 9=imread('089.bmp');a90=imread('090.bmp');a91=imread('091.bmp');a92=imread( '092.bmp');a93=imread('093.bmp');a94=imread('094.bmp');a95=imread('095.bmp'

a145=imread('145.bmp');a146=imread('146.bmp');a147=imread('147.bmp');a148=i mread('148.bmp');a149=imread('149.bmp');a150=imread('150.bmp');a151=imread( 48 '151.bmp');a152=imread('152.bmp');a153=imread('153.bmp');a154=imread('154.b mp');a155=imread('155.bmp');a156=imread('156.bmp');a157=imread('157.bmp');a 158=imread('158.bmp');a159=imread('159.bmp');a160=imread('160.bmp');a161=im read('161.bmp');a162=imread('162.bmp');a163=imread('163.bmp');a164=imread('

A=zeros(180,72,209);

A(:,:,72)=a71;A(:,:,73)=a72;A(:,:,74)=a73;A(:,:,75)=a74;A(:,:,76)=a75;A(:,: ,77)=a76;A(:,:,78)=a77;A(:,:,79)=a78;A(:,:,80)=a79;A(:,:,81)=a80;A(:,:,82)= a81;A(:,:,83)=a82;A(:,:,84)=a83;A(:,:,85)=a84;A(:,:,86)=a85;A(:,:,87)=a86;A (:,:,88)=a87;A(:,:,89)=a88;A(:,:,90)=a89;A(:,:,91)=a90;A(:,:,92)=a91;A(:,:, 93)=a92;A(:,:,94)=a93;A(:,:,95)=a94;A(:,:,96)=a95;A(:,:,97)=a96;A(:,:,98)=a 97;A(:,:,99)=a98;A(:,:,100)=a99;A(:,:,101)=a100;A(:,:,102)=a101;A(:,:,103)= a102;A(:,:,104)=a103;A(:,:,105)=a104;A(:,:,106)=a105;A(:,:,107)=a106;A(:,:, 108)=a107;A(:,:,109)=a108;A(:,:,110)=a109;A(:,:,111)=a110;A(:,:,112)=a111;A (:,:,113)=a112;A(:,:,114)=a113;A(:,:,115)=a114;A(:,:,116)=a115;A(:,:,117)=a 116;A(:,:,118)=a117;A(:,:,119)=a118;A(:,:,120)=a119;A(:,:,121)=a120;A(:,:,1 22)=a121;A(:,:,123)=a122;A(:,:,124)=a123;A(:,:,125)=a124;A(:,:,126)=a125;A( 49 :,:,127)=a126;A(:,:,128)=a127;A(:,:,129)=a128;A(:,:,130)=a129;A(:,:,131)=a1 30;A(:,:,132)=a131;A(:,:,133)=a132;A(:,:,134)=a133;A(:,:,135)=a134;A(:,:,13 6)=a135;A(:,:,137)=a136;A(:,:,138)=a137;A(:,:,139)=a138;A(:,:,140)=a139;A(: ,:,141)=a140;A(:,:,142)=a141;A(:,:,143)=a142;A(:,:,144)=a143;A(:,:,145)=a14 4;A(:,:,146)=a145;A(:,:,147)=a146;A(:,:,148)=a147;A(:,:,149)=a148;A(:,:,150 )=a149;A(:,:,151)=a150;A(:,:,152)=a151;A(:,:,153)=a152;A(:,:,154)=a153;A(:, :,155)=a154;A(:,:,156)=a155;A(:,:,157)=a156;A(:,:,158)=a157;A(:,:,159)=a158 ;A(:,:,160)=a159;A(:,:,161)=a160;A(:,:,162)=a161;A(:,:,163)=a162;A(:,:,164) =a163;A(:,:,165)=a164;A(:,:,166)=a165;A(:,:,167)=a166;A(:,:,168)=a167;A(:,: ,169)=a168;A(:,:,170)=a169;A(:,:,171)=a170;A(:,:,172)=a171;A(:,:,173)=a172;

A(:,:,174)=a173;A(:,:,175)=a174;A(:,:,176)=a175;A(:,:,177)=a176;A(:,:,178)= a177;A(:,:,179)=a178;A(:,:,180)=a179;A(:,:,181)=a180;A(:,:,182)=a181;A(:,:, 183)=a182;A(:,:,184)=a183;A(:,:,185)=a184;A(:,:,186)=a185;A(:,:,187)=a186;A (:,:,188)=a187;A(:,:,189)=a188;A(:,:,190)=a189;A(:,:,191)=a190;A(:,:,192)=a 191;A(:,:,193)=a192;A(:,:,194)=a193;A(:,:,195)=a194;A(:,:,196)=a195;A(:,:,1 97)=a196;A(:,:,198)=a197;A(:,:,199)=a198;A(:,:,200)=a199;A(:,:,201)=a200;A( :,:,202)=a201;A(:,:,203)=a202;A(:,:,204)=a203;A(:,:,205)=a204;A(:,:,206)=a2 05;A(:,:,207)=a206;A(:,:,208)=a207;A(:,:,209)=a208;

O=zeros(1,72);

blank=zeros(1,209);

q=zeros(209,72);

for i=1:209 M=A(:,:,i);

for k=1:72 for j=1:180 q(i,k)=q(i,k)+A(j,k,i);

end if (q(i,k)==45900) blank(i)=blank(i)+1;

else break;

end end end blankx=zeros(209,1);

for i=1:209 blankx(i)=blank(i);

end column1=zeros(11,1);

e=zeros(1,11);

for i=1:11 for j=1:209 50 if (blank(j)>10) e(i)=e(i)+1;

r=e(i);

column1(r)=j-1;

end end end column1 program8：

b0=imread('007.bmp');b1=imread('014.bmp');b2=imread('029.bmp');b3=imread('0 38.bmp');b4=imread('049.bmp');b5=imread('061.bmp');b6=imread('071.bmp');b7= imread('089.bmp');b8=imread('094.bmp');b9=imread('125.bmp');b10=imread('168 .bmp');

A=[b0(1,:);b1(1,:);b2(1,:);b3(1,:);b4(1,:);b5(1,:);b6(1,:);b7(1,:);b8(1,:);

b9(1,:);b10(1,:)];

B=[b0(end,:);b1(end,:);b2(end,:);b3(end,:);b4(end,:);b5(end,:);b6(end,:);b7 (end,:);b8(end,:);b9(end,:);b10(end,:)];

d=size(b0);

x=zeros(18,19);

y=zeros(18,2);

num=zeros(19,1);

order=zeros(19,1);

order(1,1)=input('enter a numeber:');

for k=1:11 for i=0:10 for j=1:d(2) if (B(order(k,1)+1,j)==A(i+1,j)) x(k,i+1)=x(k,i+1)+1;

end end end [num(k+1,1),z]=max(x(k,:));

order(k+1,1)=z-1;

end order program9：

b0=imread('013.bmp');b1=imread('016.bmp');b2=imread('021.bmp');b3=imread('0 66.bmp');b4=imread('106.bmp');b5=imread('109.bmp');b6=imread('110.bmp');b7= imread('125.bmp');b8=imread('139.bmp');b9=imread('145.bmp');b10=imread('150 .bmp');b11=imread('157.bmp');b12=imread('173.bmp');b13=imread('181.bmp');b1 51 4=imread('182.bmp');b15=imread('184.bmp');b16=imread('187.bmp');b17=imread( '197.bmp');b18=imread('204.bmp');

A=[b0(:,1),b1(:,1),b2(:,1),b3(:,1),b4(:,1),b5(:,1),b6(:,1),b7(:,1),b8(:,1), b9(:,1),b10(:,1),b11(:,1),b12(:,1),b13(:,1),b14(:,1),b15(:,1),b16(:,1),b17( :,1),b18(:,1)];

B=[b0(:,end),b1(:,end),b2(:,end),b3(:,end),b4(:,end),b5(:,end),b6(:,end),b7 (:,end),b8(:,end),b9(:,end),b10(:,end),b11(:,end),b12(:,end),b13(:,end),b14 (:,end),b15(:,end),b16(:,end),b17(:,end),b18(:,end)];

d=size(b0);

r=7;%(Because the eighth fragment is the left boundary.) x=zeros(18,19);

y=zeros(18,2);

num=zeros(19,1);

order=zeros(19,1);

order(1,1)=input('enter a numeber:');

for k=1:18 for i=0:18 for j=1:d(1) if (B(j,order(k,1)+1)==A(j,i+1)) x(k,i+1)=x(k,i+1)+1;

end end end [num(k+1,1),z]=max(x(k,:));

order(k+1,1)=z-1;

end order program10：

b0=imread('013.bmp');b1=imread('016.bmp');b2=imread('021.bmp');b3=imread('0 66.bmp');b4=imread('106.bmp');b5=imread('109.bmp');b6=imread('110.bmp');b7= imread('125.bmp');b8=imread('139.bmp');b9=imread('145.bmp');b10=imread('150 .bmp');b11=imread('157.bmp');b12=imread('173.bmp');b13=imread('181.bmp');b1 4=imread('182.bmp');b15=imread('184.bmp');b16=imread('187.bmp');b17=imread( '197.bmp');b18=imread('204.bmp');

A=[b0(:,1),b1(:,1),b2(:,1),b3(:,1),b4(:,1),b5(:,1),b6(:,1),b7(:,1),b8(:,1), b9(:,1),b10(:,1),b11(:,1),b12(:,1),b13(:,1),b14(:,1),b15(:,1),b16(:,1),b17( :,1),b18(:,1)];

d=size(b0);

r=7;%(Because the eighth fragment is the left boundary.) 52 x=zeros(18,19);

y=zeros(18,2);

num=zeros(19,1);

order=zeros(19,1);

order(1,1)=input('enter a numeber:');

for k=1:18 for i=0:18 for j=1:d(1) if (A(j,order(k,1)+1)==B(j,i+1)) x(k,i+1)=x(k,i+1)+1;

end end end [num(k+1,1),z]=max(x(k,:));

order(k+1,1)=z-1;

end for i=1:19 first(i)=order(20-i);

end order=first;

order program11：

a55=imread('055.bmp');a56=imread('056.bmp');a57=imread('057.bmp');a58=imrea d('058.bmp');a59=imread('059.bmp');a60=imread('060.bmp');a61=imread('061.bm p');a62=imread('062.bmp');a63=imread('063.bmp');a64=imread('064.bmp');a65=i mread('065.bmp');a66=imread('066.bmp');a67=imread('067.bmp');a68=imread('06 53 8.bmp');a69=imread('069.bmp');a70=imread('070.bmp');a71=imread('071.bmp');a 72=imread('072.bmp');a73=imread('073.bmp');a74=imread('074.bmp');a75=imread ('075.bmp');a76=imread('076.bmp');a77=imread('077.bmp');a78=imread('078.bmp ');a79=imread('079.bmp');a80=imread('080.bmp');a81=imread('081.bmp');a82=im read('082.bmp');a83=imread('083.bmp');a84=imread('084.bmp');a85=imread('085 .bmp');a86=imread('086.bmp');a87=imread('087.bmp');a88=imread('088.bmp');a8 9=imread('089.bmp');a90=imread('090.bmp');a91=imread('091.bmp');a92=imread( '092.bmp');a93=imread('093.bmp');a94=imread('094.bmp');a95=imread('095.bmp'

a61,a19,a78,a67,a69,a99,a162,a96,a131,a79,a63,a116,a163,a72,a6,a177,a20,a52 ,a36;

a168,a100,a76,a62,a142,a30,a41,a23,a147,a191,a50,a179,a120,a86,a195,a26,a1, a87,a18;

a38,a148,a46,a161,a24,a35,a81,a189,a122,a103,a130,a193,a88,a167,a25,a8,a9,a 105,a74;

a71,a156,a83,a132,a200,a17,a80,a33,a202,a198,a15,a133,a170,a205,a85,a152,a1 65,a27,a60;

a14,a128,a3,a159,a82,a199,a135,a12,a73,a160,a203,a169,a134,a39,a31,a51,a107 ,a115,a176;

a94,a34,a84,a183,a90,a47,a121,a42,a124,a144,a77,a112,a149,a97,a136,a164,a12 7,a58,a43;

a125,a13,a182,a109,a197,a16,a184,a110,a187,a66,a106,a150,a21,a173,a157,a181 ,a204,a139,a145;

a29,a64,a111,a201,a5,a92,a180,a48,a37,a75,a55,a44,a206,a10,a104,a98,a172,a1 71,a59;

a7,a208,a138,a158,a126,a68,a175,a45,a174,a0,a137,a53,a56,a93,a153,a70,a166, a32,a196;

a89,a146,a102,a154,a114,a40,a151,a207,a155,a140,a185,a108,a117,a4,a101,a113 ,a194,a119,a123 ];

imshow(A,[]);

program12：

a55=imread('055.bmp');a56=imread('056.bmp');a57=imread('057.bmp');a58=imrea d('058.bmp');a59=imread('059.bmp');a60=imread('060.bmp');a61=imread('061.bm 55 p');a62=imread('062.bmp');a63=imread('063.bmp');a64=imread('064.bmp');a65=i mread('065.bmp');a66=imread('066.bmp');a67=imread('067.bmp');a68=imread('06 8.bmp');a69=imread('069.bmp');a70=imread('070.bmp');a71=imread('071.bmp');a 72=imread('072.bmp');a73=imread('073.bmp');a74=imread('074.bmp');a75=imread ('075.bmp');a76=imread('076.bmp');a77=imread('077.bmp');a78=imread('078.bmp ');a79=imread('079.bmp');a80=imread('080.bmp');a81=imread('081.bmp');a82=im read('082.bmp');a83=imread('083.bmp');a84=imread('084.bmp');a85=imread('085 .bmp');a86=imread('086.bmp');a87=imread('087.bmp');a88=imread('088.bmp');a8 9=imread('089.bmp');a90=imread('090.bmp');a91=imread('091.bmp');a92=imread( '092.bmp');a93=imread('093.bmp');a94=imread('094.bmp');a95=imread('095.bmp'

A=zeros(180,72,209);

A(:,:,174)=a173;A(:,:,175)=a174;A(:,:,176)=a175;A(:,:,177)=a176;A(:,:,178)= a177;A(:,:,179)=a178;A(:,:,180)=a179;A(:,:,181)=a180;A(:,:,182)=a181;A(:,:, 183)=a182;A(:,:,184)=a183;A(:,:,185)=a184;A(:,:,186)=a185;A(:,:,187)=a186;A (:,:,188)=a187;A(:,:,189)=a188;A(:,:,190)=a189;A(:,:,191)=a190;A(:,:,192)=a 191;A(:,:,193)=a192;A(:,:,194)=a193;A(:,:,195)=a194;A(:,:,196)=a195;A(:,:,1 97)=a196;A(:,:,198)=a197;A(:,:,199)=a198;A(:,:,200)=a199;A(:,:,201)=a200;A( :,:,202)=a201;A(:,:,203)=a202;A(:,:,204)=a203;A(:,:,205)=a204;A(:,:,206)=a2 57 05;A(:,:,207)=a206;A(:,:,208)=a207;A(:,:,209)=a208;

O=zeros(1,72);

blank=zeros(1,209);

q=zeros(209,180);

for i=1:209 M=A(:,:,i);

for j=1:180 for k=1:72 q(i,j)=q(i,j)+A(j,k,i);

end if (q(i,j)==18360) blank(i)=blank(i)+1;

else break;

end end end blank program13：

a55=imread('055.bmp');a56=imread('056.bmp');a57=imread('057.bmp');a58=imrea d('058.bmp');a59=imread('059.bmp');a60=imread('060.bmp');a61=imread('061.bm p');a62=imread('062.bmp');a63=imread('063.bmp');a64=imread('064.bmp');a65=i mread('065.bmp');a66=imread('066.bmp');a67=imread('067.bmp');a68=imread('06 8.bmp');a69=imread('069.bmp');a70=imread('070.bmp');a71=imread('071.bmp');a 72=imread('072.bmp');a73=imread('073.bmp');a74=imread('074.bmp');a75=imread ('075.bmp');a76=imread('076.bmp');a77=imread('077.bmp');a78=imread('078.bmp ');a79=imread('079.bmp');a80=imread('080.bmp');a81=imread('081.bmp');a82=im 58 read('082.bmp');a83=imread('083.bmp');a84=imread('084.bmp');a85=imread('085 .bmp');a86=imread('086.bmp');a87=imread('087.bmp');a88=imread('088.bmp');a8 9=imread('089.bmp');a90=imread('090.bmp');a91=imread('091.bmp');a92=imread( '092.bmp');a93=imread('093.bmp');a94=imread('094.bmp');a95=imread('095.bmp'

A=zeros(180,72,209);

A(:,:,1)=a0;A(:,:,2)=a1;A(:,:,3)=a2;A(:,:,4)=a3;A(:,:,5)=a4;A(:,:,6)=a5;A(: ,:,7)=a6;A(:,:,8)=a7;A(:,:,9)=a8;A(:,:,10)=a9;A(:,:,11)=a10;A(:,:,12)=a11;A (:,:,13)=a12;A(:,:,14)=a13;A(:,:,15)=a14;A(:,:,16)=a15;A(:,:,17)=a16;A(:,:, 59 18)=a17;A(:,:,19)=a18;A(:,:,20)=a19;A(:,:,21)=a20;A(:,:,22)=a21;A(:,:,23)=a 22;A(:,:,24)=a23;A(:,:,25)=a24;A(:,:,26)=a25;A(:,:,27)=a26;A(:,:,28)=a27;A( :,:,29)=a28;A(:,:,30)=a29;A(:,:,31)=a30;A(:,:,32)=a31;A(:,:,33)=a32;A(:,:,3 4)=a33;A(:,:,35)=a34;A(:,:,36)=a35;A(:,:,37)=a36;A(:,:,38)=a37;A(:,:,39)=a3 8;A(:,:,40)=a39;A(:,:,41)=a40;A(:,:,42)=a41;A(:,:,43)=a42;A(:,:,44)=a43;A(: ,:,45)=a44;A(:,:,46)=a45;A(:,:,47)=a46;A(:,:,48)=a47;A(:,:,49)=a48;A(:,:,50 )=a49;A(:,:,51)=a50;A(:,:,52)=a51;A(:,:,53)=a52;A(:,:,54)=a53;A(:,:,55)=a54 ;A(:,:,56)=a55;A(:,:,57)=a56;A(:,:,58)=a57;A(:,:,59)=a58;A(:,:,60)=a59;A(:, :,61)=a60;A(:,:,62)=a61;A(:,:,63)=a62;A(:,:,64)=a63;A(:,:,65)=a64;A(:,:,66) =a65;A(:,:,67)=a66;A(:,:,68)=a67;A(:,:,69)=a68;A(:,:,70)=a69;A(:,:,71)=a70;

A(:,:,174)=a173;A(:,:,175)=a174;A(:,:,176)=a175;A(:,:,177)=a176;A(:,:,178)= a177;A(:,:,179)=a178;A(:,:,180)=a179;A(:,:,181)=a180;A(:,:,182)=a181;A(:,:, 183)=a182;A(:,:,184)=a183;A(:,:,185)=a184;A(:,:,186)=a185;A(:,:,187)=a186;A (:,:,188)=a187;A(:,:,189)=a188;A(:,:,190)=a189;A(:,:,191)=a190;A(:,:,192)=a 191;A(:,:,193)=a192;A(:,:,194)=a193;A(:,:,195)=a194;A(:,:,196)=a195;A(:,:,1 97)=a196;A(:,:,198)=a197;A(:,:,199)=a198;A(:,:,200)=a199;A(:,:,201)=a200;A( :,:,202)=a201;A(:,:,203)=a202;A(:,:,204)=a203;A(:,:,205)=a204;A(:,:,206)=a2 05;A(:,:,207)=a206;A(:,:,208)=a207;A(:,:,209)=a208;

O=zeros(1,72);

blank=zeros(1,209);

q=zeros(209,180);

for i=1:209 60 M=A(:,:,i);

for j=1:180 for k=1:72 q(i,181-j)=q(i,181-j)+A(181-j,k,i);

end if (q(i,181-j)==18360) blank(i)=blank(i)+1;

else break;

end end end blankx=blank;

blankx program14：

a55=imread('055.bmp');a56=imread('056.bmp');a57=imread('057.bmp');a58=imrea d('058.bmp');a59=imread('059.bmp');a60=imread('060.bmp');a61=imread('061.bm p');a62=imread('062.bmp');a63=imread('063.bmp');a64=imread('064.bmp');a65=i mread('065.bmp');a66=imread('066.bmp');a67=imread('067.bmp');a68=imread('06 8.bmp');a69=imread('069.bmp');a70=imread('070.bmp');a71=imread('071.bmp');a 72=imread('072.bmp');a73=imread('073.bmp');a74=imread('074.bmp');a75=imread ('075.bmp');a76=imread('076.bmp');a77=imread('077.bmp');a78=imread('078.bmp ');a79=imread('079.bmp');a80=imread('080.bmp');a81=imread('081.bmp');a82=im read('082.bmp');a83=imread('083.bmp');a84=imread('084.bmp');a85=imread('085 .bmp');a86=imread('086.bmp');a87=imread('087.bmp');a88=imread('088.bmp');a8 9=imread('089.bmp');a90=imread('090.bmp');a91=imread('091.bmp');a92=imread( '092.bmp');a93=imread('093.bmp');a94=imread('094.bmp');a95=imread('095.bmp'

);a96=imread('096.bmp');a97=imread('097.bmp');a98=imread('098.bmp');a99=imr 61 ead('099.bmp');a100=imread('100.bmp');a101=imread('101.bmp');a102=imread('1 02.bmp');a103=imread('103.bmp');a104=imread('104.bmp');a105=imread('105.bmp ');a106=imread('106.bmp');a107=imread('107.bmp');a108=imread('108.bmp');a10 9=imread('109.bmp');a110=imread('110.bmp');a111=imread('111.bmp');a112=imre ad('112.bmp');a113=imread('113.bmp');a114=imread('114.bmp');a115=imread('11 5.bmp');a116=imread('116.bmp');a117=imread('117.bmp');a118=imread('118.bmp'

A=zeros(180,72,209);

A(:,:,1)=a0;A(:,:,2)=a1;A(:,:,3)=a2;A(:,:,4)=a3;A(:,:,5)=a4;A(:,:,6)=a5;A(: ,:,7)=a6;A(:,:,8)=a7;A(:,:,9)=a8;A(:,:,10)=a9;A(:,:,11)=a10;A(:,:,12)=a11;A (:,:,13)=a12;A(:,:,14)=a13;A(:,:,15)=a14;A(:,:,16)=a15;A(:,:,17)=a16;A(:,:, 18)=a17;A(:,:,19)=a18;A(:,:,20)=a19;A(:,:,21)=a20;A(:,:,22)=a21;A(:,:,23)=a 22;A(:,:,24)=a23;A(:,:,25)=a24;A(:,:,26)=a25;A(:,:,27)=a26;A(:,:,28)=a27;A( :,:,29)=a28;A(:,:,30)=a29;A(:,:,31)=a30;A(:,:,32)=a31;A(:,:,33)=a32;A(:,:,3 4)=a33;A(:,:,35)=a34;A(:,:,36)=a35;A(:,:,37)=a36;A(:,:,38)=a37;A(:,:,39)=a3 8;A(:,:,40)=a39;A(:,:,41)=a40;A(:,:,42)=a41;A(:,:,43)=a42;A(:,:,44)=a43;A(: 62 ,:,45)=a44;A(:,:,46)=a45;A(:,:,47)=a46;A(:,:,48)=a47;A(:,:,49)=a48;A(:,:,50 )=a49;A(:,:,51)=a50;A(:,:,52)=a51;A(:,:,53)=a52;A(:,:,54)=a53;A(:,:,55)=a54 ;A(:,:,56)=a55;A(:,:,57)=a56;A(:,:,58)=a57;A(:,:,59)=a58;A(:,:,60)=a59;A(:, :,61)=a60;A(:,:,62)=a61;A(:,:,63)=a62;A(:,:,64)=a63;A(:,:,65)=a64;A(:,:,66) =a65;A(:,:,67)=a66;A(:,:,68)=a67;A(:,:,69)=a68;A(:,:,70)=a69;A(:,:,71)=a70;

A(:,:,174)=a173;A(:,:,175)=a174;A(:,:,176)=a175;A(:,:,177)=a176;A(:,:,178)= a177;A(:,:,179)=a178;A(:,:,180)=a179;A(:,:,181)=a180;A(:,:,182)=a181;A(:,:, 183)=a182;A(:,:,184)=a183;A(:,:,185)=a184;A(:,:,186)=a185;A(:,:,187)=a186;A (:,:,188)=a187;A(:,:,189)=a188;A(:,:,190)=a189;A(:,:,191)=a190;A(:,:,192)=a 191;A(:,:,193)=a192;A(:,:,194)=a193;A(:,:,195)=a194;A(:,:,196)=a195;A(:,:,1 97)=a196;A(:,:,198)=a197;A(:,:,199)=a198;A(:,:,200)=a199;A(:,:,201)=a200;A( :,:,202)=a201;A(:,:,203)=a202;A(:,:,204)=a203;A(:,:,205)=a204;A(:,:,206)=a2 05;A(:,:,207)=a206;A(:,:,208)=a207;A(:,:,209)=a208;

O=zeros(1,72);

blank=zeros(1,209);

q=zeros(209,72);

for i=1:209 M=A(:,:,i);

for k=1:72 for j=1:180 q(i,k)=q(i,k)+A(j,k,i);

end 63 if (q(i,k)==45900) blank(i)=blank(i)+1;

else break;

end end end blankx=zeros(209,1);

for i=1:209 blankx(i)=blank(i);

end column1=zeros(11,1);

e=zeros(1,11);

for i=1:11 for j=1:209 if (blank(j)>10&blank(j)<=15) e(i)=e(i)+1;

r=e(i);

column1(r)=j-1;

end end end column1 a0a=imread('000a.bmp');a1a=imread('001a.bmp');a2a=imread('002a.bmp');a3a=im read('003a.bmp');a4a=imread('004a.bmp');a5a=imread('005a.bmp');a6a=imread('

006a.bmp');a7a=imread('007a.bmp');a8a=imread('008a.bmp');a9a=imread('009a.b mp');a10a=imread('010a.bmp');a11a=imread('011a.bmp');a12a=imread('012a.bmp'

);a13a=imread('013a.bmp');a14a=imread('014a.bmp');a15a=imread('015a.bmp');a 16a=imread('016a.bmp');a17a=imread('017a.bmp');a18a=imread('018a.bmp');a19a =imread('019a.bmp');a20a=imread('020a.bmp');a21a=imread('021a.bmp');a22a=im read('022a.bmp');a23a=imread('023a.bmp');a24a=imread('024a.bmp');a25a=imrea d('025a.bmp');a26a=imread('026a.bmp');a27a=imread('027a.bmp');a28a=imread('

028a.bmp');a29a=imread('029a.bmp');a30a=imread('030a.bmp');a31a=imread('031 a.bmp');a32a=imread('032a.bmp');a33a=imread('033a.bmp');a34a=imread('034a.b mp');a35a=imread('035a.bmp');a36a=imread('036a.bmp');a37a=imread('037a.bmp'

);a38a=imread('038a.bmp');a39a=imread('039a.bmp');a40a=imread('040a.bmp');a 41a=imread('041a.bmp');a42a=imread('042a.bmp');a43a=imread('043a.bmp');a44a =imread('044a.bmp');a45a=imread('045a.bmp');a46a=imread('046a.bmp');a47a=im read('047a.bmp');a48a=imread('048a.bmp');a49a=imread('049a.bmp');a50a=imrea d('050a.bmp');a51a=imread('051a.bmp');a52a=imread('052a.bmp');a53a=imread('

053a.bmp');a54a=imread('054a.bmp');a55a=imread('055a.bmp');a56a=imread('056 64 a.bmp');a57a=imread('057a.bmp');a58a=imread('058a.bmp');a59a=imread('059a.b mp');a60a=imread('060a.bmp');a61a=imread('061a.bmp');a62a=imread('062a.bmp'

);a63a=imread('063a.bmp');a64a=imread('064a.bmp');a65a=imread('065a.bmp');a 66a=imread('066a.bmp');a67a=imread('067a.bmp');a68a=imread('068a.bmp');a69a =imread('069a.bmp');a70a=imread('070a.bmp');a71a=imread('071a.bmp');a72a=im read('072a.bmp');a73a=imread('073a.bmp');a74a=imread('074a.bmp');a75a=imrea d('075a.bmp');a76a=imread('076a.bmp');a77a=imread('077a.bmp');a78a=imread('

078a.bmp');a79a=imread('079a.bmp');a80a=imread('080a.bmp');a81a=imread('081 a.bmp');a82a=imread('082a.bmp');a83a=imread('083a.bmp');a84a=imread('084a.b mp');a85a=imread('085a.bmp');a86a=imread('086a.bmp');a87a=imread('087a.bmp'

);a88a=imread('088a.bmp');a89a=imread('089a.bmp');a90a=imread('090a.bmp');a 91a=imread('091a.bmp');a92a=imread('092a.bmp');a93a=imread('093a.bmp');a94a =imread('094a.bmp');a95a=imread('095a.bmp');a96a=imread('096a.bmp');a97a=im read('097a.bmp');a98a=imread('098a.bmp');a99a=imread('099a.bmp');a100a=imre ad('100a.bmp');a101a=imread('101a.bmp');a102a=imread('102a.bmp');a103a=imre ad('103a.bmp');a104a=imread('104a.bmp');a105a=imread('105a.bmp');a106a=imre ad('106a.bmp');a107a=imread('107a.bmp');a108a=imread('108a.bmp');a109a=imre ad('109a.bmp');a110a=imread('110a.bmp');a111a=imread('111a.bmp');a112a=imre ad('112a.bmp');a113a=imread('113a.bmp');a114a=imread('114a.bmp');a115a=imre ad('115a.bmp');a116a=imread('116a.bmp');a117a=imread('117a.bmp');a118a=imre ad('118a.bmp');a119a=imread('119a.bmp');a120a=imread('120a.bmp');a121a=imre ad('121a.bmp');a122a=imread('122a.bmp');a123a=imread('123a.bmp');a124a=imre ad('124a.bmp');a125a=imread('125a.bmp');a126a=imread('126a.bmp');a127a=imre ad('127a.bmp');a128a=imread('128a.bmp');a129a=imread('129a.bmp');a130a=imre ad('130a.bmp');a131a=imread('131a.bmp');a132a=imread('132a.bmp');a133a=imre ad('133a.bmp');a134a=imread('134a.bmp');a135a=imread('135a.bmp');a136a=imre ad('136a.bmp');a137a=imread('137a.bmp');a138a=imread('138a.bmp');a139a=imre ad('139a.bmp');a140a=imread('140a.bmp');a141a=imread('141a.bmp');a142a=imre ad('142a.bmp');a143a=imread('143a.bmp');a144a=imread('144a.bmp');a145a=imre ad('145a.bmp');a146a=imread('146a.bmp');a147a=imread('147a.bmp');a148a=imre ad('148a.bmp');a149a=imread('149a.bmp');a150a=imread('150a.bmp');a151a=imre ad('151a.bmp');a152a=imread('152a.bmp');a153a=imread('153a.bmp');a154a=imre ad('154a.bmp');a155a=imread('155a.bmp');a156a=imread('156a.bmp');a157a=imre ad('157a.bmp');a158a=imread('158a.bmp');a159a=imread('159a.bmp');a160a=imre ad('160a.bmp');a161a=imread('161a.bmp');a162a=imread('162a.bmp');a163a=imre ad('163a.bmp');a164a=imread('164a.bmp');a165a=imread('165a.bmp');a166a=imre ad('166a.bmp');a167a=imread('167a.bmp');a168a=imread('168a.bmp');a169a=imre ad('169a.bmp');a170a=imread('170a.bmp');a171a=imread('171a.bmp');a172a=imre ad('172a.bmp');a173a=imread('173a.bmp');a174a=imread('174a.bmp');a175a=imre ad('175a.bmp');a176a=imread('176a.bmp');a177a=imread('177a.bmp');a178a=imre ad('178a.bmp');a179a=imread('179a.bmp');a180a=imread('180a.bmp');a181a=imre ad('181a.bmp');a182a=imread('182a.bmp');a183a=imread('183a.bmp');a184a=imre ad('184a.bmp');a185a=imread('185a.bmp');a186a=imread('186a.bmp');a187a=imre ad('187a.bmp');a188a=imread('188a.bmp');a189a=imread('189a.bmp');a190a=imre 65 ad('190a.bmp');a191a=imread('191a.bmp');a192a=imread('192a.bmp');a193a=imre ad('193a.bmp');a194a=imread('194a.bmp');a195a=imread('195a.bmp');a196a=imre ad('196a.bmp');a197a=imread('197a.bmp');a198a=imread('198a.bmp');a199a=imre ad('199a.bmp');a200a=imread('200a.bmp');a201a=imread('201a.bmp');a202a=imre ad('202a.bmp');a203a=imread('203a.bmp');a204a=imread('204a.bmp');a205a=imre ad('205a.bmp');a206a=imread('206a.bmp');a207a=imread('207a.bmp');a208a=imre ad('208a.bmp');a0b=imread('000b.bmp');a1b=imread('001b.bmp');a2b=imread('00 2b.bmp');a3b=imread('003b.bmp');a4b=imread('004b.bmp');a5b=imread('005b.bmp ');a6b=imread('006b.bmp');a7b=imread('007b.bmp');a8b=imread('008b.bmp');a9b =imread('009b.bmp');a10b=imread('010b.bmp');a11b=imread('011b.bmp');a12b=im read('012b.bmp');a13b=imread('013b.bmp');a14b=imread('014b.bmp');a15b=imrea d('015b.bmp');a16b=imread('016b.bmp');a17b=imread('017b.bmp');a18b=imread('

018b.bmp');a19b=imread('019b.bmp');a20b=imread('020b.bmp');a21b=imread('021 b.bmp');a22b=imread('022b.bmp');a23b=imread('023b.bmp');a24b=imread('024b.b mp');a25b=imread('025b.bmp');a26b=imread('026b.bmp');a27b=imread('027b.bmp'

);a28b=imread('028b.bmp');a29b=imread('029b.bmp');a30b=imread('030b.bmp');a 31b=imread('031b.bmp');a32b=imread('032b.bmp');a33b=imread('033b.bmp');a34b =imread('034b.bmp');a35b=imread('035b.bmp');a36b=imread('036b.bmp');a37b=im read('037b.bmp');a38b=imread('038b.bmp');a39b=imread('039b.bmp');a40b=imrea d('040b.bmp');a41b=imread('041b.bmp');a42b=imread('042b.bmp');a43b=imread('

043b.bmp');a44b=imread('044b.bmp');a45b=imread('045b.bmp');a46b=imread('046 b.bmp');a47b=imread('047b.bmp');a48b=imread('048b.bmp');a49b=imread('049b.b mp');a50b=imread('050b.bmp');a51b=imread('051b.bmp');a52b=imread('052b.bmp'

);a53b=imread('053b.bmp');a54b=imread('054b.bmp');a55b=imread('055b.bmp');a 56b=imread('056b.bmp');a57b=imread('057b.bmp');a58b=imread('058b.bmp');a59b =imread('059b.bmp');a60b=imread('060b.bmp');a61b=imread('061b.bmp');a62b=im read('062b.bmp');a63b=imread('063b.bmp');a64b=imread('064b.bmp');a65b=imrea d('065b.bmp');a66b=imread('066b.bmp');a67b=imread('067b.bmp');a68b=imread('

068b.bmp');a69b=imread('069b.bmp');a70b=imread('070b.bmp');a71b=imread('071 b.bmp');a72b=imread('072b.bmp');a73b=imread('073b.bmp');a74b=imread('074b.b mp');a75b=imread('075b.bmp');a76b=imread('076b.bmp');a77b=imread('077b.bmp'

);a78b=imread('078b.bmp');a79b=imread('079b.bmp');a80b=imread('080b.bmp');a 81b=imread('081b.bmp');a82b=imread('082b.bmp');a83b=imread('083b.bmp');a84b =imread('084b.bmp');a85b=imread('085b.bmp');a86b=imread('086b.bmp');a87b=im read('087b.bmp');a88b=imread('088b.bmp');a89b=imread('089b.bmp');a90b=imrea d('090b.bmp');a91b=imread('091b.bmp');a92b=imread('092b.bmp');a93b=imread('

093b.bmp');a94b=imread('094b.bmp');a95b=imread('095b.bmp');a96b=imread('096 b.bmp');a97b=imread('097b.bmp');a98b=imread('098b.bmp');a99b=imread('099b.b mp');a100b=imread('100b.bmp');a101b=imread('101b.bmp');a102b=imread('102b.b mp');a103b=imread('103b.bmp');a104b=imread('104b.bmp');a105b=imread('105b.b mp');a106b=imread('106b.bmp');a107b=imread('107b.bmp');a108b=imread('108b.b mp');a109b=imread('109b.bmp');a110b=imread('110b.bmp');a111b=imread('111b.b mp');a112b=imread('112b.bmp');a113b=imread('113b.bmp');a114b=imread('114b.b mp');a115b=imread('115b.bmp');a116b=imread('116b.bmp');a117b=imread('117b.b 66 mp');a118b=imread('118b.bmp');a119b=imread('119b.bmp');a120b=imread('120b.b mp');a121b=imread('121b.bmp');a122b=imread('122b.bmp');a123b=imread('123b.b mp');a124b=imread('124b.bmp');a125b=imread('125b.bmp');a126b=imread('126b.b mp');a127b=imread('127b.bmp');a128b=imread('128b.bmp');a129b=imread('129b.b mp');a130b=imread('130b.bmp');a131b=imread('131b.bmp');a132b=imread('132b.b mp');a133b=imread('133b.bmp');a134b=imread('134b.bmp');a135b=imread('135b.b mp');a136b=imread('136b.bmp');a137b=imread('137b.bmp');a138b=imread('138b.b mp');a139b=imread('139b.bmp');a140b=imread('140b.bmp');a141b=imread('141b.b mp');a142b=imread('142b.bmp');a143b=imread('143b.bmp');a144b=imread('144b.b mp');a145b=imread('145b.bmp');a146b=imread('146b.bmp');a147b=imread('147b.b mp');a148b=imread('148b.bmp');a149b=imread('149b.bmp');a150b=imread('150b.b mp');a151b=imread('151b.bmp');a152b=imread('152b.bmp');a153b=imread('153b.b mp');a154b=imread('154b.bmp');a155b=imread('155b.bmp');a156b=imread('156b.b mp');a157b=imread('157b.bmp');a158b=imread('158b.bmp');a159b=imread('159b.b mp');a160b=imread('160b.bmp');a161b=imread('161b.bmp');a162b=imread('162b.b mp');a163b=imread('163b.bmp');a164b=imread('164b.bmp');a165b=imread('165b.b mp');a166b=imread('166b.bmp');a167b=imread('167b.bmp');a168b=imread('168b.b mp');a169b=imread('169b.bmp');a170b=imread('170b.bmp');a171b=imread('171b.b mp');a172b=imread('172b.bmp');a173b=imread('173b.bmp');a174b=imread('174b.b mp');a175b=imread('175b.bmp');a176b=imread('176b.bmp');a177b=imread('177b.b mp');a178b=imread('178b.bmp');a179b=imread('179b.bmp');a180b=imread('180b.b mp');a181b=imread('181b.bmp');a182b=imread('182b.bmp');a183b=imread('183b.b mp');a184b=imread('184b.bmp');a185b=imread('185b.bmp');a186b=imread('186b.b mp');a187b=imread('187b.bmp');a188b=imread('188b.bmp');a189b=imread('189b.b mp');a190b=imread('190b.bmp');a191b=imread('191b.bmp');a192b=imread('192b.b mp');a193b=imread('193b.bmp');a194b=imread('194b.bmp');a195b=imread('195b.b mp');a196b=imread('196b.bmp');a197b=imread('197b.bmp');a198b=imread('198b.b mp');a199b=imread('199b.bmp');a200b=imread('200b.bmp');a201b=imread('201b.b mp');a202b=imread('202b.bmp');a203b=imread('203b.bmp');a204b=imread('204b.b mp');a205b=imread('205b.bmp');a206b=imread('206b.bmp');a207b=imread('207b.b mp');a208b=imread('208b.bmp');A=zeros(180,72,418);A(:,:,1)=a0a;A(:,:,2)=a1a ;A(:,:,3)=a2a;A(:,:,4)=a3a;A(:,:,5)=a4a;A(:,:,6)=a5a;A(:,:,7)=a6a;A(:,:,8)= a7a;A(:,:,9)=a8a;A(:,:,10)=a9a;A(:,:,11)=a10a;A(:,:,12)=a11a;A(:,:,13)=a12a ;A(:,:,14)=a13a;A(:,:,15)=a14a;A(:,:,16)=a15a;A(:,:,17)=a16a;A(:,:,18)=a17a ;A(:,:,19)=a18a;A(:,:,20)=a19a;A(:,:,21)=a20a;A(:,:,22)=a21a;A(:,:,23)=a22a ;A(:,:,24)=a23a;A(:,:,25)=a24a;A(:,:,26)=a25a;A(:,:,27)=a26a;A(:,:,28)=a27a ;A(:,:,29)=a28a;A(:,:,30)=a29a;A(:,:,31)=a30a;A(:,:,32)=a31a;A(:,:,33)=a32a ;A(:,:,34)=a33a;A(:,:,35)=a34a;A(:,:,36)=a35a;A(:,:,37)=a36a;A(:,:,38)=a37a ;A(:,:,39)=a38a;A(:,:,40)=a39a;A(:,:,41)=a40a;A(:,:,42)=a41a;A(:,:,43)=a42a ;A(:,:,44)=a43a;A(:,:,45)=a44a;A(:,:,46)=a45a;A(:,:,47)=a46a;A(:,:,48)=a47a ;A(:,:,49)=a48a;A(:,:,50)=a49a;A(:,:,51)=a50a;A(:,:,52)=a51a;A(:,:,53)=a52a ;A(:,:,54)=a53a;A(:,:,55)=a54a;A(:,:,56)=a55a;A(:,:,57)=a56a;A(:,:,58)=a57a ;A(:,:,59)=a58a;A(:,:,60)=a59a;A(:,:,61)=a60a;A(:,:,62)=a61a;A(:,:,63)=a62a ;A(:,:,64)=a63a;A(:,:,65)=a64a;A(:,:,66)=a65a;A(:,:,67)=a66a;A(:,:,68)=a67a 67 ;A(:,:,69)=a68a;A(:,:,70)=a69a;A(:,:,71)=a70a;A(:,:,72)=a71a;A(:,:,73)=a72a ;A(:,:,74)=a73a;A(:,:,75)=a74a;A(:,:,76)=a75a;A(:,:,77)=a76a;A(:,:,78)=a77a ;A(:,:,79)=a78a;A(:,:,80)=a79a;A(:,:,81)=a80a;A(:,:,82)=a81a;A(:,:,83)=a82a ;A(:,:,84)=a83a;A(:,:,85)=a84a;A(:,:,86)=a85a;A(:,:,87)=a86a;A(:,:,88)=a87a ;A(:,:,89)=a88a;A(:,:,90)=a89a;A(:,:,91)=a90a;A(:,:,92)=a91a;A(:,:,93)=a92a ;A(:,:,94)=a93a;A(:,:,95)=a94a;A(:,:,96)=a95a;A(:,:,97)=a96a;A(:,:,98)=a97a ;A(:,:,99)=a98a;A(:,:,100)=a99a;A(:,:,101)=a100a;A(:,:,102)=a101a;A(:,:,103 )=a102a;A(:,:,104)=a103a;A(:,:,105)=a104a;A(:,:,106)=a105a;A(:,:,107)=a106a ;A(:,:,108)=a107a;A(:,:,109)=a108a;A(:,:,110)=a109a;A(:,:,111)=a110a;A(:,:, 112)=a111a;A(:,:,113)=a112a;A(:,:,114)=a113a;A(:,:,115)=a114a;A(:,:,116)=a1 15a;A(:,:,117)=a116a;A(:,:,118)=a117a;A(:,:,119)=a118a;A(:,:,120)=a119a;A(: ,:,121)=a120a;A(:,:,122)=a121a;A(:,:,123)=a122a;A(:,:,124)=a123a;A(:,:,125) =a124a;A(:,:,126)=a125a;A(:,:,127)=a126a;A(:,:,128)=a127a;A(:,:,129)=a128a;

A(:,:,130)=a129a;A(:,:,131)=a130a;A(:,:,132)=a131a;A(:,:,133)=a132a;A(:,:,1 34)=a133a;A(:,:,135)=a134a;A(:,:,136)=a135a;A(:,:,137)=a136a;A(:,:,138)=a13 7a;A(:,:,139)=a138a;A(:,:,140)=a139a;A(:,:,141)=a140a;A(:,:,142)=a141a;A(:, :,143)=a142a;A(:,:,144)=a143a;A(:,:,145)=a144a;A(:,:,146)=a145a;A(:,:,147)= a146a;A(:,:,148)=a147a;A(:,:,149)=a148a;A(:,:,150)=a149a;A(:,:,151)=a150a;A (:,:,152)=a151a;A(:,:,153)=a152a;A(:,:,154)=a153a;A(:,:,155)=a154a;A(:,:,15 6)=a155a;A(:,:,157)=a156a;A(:,:,158)=a157a;A(:,:,159)=a158a;A(:,:,160)=a159 a;A(:,:,161)=a160a;A(:,:,162)=a161a;A(:,:,163)=a162a;A(:,:,164)=a163a;A(:,: ,165)=a164a;A(:,:,166)=a165a;A(:,:,167)=a166a;A(:,:,168)=a167a;A(:,:,169)=a 168a;A(:,:,170)=a169a;A(:,:,171)=a170a;A(:,:,172)=a171a;A(:,:,173)=a172a;A( :,:,174)=a173a;A(:,:,175)=a174a;A(:,:,176)=a175a;A(:,:,177)=a176a;A(:,:,178 )=a177a;A(:,:,179)=a178a;A(:,:,180)=a179a;A(:,:,181)=a180a;A(:,:,182)=a181a ;A(:,:,183)=a182a;A(:,:,184)=a183a;A(:,:,185)=a184a;A(:,:,186)=a185a;A(:,:, 187)=a186a;A(:,:,188)=a187a;A(:,:,189)=a188a;A(:,:,190)=a189a;A(:,:,191)=a1 90a;A(:,:,192)=a191a;A(:,:,193)=a192a;A(:,:,194)=a193a;A(:,:,195)=a194a;A(: ,:,196)=a195a;A(:,:,197)=a196a;A(:,:,198)=a197a;A(:,:,199)=a198a;A(:,:,200) =a199a;A(:,:,201)=a200a;A(:,:,202)=a201a;A(:,:,203)=a202a;A(:,:,204)=a203a;

A(:,:,205)=a204a;A(:,:,206)=a205a;A(:,:,207)=a206a;A(:,:,208)=a207a;A(:,:,2 09)=a208a;A(:,:,210)=a0b;A(:,:,211)=a1b;A(:,:,212)=a2b;A(:,:,213)=a3b;A(:,: ,214)=a4b;A(:,:,215)=a5b;A(:,:,216)=a6b;A(:,:,217)=a7b;A(:,:,218)=a8b;A(:,: ,219)=a9b;A(:,:,220)=a10b;A(:,:,221)=a11b;A(:,:,222)=a12b;A(:,:,223)=a13b;A (:,:,224)=a14b;A(:,:,225)=a15b;A(:,:,226)=a16b;A(:,:,227)=a17b;A(:,:,228)=a 18b;A(:,:,229)=a19b;A(:,:,230)=a20b;A(:,:,231)=a21b;A(:,:,232)=a22b;A(:,:,2 33)=a23b;A(:,:,234)=a24b;A(:,:,235)=a25b;A(:,:,236)=a26b;A(:,:,237)=a27b;A( :,:,238)=a28b;A(:,:,239)=a29b;A(:,:,240)=a30b;A(:,:,241)=a31b;A(:,:,242)=a3 2b;A(:,:,243)=a33b;A(:,:,244)=a34b;A(:,:,245)=a35b;A(:,:,246)=a36b;A(:,:,24 7)=a37b;A(:,:,248)=a38b;A(:,:,249)=a39b;A(:,:,250)=a40b;A(:,:,251)=a41b;A(: ,:,252)=a42b;A(:,:,253)=a43b;A(:,:,254)=a44b;A(:,:,255)=a45b;A(:,:,256)=a46 b;A(:,:,257)=a47b;A(:,:,258)=a48b;A(:,:,259)=a49b;A(:,:,260)=a50b;A(:,:,261 )=a51b;A(:,:,262)=a52b;A(:,:,263)=a53b;A(:,:,264)=a54b;A(:,:,265)=a55b;A(:, :,266)=a56b;A(:,:,267)=a57b;A(:,:,268)=a58b;A(:,:,269)=a59b;A(:,:,270)=a60b 68 ;A(:,:,271)=a61b;A(:,:,272)=a62b;A(:,:,273)=a63b;A(:,:,274)=a64b;A(:,:,275) =a65b;A(:,:,276)=a66b;A(:,:,277)=a67b;A(:,:,278)=a68b;A(:,:,279)=a69b;A(:,: ,280)=a70b;A(:,:,281)=a71b;A(:,:,282)=a72b;A(:,:,283)=a73b;A(:,:,284)=a74b;

A(:,:,285)=a75b;A(:,:,286)=a76b;A(:,:,287)=a77b;A(:,:,288)=a78b;A(:,:,289)= a79b;A(:,:,290)=a80b;A(:,:,291)=a81b;A(:,:,292)=a82b;A(:,:,293)=a83b;A(:,:, 294)=a84b;A(:,:,295)=a85b;A(:,:,296)=a86b;A(:,:,297)=a87b;A(:,:,298)=a88b;A (:,:,299)=a89b;A(:,:,300)=a90b;A(:,:,301)=a91b;A(:,:,302)=a92b;A(:,:,303)=a 93b;A(:,:,304)=a94b;A(:,:,305)=a95b;A(:,:,306)=a96b;A(:,:,307)=a97b;A(:,:,3 08)=a98b;A(:,:,309)=a99b;A(:,:,310)=a100b;A(:,:,311)=a101b;A(:,:,312)=a102b ;A(:,:,313)=a103b;A(:,:,314)=a104b;A(:,:,315)=a105b;A(:,:,316)=a106b;A(:,:, 317)=a107b;A(:,:,318)=a108b;A(:,:,319)=a109b;A(:,:,320)=a110b;A(:,:,321)=a1 11b;A(:,:,322)=a112b;A(:,:,323)=a113b;A(:,:,324)=a114b;A(:,:,325)=a115b;A(: ,:,326)=a116b;A(:,:,327)=a117b;A(:,:,328)=a118b;A(:,:,329)=a119b;A(:,:,330) =a120b;A(:,:,331)=a121b;A(:,:,332)=a122b;A(:,:,333)=a123b;A(:,:,334)=a124b;

A(:,:,335)=a125b;A(:,:,336)=a126b;A(:,:,337)=a127b;A(:,:,338)=a128b;A(:,:,3 39)=a129b;A(:,:,340)=a130b;A(:,:,341)=a131b;A(:,:,342)=a132b;A(:,:,343)=a13 3b;A(:,:,344)=a134b;A(:,:,345)=a135b;A(:,:,346)=a136b;A(:,:,347)=a137b;A(:, :,348)=a138b;A(:,:,349)=a139b;A(:,:,350)=a140b;A(:,:,351)=a141b;A(:,:,352)= a142b;A(:,:,353)=a143b;A(:,:,354)=a144b;A(:,:,355)=a145b;A(:,:,356)=a146b;A (:,:,357)=a147b;A(:,:,358)=a148b;A(:,:,359)=a149b;A(:,:,360)=a150b;A(:,:,36 1)=a151b;A(:,:,362)=a152b;A(:,:,363)=a153b;A(:,:,364)=a154b;A(:,:,365)=a155 b;A(:,:,366)=a156b;A(:,:,367)=a157b;A(:,:,368)=a158b;A(:,:,369)=a159b;A(:,: ,370)=a160b;A(:,:,371)=a161b;A(:,:,372)=a162b;A(:,:,373)=a163b;A(:,:,374)=a 164b;A(:,:,375)=a165b;A(:,:,376)=a166b;A(:,:,377)=a167b;A(:,:,378)=a168b;A( :,:,379)=a169b;A(:,:,380)=a170b;A(:,:,381)=a171b;A(:,:,382)=a172b;A(:,:,383 )=a173b;A(:,:,384)=a174b;A(:,:,385)=a175b;A(:,:,386)=a176b;A(:,:,387)=a177b ;A(:,:,388)=a178b;A(:,:,389)=a179b;A(:,:,390)=a180b;A(:,:,391)=a181b;A(:,:, 392)=a182b;A(:,:,393)=a183b;A(:,:,394)=a184b;A(:,:,395)=a185b;A(:,:,396)=a1 86b;A(:,:,397)=a187b;A(:,:,398)=a188b;A(:,:,399)=a189b;A(:,:,400)=a190b;A(: ,:,401)=a191b;A(:,:,402)=a192b;A(:,:,403)=a193b;A(:,:,404)=a194b;A(:,:,405) =a195b;A(:,:,406)=a196b;A(:,:,407)=a197b;A(:,:,408)=a198b;A(:,:,409)=a199b;

A(:,:,410)=a200b;A(:,:,411)=a201b;A(:,:,412)=a202b;A(:,:,413)=a203b;A(:,:,4 14)=a204b;A(:,:,415)=a205b;A(:,:,416)=a206b;A(:,:,417)=a207b;A(:,:,418)=a20 8b;

blank=zeros(1,418);

q=zeros(418,72);

for i=1:418 M=A(:,:,i);

for k=1:72 for j=1:180 q(i,k)=q(i,k)+A(j,k,i);

end if (q(i,k)==45900) 69 blank(i)=blank(i)+1;

else break;

end end end blankx=zeros(418,1);

for i=1:418 blankx(i)=blank(i);

end column1=zeros(11,1);

e=zeros(1,22);

for i=1:22 for j=1:418 if (blank(j)>10&blank(j)<=15) e(i)=e(i)+1;

r=e(i);

column1(r)=j-1;

end end end column1 for i=1:4 column1a(i)=column1(i);

end column1a for j=5:11 column1b(j)=column1(j)-209;

end column1b 70

[3] 褚宝增,齐良平,平面曲线与空间曲线曲率及其算法[J].德州学院学报,2013.4,第 92 卷第 2 期. [4] 司守奎,孙玺菁,数学建模算法与应用[M].北京国防工业出版社,2011. [5] ...

2014年1月2日... 记者今日从河海大学获悉:2013全国大学生数学建模竞赛获奖名单近日揭晓,河海大学由周忠国指导,大禹学院杨捷、沈亚雄、雷浩组成的代表队获全国一等奖. ...

2013年12月23日... 近日,2013年度全国大学生数学建模竞赛成绩公布,中国人民大学共有48支队伍获奖,其中3支队伍获全国一等奖,5支队伍获全国二等奖,20支队伍获北京市一...

2013年数学建模竞赛全国一等奖,2013全国数学建模竞赛,数学建模一等奖论文,数学建模国家一等奖

时间：2012-03-26 来源: 泥巴往事网

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