{"defaultlang":"zh","titlegroup":{"articletitle":[{"lang":"zh","data":[{"name":"text","data":"三维枪弹痕点云数据处理及特征提取研究"}]},{"lang":"en","data":[{"name":"text","data":"Processing and feature extraction for three-dimensional bullet point cloud data"}]}]},"contribgroup":{"author":[{"name":[{"lang":"zh","surname":"马","givenname":"鑫","namestyle":"eastern","prefix":""},{"lang":"en","surname":"MA","givenname":"Xin","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"},{"rid":"aff2","text":"2"}],"role":["first-author"],"bio":[{"lang":"zh","text":["马鑫(1990-),男,内蒙古巴彦淖尔人,硕士研究生,主要从事数字图像处理方面的研究。E-mail:cnqqqf@163.com"],"graphic":[],"data":[[{"name":"text","data":"马鑫(1990-),男,内蒙古巴彦淖尔人,硕士研究生,主要从事数字图像处理方面的研究。E-mail:"},{"name":"text","data":"cnqqqf@163.com"}]]}],"email":"cnqqqf@163.com","deceased":false},{"name":[{"lang":"zh","surname":"魏","givenname":"仲慧","namestyle":"eastern","prefix":""},{"lang":"en","surname":"WEI","givenname":"Zhong-hui","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"}],"role":["corresp"],"corresp":[{"rid":"cor2","lang":"zh","text":"魏仲慧(1961-),女,吉林长春人,研究员,博士生导师,主要从事数字图像处理、图像储存等方面的研究。E-mail:wzhlvp@sohu.com","data":[{"name":"text","data":"魏仲慧(1961-),女,吉林长春人,研究员,博士生导师,主要从事数字图像处理、图像储存等方面的研究。E-mail:wzhlvp@sohu.com"}]}],"email":"wzhlvp@sohu.com","deceased":false},{"name":[{"lang":"zh","surname":"何","givenname":"昕","namestyle":"eastern","prefix":""},{"lang":"en","surname":"HE","givenname":"Xin","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"}],"role":[],"deceased":false},{"name":[{"lang":"zh","surname":"于","givenname":"国栋","namestyle":"eastern","prefix":""},{"lang":"en","surname":"YU","givenname":"Guo-dong","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff3","text":"3"}],"role":[],"deceased":false}],"aff":[{"id":"aff1","intro":[{"lang":"zh","label":"1","text":"中国科学院 长春光学精密机械与物理研究所, 吉林 长春 130033","data":[{"name":"text","data":"中国科学院 长春光学精密机械与物理研究所, 吉林 长春 130033"}]},{"lang":"en","label":"1","text":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China","data":[{"name":"text","data":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}]}]},{"id":"aff2","intro":[{"lang":"zh","label":"2","text":"中国科学院大学, 北京 100049","data":[{"name":"text","data":"中国科学院大学, 北京 100049"}]},{"lang":"en","label":"2","text":"University of Chinese Academy of Sciences, Beijing 100049, China","data":[{"name":"text","data":"University of Chinese Academy of Sciences, Beijing 100049, China"}]}]},{"id":"aff3","intro":[{"lang":"zh","label":"3","text":"白城兵器试验中心, 吉林 白城 137001","data":[{"name":"text","data":"白城兵器试验中心, 吉林 白城 137001"}]},{"lang":"en","label":"3","text":"Baicheng Ordnance Test Center, Baicheng 137001, China","data":[{"name":"text","data":"Baicheng Ordnance Test Center, Baicheng 137001, China"}]}]}]},"abstracts":[{"lang":"zh","data":[{"name":"p","data":[{"name":"text","data":"为了解决传统算法中弹痕图像深度特征信息丢失的问题，本文提出一种能够计算出弹痕图像深度特征参数信息的三维点云图像特征提取算法。该方法根据棱线斜率变化从局部极值点中找到特征点，运用线性拟合法构建三角形对特征参数值进行计算，确定弹痕特征参数值的相似范围，通过利用相似范围对未知弹头进行判别，实现弹痕和枪的一致性确认。实验结果表明：所提出的算法在现有样本的条件下，弹痕比对的正确识别率达到90%以上，单组弹痕数据的转换、特征提取和参数计算共用时32.7 s。算法满足弹痕比对需求，可以对后续弹痕比对提供可信依据，具有一定的理论价值和实用意义。"}]}]},{"lang":"en","data":[{"name":"p","data":[{"name":"text","data":"In order to solve the problem of bullet marks image depth feature information loss in traditional algorithm, we propose a three-dimensional bullet point cloud image feature extraction algorithm. The feature points are extracted from the local extremal points according to the change of ridge's slope. And the linear fitting method is utilized to construct the triangle in order to calculate the characteristic parameters and define the similar range of the characteristic parameters. Finally, the unknown bullet is discriminated through the similar range to ensure the consistency between the bullet and the gun. The experimental results show that correct recognition rate of bullet comparison reaches more than 90% under the condition of existing sample, and data processing of a single set of bullet data spends 32.7 s. The proposed algorithm satisfies the bullet comparison demand, provides credible basis for the following bullet comparison and has certain theory value and practical significance."}]}]}],"keyword":[{"lang":"zh","data":[[{"name":"text","data":"枪弹痕"}],[{"name":"text","data":"深度特征信息"}],[{"name":"text","data":"点云"}],[{"name":"text","data":"斜率"}],[{"name":"text","data":"相似范围"}]]},{"lang":"en","data":[[{"name":"text","data":"bullet marks"}],[{"name":"text","data":"depth feature information"}],[{"name":"text","data":"point cloud"}],[{"name":"text","data":"slope"}],[{"name":"text","data":"similar range"}]]}],"highlights":[],"body":[{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"1"}],"title":[{"name":"text","data":"引 言"}],"level":"1","id":"s1"}},{"name":"p","data":[{"name":"text","data":"枪弹痕识别技术是侦破案件的重要刑侦手段，主要通过研究子弹发射后遗留在弹头和弹壳上的痕迹特征信息，来进行识别鉴定并最终识别出对应枪支的相关信息。然而弹头痕迹细小难辨，给识别造成很大困难，传统的二维图像信息缺乏图像深度信息，无法从多角度观察弹痕特征，也无法测量弹痕的深度、宽度、角度等关键信息，然而这些信息也是弹痕比对的重要依据，因此此类信息的缺失在后续比对时造成了很大的困难也极易造成误配。"}]},{"name":"p","data":[{"name":"text","data":"目前，加拿大法医公司在这一领域已经进行了20多年的研究，所研制的枪弹痕自动对比检索系统较为先进"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"1","type":"bibr","rid":"b1","data":[{"name":"text","data":"1"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"，不仅可以生成高分辨率的二维弹痕图像、三维形貌图像还有二维和三维融合的弹痕图像，而且能够实现自动对比和检索，但是对硬件有非常高的精度要求。新一代的IBIS更是增强了三维形貌显示的功能，也提出了弹痕深度，宽度等信息在弹痕对比中的重要性。在国内，由黄志松等提出的提取弹头展平面标志线法"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"2","type":"bibr","rid":"b2","data":[{"name":"text","data":"2"}]}},{"name":"text","data":"]"}]},{"name":"text","data":",乔培玉等"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"3","type":"bibr","rid":"b3","data":[{"name":"text","data":"3"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"提出了基于高斯滤波中线的子弹三维图像特征提取的方法,这些方法消除了子弹变形时特征提取的困难，通过对比子弹切面曲线图来进行弹痕的匹配，对子弹整体三维轮廓特征提取效果较好，但无法对三维弹痕棱线特征进行提取，在子弹切面位置选取时容易产生误差，造成切面曲线图不匹配。同时丢失了弹痕图像中重要的深度特征信息，不能对棱线特征参数进行对比和评定。"}]},{"name":"p","data":[{"name":"text","data":"针对以上问题本文提出一种能够计算弹痕图像深度特征信息的特征提取算法。通过对三维弹痕数据的分析，运用非极大值抑制和斜率的方法找到弹痕棱线特征点，针对特征点进行线性拟合并计算各特征参数值，最终对参数值进行判别来确定枪和子弹是否匹配。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"2"}],"title":[{"name":"text","data":"弹痕点云数据预处理"}],"level":"1","id":"s2"}},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"2.1"}],"title":[{"name":"text","data":"弹痕特征介绍"}],"level":"2","id":"s2-1"}},{"name":"p","data":[{"name":"text","data":"弹痕主要集中于弹头的圆柱部分。在子弹发射过程中，弹头在进入线膛内旋转前进，受到摩擦力、剪切力、导旋力等作用后，留下了各种射击痕迹。这些痕迹能反映出枪械特征，对后续识别有很高适用价值。"}]},{"name":"p","data":[{"name":"text","data":"根据弹头痕迹不同的产生过程进行分类，可以分为四类，分别是：进膛痕迹、拔膛痕迹、坡膛痕迹和线膛痕迹。枪弹痕研究主要是针对坡膛和线膛痕迹，它们与枪管内部有着密切的联系"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"4","type":"bibr","rid":"b4","data":[{"name":"text","data":"4"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。"}]},{"name":"p","data":[{"name":"text","data":"根据公安部门现行方法和实际工作经验,具体定义了弹头痕迹识别特征区域：以弹头阳膛线痕迹中次棱痕迹为基准中心，弹头圆柱部分中包含坡膛痕迹、次棱痕迹以及小线纹痕迹，且距离弹头底部(以弹底卷屑痕迹为基准)0.25 mm区域。如"},{"name":"xref","data":{"text":"图 1","type":"fig","rid":"Figure1","data":[{"name":"text","data":"图 1"}]}},{"name":"text","data":"所示。"}]},{"name":"fig","data":{"id":"Figure1","caption":[{"lang":"zh","label":[{"name":"text","data":"图1"}],"title":[{"name":"text","data":"弹痕采集区域及二维图像"}]},{"lang":"en","label":[{"name":"text","data":"Fig 1"}],"title":[{"name":"text","data":"Collecting region of bullet and 2D image"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594089&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594089&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594089&type=middle"}]}}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"2.2"}],"title":[{"name":"text","data":"弹痕点云数据分析与转化"}],"level":"2","id":"s2-2"}},{"name":"p","data":[{"name":"text","data":"通常弹痕点云三维数据是通过三维形貌显微镜采集的，测量的基准平面取为固定在测量设备上的空间直角坐标系的"},{"name":"italic","data":[{"name":"text","data":"xoy"}]},{"name":"text","data":"平面。本文所采集的弹痕点云数据沿"},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"text","data":"轴和"},{"name":"italic","data":[{"name":"text","data":"y"}]},{"name":"text","data":"轴的测量步长均为3.3 μm，在"},{"name":"italic","data":[{"name":"text","data":"z"}]},{"name":"text","data":"轴方向的测量精度为1 μm。由数据采集过程可知，"},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"text","data":"和"},{"name":"italic","data":[{"name":"text","data":"y"}]},{"name":"text","data":"只表示步长，"},{"name":"italic","data":[{"name":"text","data":"z"}]},{"name":"text","data":"表示了测量点与基准面的相对距离。通过三维形貌显微镜测量子弹表面粗糙度能够获得一组3×"},{"name":"italic","data":[{"name":"text","data":"n"}]},{"name":"text","data":"的二维数据以矩阵方式记为："}]},{"name":"p","data":[{"name":"text","data":" "},{"name":"dispformula","data":{"label":[{"name":"text","data":"1"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594096&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594096&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594096&type=middle"}}}],"id":"yjyxs-31-9-889-E1"}},{"name":"text","data":" "}]},{"name":"p","data":[{"name":"text","data":"其中"},{"name":"italic","data":[{"name":"text","data":"a"},{"name":"sub","data":[{"name":"text","data":"1i,(i=1,2...n)"}]}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"a"},{"name":"sub","data":[{"name":"text","data":"2i,(i=1,2...n)"}]}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"a"},{"name":"sub","data":[{"name":"text","data":"3i,(i=1,2...n)"}]}]},{"name":"text","data":"分别表示第"},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"个测量点在测量系统坐标系中到"},{"name":"italic","data":[{"name":"text","data":"yoz,xoz,xoy"}]},{"name":"text","data":"三个平面的距离"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"5","type":"bibr","rid":"b5","data":[{"name":"text","data":"5"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。矩阵 A包含测量点在空间内完整的三维信息，但数据形式不适应计算机进行滤波、旋转、平移、显示等操作，因此需将矩阵 A进行一定形式的变换以适应计算机处理。分析矩阵 A可得如下性质："}]},{"name":"p","data":[{"name":"text","data":" "},{"name":"dispformula","data":{"label":[],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594106&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594106&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594106&type=middle"}}}],"id":"yjyxs-31-9-889-FE1"}},{"name":"text","data":" "}]},{"name":"p","data":[{"name":"text","data":" "},{"name":"dispformula","data":{"label":[{"name":"text","data":"2"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594114&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594114&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594114&type=middle"}}}],"id":"yjyxs-31-9-889-E2"}},{"name":"text","data":" "}]},{"name":"p","data":[{"name":"text","data":"根据上述性质,可将矩阵 A转换成"},{"name":"italic","data":[{"name":"text","data":"t×k"}]},{"name":"text","data":"阶矩阵"},{"name":"inlineformula","data":[{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594281&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594281&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594281&type=middle"}}}]},{"name":"text","data":"，"}]},{"name":"p","data":[{"name":"text","data":"其中"},{"name":"italic","data":[{"name":"text","data":"b"},{"name":"sub","data":[{"name":"text","data":"ij"}]},{"name":"text","data":"=a"},{"name":"sub","data":[{"name":"text","data":"3,i·(k－1)+j"}]}]},{"name":"text","data":"，以"},{"name":"italic","data":[{"name":"text","data":"b"},{"name":"sub","data":[{"name":"text","data":"11"}]}]},{"name":"text","data":"为原点，矩阵行方向自左向右建立"},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"text","data":"轴，列方向自下而上建立"},{"name":"italic","data":[{"name":"text","data":"y"}]},{"name":"text","data":"轴，通过行间距与列间距表征式(2)中Δ"},{"name":"italic","data":[{"name":"text","data":"a"}]},{"name":"text","data":"，则"},{"name":"italic","data":[{"name":"text","data":"B(x,y)"}]},{"name":"text","data":"完全并直观地表示三维测量结果中各点位置关系与深度信息，同时"},{"name":"italic","data":[{"name":"text","data":"B(x,y)"}]},{"name":"text","data":"在形式上更便于计算机对数据进行各种处理操作。"}]},{"name":"p","data":[{"name":"text","data":"由于"},{"name":"italic","data":[{"name":"text","data":"x，y"}]},{"name":"text","data":"是等步长变化的，因此只需要选取xoy平面作为基准面，对z进行分析即可。分析数据可知x每隔662组数据点会有一个重复，通过"},{"name":"italic","data":[{"name":"text","data":"Matlab"}]},{"name":"text","data":"对这662组数据点的x，z坐标进行提取可以得到一条二维曲线"},{"name":"italic","data":[{"name":"text","data":"f(x，z)"}]},{"name":"text","data":"，它包含了当"},{"name":"italic","data":[{"name":"text","data":"y"}]},{"name":"text","data":"=1时，所有的"},{"name":"italic","data":[{"name":"text","data":"x，z"}]},{"name":"text","data":"值。由这样的"},{"name":"italic","data":[{"name":"text","data":"t"}]},{"name":"text","data":"条曲线构成了弹痕图像的三维曲面。因此对于本文处理的弹痕数据可以映射到662×450的矩阵上，即"},{"name":"italic","data":[{"name":"text","data":"t"}]},{"name":"text","data":"=450"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"6","type":"bibr","rid":"b6","data":[{"name":"text","data":"6"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。"}]},{"name":"p","data":[{"name":"text","data":"通过点云数据分析把三维点云数据转化为二维矩阵上进行研究。因此将弹痕数据进行提取，使三维空间的数据变成多个二维数据，将三维曲面图转化成向"},{"name":"italic","data":[{"name":"text","data":"y"}]},{"name":"text","data":"轴延伸的多条二维曲线图。如"},{"name":"xref","data":{"text":"图 2","type":"fig","rid":"Figure2","data":[{"name":"text","data":"图 2"}]}},{"name":"text","data":"所示。"}]},{"name":"fig","data":{"id":"Figure2","caption":[{"lang":"zh","label":[{"name":"text","data":"图2"}],"title":[{"name":"text","data":"由二维曲线构成的三维曲面"}]},{"lang":"en","label":[{"name":"text","data":"Fig 2"}],"title":[{"name":"text","data":"3D surface be composed of 2D curve"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594125&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594125&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594125&type=middle"}]}}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3"}],"title":[{"name":"text","data":"弹痕特征提取"}],"level":"1","id":"s3"}},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3.1"}],"title":[{"name":"text","data":"弹痕特征提取算法介绍"}],"level":"2","id":"s3-1"}},{"name":"p","data":[{"name":"text","data":"在国内外鲜有对枪弹痕三维点云数据的特征提取算法的研究，因此只能通过参考传统三维点云数据特征提取算法进行研究实验。传统的三维点云数据特征提取的算法主要有：利用法向矢量提取特征点、利用曲率提取特征点、利用体积积分不变量提取特征点等方法"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"7","type":"bibr","rid":"b7","data":[{"name":"text","data":"7"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。(1)利用法向矢量提取特征点的方法是选取任意点,通过比较和相邻各点法向量夹角大小来判断是否是特征点。这种方法计算简单，快捷。但是阈值大小的选取很难确定，不同特征也需要选取不同的阈值，部分邻近点无法被提取到，容易造成信息的丢失。因此，通过法向量提取特征点的方法更适用于简单平滑的点云模型。(2)利用曲率提取特征点的方法计算量比较大，该算法主要是利用最小二乘法拟合二次曲面，从而计算出平均曲率，再将局部平均曲率与均值做比较来提取特征点。这种方法能够更加完整的提取点云的特征点，然而，提取特征点的阈值以曲率平均值为基准，受噪声点影响会比较大。另外，弹痕的线膛痕迹部分两棱线之间的曲率较小，很难通过曲率来提取，这样就无法计算棱线宽度，不利于后期的对比。(3)利用体积积分不变量提取特征点的方法是通过点云的平均曲率计算出点云体积积分不变量，去除其中体积积分不变量为0的点进而得到特征点。这种方法同样是利用点云的平均曲率，也不适合弹痕点云的数据处理。"}]},{"name":"p","data":[{"name":"text","data":"传统的点云特征提取算法对三维弹痕点云图像处理的适用性较差。通过各个点云特征提取算法的比较，又基于三维弹痕点云数据的分析，本文提出了局部寻找极值点并通过斜率变化精确极值点位置的算法来提取三维弹痕点云的特征"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"8","type":"bibr","rid":"b8","data":[{"name":"text","data":"8"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。这种算法对三维弹痕点云图像处理的适用性较好，可以准确的提取到弹痕的棱线峰值、谷值特征点。然后沿着y轴方向延伸，提取出整条特征棱线，并能够计算棱线的宽度、高度和角度，为后期比对提供了可靠的数据依据。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3.2"}],"title":[{"name":"text","data":"弹痕特征提取算法实现过程"}],"level":"2","id":"s3-2"}},{"name":"p","data":[{"name":"text","data":"由点云数据分析可知，三维曲面可以用多条二维曲线来表示，因此可以只针对一条曲线来进行分析。在"},{"name":"italic","data":[{"name":"text","data":"o"}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"xz"}]},{"name":"text","data":"平面内对数据进行抽取，得到一条二维曲线函数"},{"name":"italic","data":[{"name":"text","data":"f(x，z)"}]},{"name":"text","data":"，在函数中提取局部极大值和极小值点。这个过程可以根据类似非极大值抑制的方法，通过和邻域内的点进行比较，标记出极大值点。由于"},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"text","data":"是按等步长变化的，所以极大值点"},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"text","data":"满足"},{"name":"italic","data":[{"name":"text","data":"f(x)"}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"f(x±Δx)"}]},{"name":"text","data":">"},{"name":"text","data":"0，极小值点满足"},{"name":"italic","data":[{"name":"text","data":"f(x)"}]},{"name":"text","data":"-"},{"name":"italic","data":[{"name":"text","data":"f"}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"text","data":"±Δ"},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"text","data":")"},{"name":"text","data":"<"},{"name":"text","data":"0。找出极大值和极小值后，可以基本确定弹痕棱线特征点的位置范围。"}]},{"name":"p","data":[{"name":"text","data":"由于数据中存在离群点、噪声点的干扰，造成初步提取极值点的精确度不高，因此需要进一步确定极值点的位置。如果某一点处的斜率变化越大，则该点为特征点的可能性就越大"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"9","type":"bibr","rid":"b9","data":[{"name":"text","data":"9"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。通过比较相邻两极值点的斜率变化程度,精确提取特征点。在"},{"name":"italic","data":[{"name":"text","data":"o-xz"}]},{"name":"text","data":"平面内，相邻两个极值点之间的斜率可以表示为："}]},{"name":"p","data":[{"name":"text","data":" "},{"name":"dispformula","data":{"label":[{"name":"text","data":"3"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594138&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594138&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594138&type=middle"}}}],"id":"yjyxs-31-9-889-E3"}},{"name":"text","data":" "}]},{"name":"p","data":[{"name":"text","data":"由初步提取的极值点和公式(3)可以求得"},{"name":"italic","data":[{"name":"text","data":"k"},{"name":"sub","data":[{"name":"text","data":"AB"}]},{"name":"text","data":"、k"},{"name":"sub","data":[{"name":"text","data":"BC"}]}]},{"name":"text","data":"，斜率产生由正向负突变的位置点为B点，即为棱线的峰值点，也就是极大值特征点，而斜率由负向正突变的位置点A、C为棱线的谷值，也就是极小值特征点。"}]},{"name":"p","data":[{"name":"text","data":"通过这种算法，能够确定每条二维曲线上的极大值和极小值特征点，并进行标记。显示的外部标记能够有效地将图像分割成不同的区域"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"10","type":"bibr","rid":"b10","data":[{"name":"text","data":"10"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"，突出了弹痕特征的显示。最后，在三维空间坐标上延伸，能够得到标记后完整的三维曲面图，所标记的部分则为三维棱线的特征轮廓。如"},{"name":"xref","data":{"text":"图 3","type":"fig","rid":"Figure3","data":[{"name":"text","data":"图 3"}]}},{"name":"text","data":"所示。"}]},{"name":"fig","data":{"id":"Figure3","caption":[{"lang":"zh","label":[{"name":"text","data":"图3"}],"title":[{"name":"text","data":"三维棱线特征图"}]},{"lang":"en","label":[{"name":"text","data":"Fig 3"}],"title":[{"name":"text","data":"3D feature image of the ridge"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594212&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594212&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594212&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"特征点被标记后，可以清晰地显示弹痕棱线的特征轮廓，因此可以基于弹痕棱线特征轮廓形状来计算棱线的各个特征参数值，如：宽度，高度，角度等。由每条弹痕二维曲线相邻的特征点进行线性拟合，如"},{"name":"xref","data":{"text":"图 4","type":"fig","rid":"Figure4","data":[{"name":"text","data":"图 4"}]}},{"name":"text","data":"所示。"}]},{"name":"fig","data":{"id":"Figure4","caption":[{"lang":"zh","label":[{"name":"text","data":"图4"}],"title":[{"name":"text","data":"弹痕棱线二维曲线图"}]},{"lang":"en","label":[{"name":"text","data":"Fig 4"}],"title":[{"name":"text","data":"2D curve image of bullet ridge"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594221&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594221&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594221&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"通过最小二乘法可以计算出对于"},{"name":"italic","data":[{"name":"text","data":"z=bx+a"}]},{"name":"text","data":"的直线，并根据相关系数"},{"name":"italic","data":[{"name":"text","data":"r"}]},{"name":"text","data":"的计算找出其中拟合程度最好的直线。即："}]},{"name":"p","data":[{"name":"text","data":" "},{"name":"dispformula","data":{"label":[{"name":"text","data":"4"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594230&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594230&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594230&type=middle"}}}],"id":"yjyxs-31-9-889-E4"}},{"name":"text","data":" "}]},{"name":"p","data":[{"name":"text","data":"由拟合直线AB、BC和基平面AC构建一个三角形。由于已经求得被标记棱线特征极小值和极大值特征点的坐标数据,设三点坐标分别为"},{"name":"italic","data":[{"name":"text","data":"A(x"},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":",z"},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"),B(x"},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":",z"},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"),C(x"},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":",z"},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":")"}]},{"name":"text","data":"因此宽度可以根据两个相邻极小值点的欧式距离来计算，即："}]},{"name":"p","data":[{"name":"text","data":" "},{"name":"dispformula","data":{"label":[{"name":"text","data":"5"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594238&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594238&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594238&type=middle"}}}],"id":"yjyxs-31-9-889-E5"}},{"name":"text","data":" "}]},{"name":"p","data":[{"name":"text","data":"角度是指AB与AC所成向量的夹角。已知二维曲线极值点坐标位置后,角度"},{"name":"italic","data":[{"name":"text","data":"θ"}]},{"name":"text","data":"可以表示成："}]},{"name":"p","data":[{"name":"text","data":" "},{"name":"dispformula","data":{"label":[{"name":"text","data":"6"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594247&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594247&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594247&type=middle"}}}],"id":"yjyxs-31-9-889-E6"}},{"name":"text","data":" "}]},{"name":"p","data":[{"name":"text","data":"已构建的三角形ABC面积S可以通过三点坐标行列式的绝对值求得。如公式(7)："}]},{"name":"p","data":[{"name":"text","data":" "},{"name":"dispformula","data":{"label":[{"name":"text","data":"7"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594256&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594256&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594256&type=middle"}}}],"id":"yjyxs-31-9-889-E7"}},{"name":"text","data":" "}]},{"name":"p","data":[{"name":"text","data":"计算出面积后利用公式(8)就能够求出棱线的高度："}]},{"name":"p","data":[{"name":"text","data":" "},{"name":"dispformula","data":{"label":[{"name":"text","data":"8"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594265&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594265&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594265&type=middle"}}}],"id":"yjyxs-31-9-889-E8"}},{"name":"text","data":" "}]},{"name":"p","data":[{"name":"text","data":"通过这种算法对每条二维曲线进行计算，能够获得每条曲线上的特征点参数数据。最后对数据进行整理，将计算得到的所有的高度取均值作为棱线的高度值，所有的宽度取均值作为棱线的宽度值，所有的角度取均值作为棱线的角度值。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3.3"}],"title":[{"name":"text","data":"实验结果与对比"}],"level":"2","id":"s3-3"}},{"name":"p","data":[{"name":"text","data":"本文通过Matlab对弹痕三维点云数据进行特征提取仿真，实现了三维点云数据的特征提取、特征点标记以及特征参数的计算和输出"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"11","type":"bibr","rid":"b11","data":[{"name":"text","data":"11"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"。针对同一支枪射出的不同的弹头进行实验图像及数据对比，总结计算出同一支枪射出的不同弹头所具有的特征参数的相似限定范围。然后对未知弹头进行实验数据计算和对比，观测未知弹头痕迹特征参数是否满足相似限定范围，最终判定其是否为同一支枪射出。"}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3.3.1"}],"title":[{"name":"text","data":"实验图像对比"}],"level":"3","id":"s3-3-1"}},{"name":"p","data":[{"name":"text","data":"实验图像是运用本文所提出的特征提取算法通过Matlab进行仿真所得。明显的弹痕棱线轮廓特征信息被提取出并标记，这便于后续特征参数信息的计算。同时可以在图像上观察到同一支枪发射出的两发子弹在弹痕上具有一些共同点，如：弹痕线条的条数、弹痕间的距离等。如"},{"name":"xref","data":{"text":"图 5","type":"fig","rid":"Figure5","data":[{"name":"text","data":"图 5"}]}},{"name":"text","data":"所示。"}]},{"name":"fig","data":{"id":"Figure5","caption":[{"lang":"zh","label":[{"name":"text","data":"图5"}],"title":[{"name":"text","data":"三维棱线特征提取图像对比"}]},{"lang":"en","label":[{"name":"text","data":"Fig 5"}],"title":[{"name":"text","data":"Contrast amongimages of 3D ridge feature extraction"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594274&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594274&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1594274&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"由于弹痕特征的细微难辨，仅从图像上对比说明弹痕的相似性还是不够的。为了验证弹痕特征提取的准确性，需要对弹痕特征进行匹配和对比。所以在对实验数据进行对比前，弹痕点云图像的配准是必不可少的，因为只有在同一位置的弹痕特征参数对比才是有意义的。"}]},{"name":"p","data":[{"name":"text","data":"本文弹痕点云的初始配准是利用了点云主方向贴合法实现了自动初始配准，用来缩小点云之间旋转和平移错位"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"12","type":"bibr","rid":"b12","data":[{"name":"text","data":"12"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"；精确配准应用显著纹理特征的经典迭代最近点(ICP)的方法,将显著性强的特征点赋予较大权重，主痕迹特征棱线的显著性强，率先进行配准，然后又根据方向特征的ICP算法进行了精确配准"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"13","type":"bibr","rid":"b13","data":[{"name":"text","data":"13"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"14","type":"bibr","rid":"b14","data":[{"name":"text","data":"14"}]}}],"rid":["b13","b14"],"text":"13-14","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"。经过点云图像配准以后，还需要进行定量的实验计算与对比，对比同枪和不同枪射出的弹头。通过计算未知弹头痕迹特征参数值的差异，判别参数值是否能够满足相似限定范围，进而确定未知弹头是否同枪。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3.3.2"}],"title":[{"name":"text","data":"实验数据对比"}],"level":"3","id":"s3-3-2"}},{"name":"p","data":[{"name":"text","data":"实验数据结果如"},{"name":"xref","data":{"text":"表 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1","type":"table","rid":"Table1","data":[{"name":"text","data":"表 1"}]}},{"name":"text","data":"对应的参数相似限定范围。而不同枪打出的子弹在这3个参数差值上都不能完全满足相似限定范围。经过300组三维弹痕数据的实验计算与比对，证明本文的算法正确识别率在90%以上。单组弹痕数据的转换、特征提取和参数的计算共用时32.7 s。然而传统算法中，通过计算子弹切面曲线图之间的互相关值进行比对，正确识别率在82%左右，而且切面曲线选取需要进行人工干预，整体对比识别过程大约用时两分钟。所以本文算法不论正确识别率还是运行速度上均有较大程度的提高。 因此，实验得到了很好的效果，结果表明基于斜率变化的特征提取算法可以准确的提取出三维弹痕图像的特征参数信息，通过后续实验数据比对，达到了可以判别枪弹一致性的要求。"}]}]}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"4"}],"title":[{"name":"text","data":"结 论"}],"level":"1","id":"s4"}},{"name":"p","data":[{"name":"text","data":"本文针对三维弹痕点云数据进行分析，将三维数据转换到二维矩阵上来，对局部极值点初步定位，通过斜率变化的计算精确定位极值特征点并标记，最终提取出三维弹痕棱线深度特征，计算出各特征参数差值并进行实验对比。实验结果取得了很好的特征提取效果，能够满足弹痕比对的需求，在一定程度上为枪弹痕三维点云特征提取提供了进一步的研究方向。"}]},{"name":"p","data":[{"name":"text","data":"本文算法具有运行速度快，精确度较高，稳定性好等特点。通过与传统算法对比，在现有样本的条件下，本文算法将正确识别率由82%提高到了90%以上。由于减少了人工选择子弹切面位置的过程，单组弹痕数据的对比由两分钟缩减到32.7 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All rights reserved."}],"type":"copyright"}],"year":"2016"}},"appendix":[],"type":"research-article","ethics":[],"backSec":[],"supplementary":[],"journalTitle":"液晶与显示","issue":"9","volume":"31","originalSource":[]}