CN103489190B - 图像特征曲线提取方法及系统 - Google Patents

图像特征曲线提取方法及系统 Download PDF

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CN103489190B
CN103489190B CN201310444485.9A CN201310444485A CN103489190B CN 103489190 B CN103489190 B CN 103489190B CN 201310444485 A CN201310444485 A CN 201310444485A CN 103489190 B CN103489190 B CN 103489190B
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尹康学
黄惠
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Shenzhen Institute of Advanced Technology of CAS
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Abstract

本发明涉及一种图像特征曲线提取方法，包括如下步骤：在要提取特征曲线的图像上沿其特征边缘画一条近似曲线；得到所述图像中的短边缘；以上述所画的曲线为边界条件计算得到一个调和向量场；利用所述调和向量场过滤上述图像中的短边缘；用上述图像中剩下的短边缘为边界条件更新向量场；及通过极小化样条曲线在该向量场中的能量得到所述图像最优的特征曲线。本发明还涉及一种图像特征曲线提取系统。本发明所得图像特征曲线能够即保证光滑又保证弯曲特征。

Description

图像特征曲线提取方法及系统
技术领域
本发明涉及一种图像特征曲线提取方法及系统。
背景技术
图像特征曲线提取是图像处理领域中重要的研究方向。目前已有的交互式图像特征曲线提取的方法主要有：动态蛇（dynamicsnakes），智能剪刀（intelligentscissors）等。
动态蛇是一种重要的基于边缘的交互式图像特征曲线提取方法。在Kass等人于1987年首次提出Snake模型之后，人们对该模型的能量函数和求解方法不断地进行改进，提出了许多新的Snake模型及改进。动态蛇方法的基本思想很简单，它以由一些控制点生成的样条曲线为模板，通过模板自身的弹性形变，与图像局部特征相匹配达到调和，即某种能量函数极小化，完成对图像特征曲线的提取。然而，动态蛇方法存在如下不足：对初始曲线位置要求严格，初始曲线必须非常接近目标真实轮廓，否则将得不到好的收敛结果；对凹陷的目标轮廓得不到好的收敛效果；迭代速度慢且收敛效果不好。
智能剪刀是一种非常经典的半自动图像特征曲线提取方法。用户只要沿着图片上的边缘粗略的移动鼠标，智能剪刀方法就能估计出较精确的边缘曲线。它使用拉普拉斯过零特征函数、梯度大小和梯度方向给像素点赋予权值，使用动态规划求解最优路径的方法求解两点间的目标边缘。随着鼠标的移动，智能剪刀能比较准确、快速地提取目标的边缘。当鼠标移动到目标边缘附近时，智能剪刀能自动地吸附到目标边缘上。智能剪刀方法亦存在如下缺点：不能识别用户的错误输入；所得曲线不够光滑。
发明内容
有鉴于此，有必要提供一种图像特征曲线提取方法及系统。
本发明提供一种图像特征曲线提取方法，该方法包括如下步骤：a.在要提取特征曲线的图像上沿其特征边缘画一条曲线；b.得到所述图像中的短边缘；c.以上述所画的曲线为边界条件计算得到一个调和向量场；d.利用所述调和向量场过滤上述图像中的短边缘；e.用上述图像中剩下的短边缘为边界条件更新向量场；及f.通过极小化样条曲线在该向量场中的能量得到所述图像最优的特征曲线。
其中，所述的步骤b中得到图像中的短边缘可以采用canny算法、Prewitt算法、Sobel算法或者Kirsch算法。
所述的步骤c具体包括：以步骤a中所画的曲线作为二维流形的边界，将边界处曲线的切向量作为边界值，求解Δu＝0（u为向量场）得到调和向量场。
所述的步骤d包括：给每条短边缘定义一个分值：Score=α1*自身长度–α2*与调和向量场的平均夹角–α3*平均曲率–α4*与用户所画的曲线的平均距离。其中，α1，α2，α3，α4分别为各项权重。
所述的特征曲线为如下目标函数：
f(C)＝Edistance(C)+Evector(C)+Esmooth(C)
其中，C为三次B样条曲线，Edistance(C)定义短边缘上所有像素到C的距离之和，Evector(C)为沿C对C的切线和向量场的夹角的积分，Esmooth(C)为C的光滑程度可以用曲率来衡量。
本发明提供一种图像特征曲线提取系统，包括相互电性连接的输入模块、短边缘获取模块、计算模块、过滤模块、更新模块及特征曲线获取模块，其中：所述输入模块用于接收在要提取特征曲线的图像上沿其特征边缘所画的一条曲线；所述短边缘获取模块用于得到所述图像中的短边缘；所述计算模块用于以用户所画的曲线为边界条件计算得到一个调和向量场；所述过滤模块用于利用调和向量场过滤上述图像中的短边缘；所述更新模块用于用上述图像中剩下的短边缘作为边界条件更新向量场；所述特征曲线获取模块用于通过极小化样条曲线在该向量场中的能量得到所述图像最优的特征曲线。
其中，所述的得到图像中的短边缘可以采用canny算法、Prewitt算法、Sobel算法或者Kirsch算法。
所述的计算模块用于以上述输入模块接收的曲线作为二维流形的边界，将边界处曲线的切向量作为边界值，求解Δu＝0（u为向量场）得到调和向量场。
所述的所述过滤模块用于：给每条短边缘定义一个分值：Score=α1*自身长度–α2*与调和向量场的平均夹角–α3*平均曲率–α4*与用户所画的曲线的平均距离。其中，α1，α2，α3，α4分别为各项权重。
所述的特征曲线为如下目标函数：
f(C)＝Edistance(C)+Evector(C)+Esmooth(C)
其中，C为三次B样条曲线，Edistance(C)定义短边缘上所有像素到C的距离之和，Evector(C)为沿C对C的切线和向量场的夹角的积分，Esmooth(C)为C的光滑程度可以用曲率来衡量。
本发明所提供的图像特征曲线提取方法及系统，通过引入调和向量场，将用户的交互和图像本身的信息自然的结合到一起；综合考虑多种信息，因而对用户的错误输入不敏感，对于有弯曲凹陷的目标曲线也可以获得很好的结果；求解特征曲线时，同时考虑与向量场的一致性、到短边缘的距离、光滑性三项，从而使结果更加稳定，容易快速收敛到最优解，并且所得图像特征曲线能够即保证光滑又保证弯曲特征。
附图说明
图1为本发明图像特征曲线提取方法的流程图；
图2为本发明图像特征曲线提取系统的硬件架构图。
具体实施方式
下面结合附图及具体实施例对本发明作进一步详细的说明。
参阅图1所示，是本发明图像特征曲线提取方法较佳实施例的作业流程图。
步骤S401，在要提取特征曲线的图像上沿其特征边缘画一条曲线。具体而言，用户可以使用如opencv、MFC、QT等程序库开发的软件手动在所述图像上沿其特征边缘近似地画一条曲线。
步骤S402，得到所述图像中的短边缘。在本实施例中使用Canny算法得到所述图像中的短边缘，也可使用其他边缘检测算法代替canny算法，比如Prewitt算法、Sobel算法、Kirsch算法等。
具体步骤如下：
1）使用高斯滤波器对所述图像进行滤波，以消除噪声；
2）针对所述图像中每一个像素，计算其横向与纵向两方向的微分近似，以得到像素的梯度大小和方向；
3）对上述得到的像素的梯度进行“非极大抑制”：如果该像素的梯度不是局部最大值，则将其置为0；如果该像素的梯度是局部最大值，则保持其不变。其中，所述局部是指以该像素为中心的一个小邻域，该邻域的半径可以根据用户的需求设置。
4）对上述像素通过其梯度进行过滤以得到潜在的边缘像素。也即，将上述像素的梯度使用一个高阈值和一个低阈值进行过滤，剩下的像素为潜在的边缘像素。所述边缘像素，其梯度介于高阈值和低阈值之间。
5）对上述边缘像素进行连接得到所述图像中的短边缘。
步骤S403，以用户所画的曲线为边界条件计算得到一个调和向量场。所述调和向量场为无旋向量场，即向量场各处旋度为零。具体而言，以用户在步骤S401中所画的曲线作为二维流形的边界，将边界处曲线的切向量作为边界值，求解Δu＝0（u为向量场）即得到调和向量场。
求解时，将u的x、y分量分开来分别求解，这样就将该问题转化为两个狄利克雷约束条件下的偏微分方程。
argminuΔus.t.u0＝b
其中Δu为向量场u的拉普拉斯算子，u0为求解后向量场的边界值，b为由用户定义的曲线确定的边界值。
步骤S404，利用调和向量场过滤上述图像中的短边缘。具体步骤如下：给每条短边缘定义一个分值：Score=α1*自身长度–α2*与调和向量场的平均夹角–α3*平均曲率–α4*与用户所画的曲线的平均距离。其中，α1，α2，α3，α4分别为各项权重。通过组合α1，α2，α3，α4这四项，就可以根据如下规则保留短边缘：保留的短边缘要尽可能长；保留的短边缘切向要尽可能与调和向量场一致；保留的短边缘曲率要小；保留的短边缘要靠近用户所画的曲线。
步骤S405，用上述图像中剩下的短边缘作为边界条件更新向量场。具体而言，以上述图像中剩下的短边缘作为二维流形的边界，将边界处曲线的切向量作为边界值，求解Δu＝0（u为向量场）即更新调和向量场。具体方法可参照步骤S403。
步骤S406，通过极小化样条曲线在该向量场中的能量得到所述图像最优的特征曲线。具体步骤如下：
在本实施例中使用三次B样条来表示特征曲线，也可使用其他自由曲线代替三次B样条曲线，比如贝塞尔曲线、非均匀有理B样条等。
本实施例使用用户所画的曲线作为初始值，并定义特征曲线为如下目标函数：
f(C)＝Edistance(C)+Evector(C)+Esmooth(C)
其中，C为三次B样条曲线，Edistance(C)定义短边缘上所有像素到C的距离之和，Evector(C)为沿C对C的切线和向量场的夹角的积分，Esmooth(C)为C的光滑程度可以用曲率来衡量。
最小化f(C)是一个无约束优化问题，本实施例使用BFGS算法来求解所述特征曲线。也可使用其他优化算法代替BFGS算法，比如最速下降法，牛顿法等。
参阅图2所示，是本发明图像特征曲线提取系统的硬件架构图。该系统包括相互电性连接的输入模块、短边缘获取模块、计算模块、过滤模块、更新模块及特征曲线获取模块。
所述输入模块用于接收在要提取特征曲线的图像上沿其特征边缘所画的一条曲线。具体而言，用户使用如opencv、MFC、QT等程序库开发的软件手动在所述图像上沿其特征边缘近似地画一条曲线，所述输入模块接收上述用户所画的曲线。
所述短边缘获取模块用于得到所述图像中的短边缘。在本实施例中所述短边缘获取使用Canny算法得到所述图像中的短边缘，也可使用其他边缘检测算法代替canny算法，比如Prewitt算法、Sobel算法、Kirsch算法等。
具体如下：
1）使用高斯滤波器对所述图像进行滤波，以消除噪声；
2）针对所述图像中每一个像素，计算其横向与纵向两方向的微分近似，以得到像素的梯度大小和方向；
3）对上述得到的像素的梯度进行“非极大抑制”：如果该像素的梯度不是局部最大值，则将其置为0；如果该像素的梯度是局部最大值，则保持其不变。其中，所述局部是指以该像素为中心的一个小邻域，该邻域的半径可以根据用户的需求设置。
4）对上述像素通过其梯度进行过滤以得到潜在的边缘像素。也即，将上述像素的梯度使用一个高阈值和一个低阈值进行过滤，剩下的像素为潜在的边缘像素。所述边缘像素，其梯度介于高阈值和低阈值之间。
5）对上述边缘像素进行连接得到所述图像中的短边缘。
所述计算模块用于以用户所画的曲线为边界条件计算得到一个调和向量场。所述调和向量场为无旋向量场，即向量场各处旋度为零。具体而言，以用户在输入模块中所画的曲线作为二维流形的边界，将边界处曲线的切向量作为边界值，求解Δu＝0（u为向量场）即得到调和向量场。
求解时，将u的x、y分量分开来分别求解，这样就将该问题转化为两个狄利克雷约束条件下的偏微分方程。
argminuΔus.t.u0＝b
其中Δu为向量场u的拉普拉斯算子，u0为求解后向量场的边界值，b为由用户定义的曲线确定的边界值。
所述过滤模块用于利用调和向量场过滤上述图像中的短边缘。具体步骤如下：所述过滤模块给每条短边缘定义一个分值：Score=α1*自身长度–α2*与调和向量场的平均夹角–α3*平均曲率–α4*与用户所画的曲线的平均距离。其中，α1，α2，α3，α4分别为各项权重。通过组合α1，α2，α3，α4这四项，就可以根据如下规则保留短边缘：保留的短边缘要尽可能长；保留的短边缘切向要尽可能与调和向量场一致；保留的短边缘曲率要小；保留的短边缘要靠近用户所画的曲线。
所述更新模块用于用上述图像中剩下的短边缘作为边界条件更新向量场。具体而言，所述更新模块以上述图像中剩下的短边缘作为二维流形的边界，将边界处曲线的切向量作为边界值，求解Δu＝0（u为向量场）即更新调和向量场。
所述特征曲线获取模块用于通过极小化样条曲线在该向量场中的能量得到所述图像最优的特征曲线。具体如下：
在本实施例中使用三次B样条来表示特征曲线，也可使用其他自由曲线代替三次B样条曲线，比如贝塞尔曲线、非均匀有理B样条等。
本实施例使用用户所画的曲线作为它的初始值，并定义特征曲线为如下目标函数：
f(C)＝Edistance(C)+Evector(C)+Esmooth(C)
其中，C为三次B样条曲线，Edistance(C)定义短边缘上所有像素到C的距离之和，Evector(C)为沿C对C的切线和向量场的夹角的积分，Esmooth(C)为C的光滑程度可以用曲率来衡量。
最小化f(C)是一个无约束优化问题，本实施例使用BFGS算法来求解所述特征曲线。也可使用其他优化算法代替BFGS算法，比如最速下降法，牛顿法等。
虽然本发明参照当前的较佳实施方式进行了描述，但本领域的技术人员应能理解，上述较佳实施方式仅用来说明本发明，并非用来限定本发明的保护范围，任何在本发明的精神和原则范围之内，所做的任何修饰、等效替换、改进等，均应包含在本发明的权利保护范围之内。

Claims (6)

1.一种图像特征曲线提取方法，其特征在于，该方法包括如下步骤：
a.在要提取特征曲线的图像上沿其特征边缘画一条曲线，所述的特征曲线为如下目标函数：
f(C)＝Edistance(C)+Evector(C)+Esmooth(C)
其中，C为三次B样条曲线，Edistance(C)定义短边缘上所有像素到C的距离之和，Evector(C)为沿C对C的切线和向量场的夹角的积分，Esmooth(C)为C的光滑程度可以用曲率来衡量；
b.得到所述图像中的短边缘；
c.以上述所画的曲线为边界条件计算得到一个调和向量场；
d.利用所述调和向量场过滤上述图像中的短边缘；
e.用上述图像中剩下的短边缘为边界条件更新向量场；及
f.通过极小化样条曲线在该向量场中的能量得到所述图像最优的特征曲线；
其中，所述的步骤c具体包括：以步骤a中所画的曲线作为二维流形的边界，将边界处曲线的切向量作为边界值，求解Δu＝0(u为向量场)得到调和向量场。
2.如权利要求1所述的方法，其特征在于，所述的步骤b中得到图像中的短边缘可以采用canny算法、Prewitt算法、Sobel算法或者Kirsch算法。
3.如权利要求1所述的方法，其特征在于，所述的步骤d包括：给每条短边缘定义一个分值：Score＝α1*自身长度–α2*与调和向量场的平均夹角–α3*平均曲率–α4*与用户所画的曲线的平均距离，其中，α1，α2，α3，α4分别为各项权重。
4.一种图像特征曲线提取系统，其特征在于，该系统包括相互电性连接的输入模块、短边缘获取模块、计算模块、过滤模块、更新模块及特征曲线获取模块，其中：
所述输入模块用于接收在要提取特征曲线的图像上沿其特征边缘所画的一条曲线，所述的特征曲线为如下目标函数：
f(C)＝Edistance(C)+Evector(C)+Esmooth(C)
其中，C为三次B样条曲线，Edistance(C)定义短边缘上所有像素到C的距离之和，Evector(C)为沿C对C的切线和向量场的夹角的积分，Esmooth(C)为C的光滑程度可以用曲率来衡量；
所述短边缘获取模块用于得到所述图像中的短边缘；
所述计算模块用于以用户所画的曲线为边界条件计算得到一个调和向量场；
所述过滤模块用于利用调和向量场过滤上述图像中的短边缘；
所述更新模块用于用上述图像中剩下的短边缘作为边界条件更新向量场；
所述特征曲线获取模块用于通过极小化样条曲线在该向量场中的能量得到所述图像最优的特征曲线；
其中，所述计算模块具体用于以所述输入模块接收的曲线作为二维流形的边界，将边界处曲线的切向量作为边界值，求解Δu＝0(u为向量场)得到调和向量场。
5.如权利要求4所述的系统，其特征在于，所述的得到图像中的短边缘可以采用canny算法、Prewitt算法、Sobel算法或者Kirsch算法。
6.如权利要求4所述的系统，其特征在于，所述的所述过滤模块用于：给每条短边缘定义一个分值：Score＝α1*自身长度–α2*与调和向量场的平均夹角–α3*平均曲率–α4*与用户所画的曲线的平均距离，其中，α1，α2，α3，α4分别为各项权重。
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Record date: 20231212

Application publication date: 20140101

Assignee: Shenzhen Weigao Investment Development Co.,Ltd.

Assignor: SHENZHEN INSTITUTES OF ADVANCED TECHNOLOGY CHINESE ACADEMY OF SCIENCES

Contract record no.: X2023980051257

Denomination of invention: Image feature curve extraction method and system

Granted publication date: 20160511

License type: Common License

Record date: 20231212