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图像匹配中英对照翻译

图像匹配中英对照翻译
图像匹配中英对照翻译

基于局部不变特征和直方图相似距离的图像匹配原文来自IEEE“Image Matching Based on Local Invariant Feature”

摘要:本文将一种基于局部不变的特征描述符ARPIH与直方图相关性判断结合起来,提出了一种新的图像匹配算法。本方法保留了ARPIH描述的优点,在匹配旋转、亮度变化、透视等畸变图像时显示出了鲁棒性。通过求取模板图像和目标图像的两个描述直方图间的相似点的个数进行相似性匹配,提高了匹配精度。该方法在几何形变和光照变化的图像中显示出其较好的匹配结果。

关键词:图像匹配局部不变特征APPIH 直方图相似性距离

一、引言

图像匹配就是在目标图像中找出与模板图像相同或相似的部分。随着技术的发展,图像匹配在现代航天、军事、医学、工业等很多应用的信息处理中都是十分重要的。因为图像成像条件(比如:光照条件、视角、旋转和传感器)的变化,对图像匹配的要求越来越多。在存在图像畸变的情况下,如何找到一个快速的具有高鲁棒性的图像匹配算法成为了研究的重点内容。

近期研究表明,利用图像的局部信息足以描述图像包含的内容[2],并可利用其进行图像匹配而避免图像分割带来的误差。Lowe[3]把局部DOG极值点作为兴趣点,并通过计算局部图像梯度直方图提出一个特定的局部描述符。Schmidt和Mohr[4]证明了局部信息足以用来进行图像识别。他们把Harris角点作为兴趣点,然后从它领域提炼出旋转不变描述符。这个描述符可以保证对旋转图像的正确匹配。Tuytelaars和Van Goal在角点和灰度极值构造一个小的仿射不变区域。所有的方法在搜索特定的平行四边形结构时是一样的,[3]和[4]是灰度不变的,[5]是仿射不变的。雷钦和文高[6]提出了一个新的局部不变描述符—角放射分割强度直方图(APPIH),它是用一系列灰度,旋转不变特征描述符来描述图像的。这种方法可以解决图像匹配中的几何畸变和光照变化问题,但是操作复杂,匹配时间长。

相似性度量,即用一些测度来确定匹配特征间的相似度,往往需要一个代价函数或者距离函数。经典的相似性度量包括相关函数和闵科夫斯基距离[7]。近来,人们用Hausdorff距离[8],互信息[9]作为匹配测度。Hausdorff距离具有对噪声十分敏感的优点,分段Hausdorff距离可以用来处理掩盖的目标,但它需要很长的计算时间。基于互信息的方法在医学图像匹配中得到广泛的应用,因为它对光照变化不敏感,但它也有缺陷,计算复杂且要求图像具有很大的重叠区域。基于通过计算像素灰度值差异的传统匹配方法的性能会因为灰度值的差异和模板图像与目标图像之间的失真而降低。文献[10]提出了一种名为ML距离的新的图像匹配方法。它是计算模板图像与目标图像间的相似点个数,而不是计算二者间灰度值的距离。因此相较于传统的灰度相似匹配,该方法大大提高了匹配的稳

定度,而且操作简单,降低了匹配时间。但该方法不能用来对几何畸变(如旋转)的图像进行图像匹配。在ML 距离的基础上,本文中我们提出一种新的基于直方图相似距离的匹配方法(HSD );而且,我们巧妙的将APPIH 和HSD 结合起来。通过APPIH 构造的强直方图被视为一幅图像,然后计算两个直方图之间的相似度来实现畸变匹配,比如:旋转、光照变化和局部遮挡。

二、 局部不变描述符

A . 局部不变区域

基于局部不变信息的图像匹配要求寻找一个在图像灰度级及旋转变化后仍保持不变的局部图像区域。K. Mikolajczyk 和C. Schmid[11] 提出的算法可表示一个这样不变的区域( x , y , s , a) ,其中:( x ,y) 表示区域中的一点;s 表示此点的灰度级;a 表示此点所属的区域[3]。

B . APPIH 描述符

图1 说明了ARPIH 描述符[ 4 ] 的结构。将一个图像区域按图1 (a) 中所表示的方法将其细分为18 个子区域。其中划分的角度θ分别为(π/ 3 ,2π/ 3 ,π,4π/ 3 ,5π/ 3 ,2π) ,其半径r 之比依据经验取值为0157 ∶0185 ∶1 ,使得各个子区域中像素点的个数基本一致。

图中的数字为各个子区域的编号。图1 (c) 即为ARPIH 描述符。

ARPIH 描述符是一个体现图像区域内像素点灰度值分布及子区域间几何关系的二维直方图。直方图的x 轴是子区域的编号,y 轴是灰度级(0—255) ,被均匀划分为18 个灰度范围。将每一子区域中的像素点按其灰度值划分到各个灰度范围中,例如:ARPIH 中, z 轴H (11 ,9)表示第11 号子区域中灰度值在(115 ,129)范围内的点的个数。通过使用ARPIH 描述符,将2 个图像区域的匹配转化成为 2 幅直方图的匹配,减少了计算的复杂性,且拥有良好的抗畸变能力。

三、HSD

A .MSD 和MLD

当匹配两幅图像时,对应点的相似关系是要考虑的最主要的问题。所以相似测度只考虑两幅图像中的对应点之间的距离,就是说不用再计算一个集合中所有点到一个点的距离。首先,我们计算图像中每对对应点之间的相似性,然后由相似度的最小绝对误差来得到两幅图像的距离。

定义模板图像为(,)S m n ,它的大小为M N ?,目标图像为(,)I u v ,大小为U V ?。模板图像在目标图像中的位置为(,)i j ,假设'(,)(,)S m n I i m j n =++,(,)d i j 表示大小相同的图像窗口之间的距离函数,**(,)i j 表示最佳的匹配位置,P 是匹配范围,P 的定义如下:

{(,)|0,0}(1)P i j i U M j V N =≤≤-≤≤-

基于传统的绝对误差均值算法(MAD )的距离测度函数是如下定义的:

'111(,)((,),(,))(2)M N MAD m n d i j R

S m n S m n MN ===∑∑

其中

''((,),(,))|(,)(,)|(3)MAD R S m n S m n S m n S m n =-

最佳匹配位置为:

**(,)min{(,)|(,)}(4)d i j d i j i j P =∈

在这个算法中,每一个点对匹配结果做相同的贡献,所以它的性能容易因为噪声点和区域遮蔽而降低。

MLD 在文献10中如下定义:

'111(,)((,),(,))(5)M N MAD

m n d i j R S m n S m n MN ===∑∑

其中

''1,|(,)(,)|((,),(,))(6)0,MAD S m n S m n T R S m n S m n else ?-≤=??

其中(,)d i j 表示相似度,所以最佳匹配位置为:

**(,)max{(,)|(,)}(7)d i j d i j i j P =∈

两个算法的区别在于前者计算所有像素灰度等级的差别的绝对值之和,然而后者参与计算只是相似的点。而且,在相关平面中找最相似的位置时,MAD 需要找谷点,但是MLD 需要找峰值。这样在计算时,我们只需要考虑模板图像和目标图像相似的点来测度相似度,抛弃掉和模板图像差别很大的点。综上所述,这个算法比传统的相似匹配好,因为它很好的回避了由噪声引起的宽的而且不明显的峰值。

B .HSD

基于MLD 的想法,提出HSD 的定义。假设对于有相同大小M N ?的图像的

两个直方图,分别为(,)H m n 和'(,)H m n 。当这两个直方图满足以下条件时我们

认为它们是相似的:

1(8)HSD D T ≥

'11

((,),(,))

(9)M N HSD HSD m n D R H m n H m n ===∑∑ '2'1,|(,)(,)|((,),(,))(10)0,HSD H m n H m n T R H m n H m n else ?-≤?=???

其中,1T 和2T 是预先建立的阀值。

匹配步骤

这个匹配算法的匹配步骤如下:

Step1:用Bresenham 算法计算模板图像的ARPIH 。 Step2:从目标图像中的坐上角开始选择和模板图像大小一样的子图像,并

计算其ARPIH 。

Step3:匹配两个直方图并计算HSD D ,将其存入到数组中并记录其相关联的的位置。

Step4:在目标图像中滑动模板图像,搜寻和模板图像一样大小的子图像,计算ARPIH 。 Step5:重复第三步和第四步直到扫描完整个目标图像,匹配位置即为有最

大的

HSD D 的区域。 四、结果与讨论

用这个算法我们在很多变形图像,如旋转,透视,照度不均和换位,上做了实验来确认其健壮性和优越性。 我们选择一个半径为53的圆形模板,目标图像大小为256*256.图二展示了用本文阐述的算法对原始图像,旋转图像,透视图像,照度不均图像的匹配结果。其中,黑色的圆圈指出了匹配的区域,在?中的交集中的像素位置即为有最大的HSD D 的对应的点;也是匹配区域的圆心。图三展示了MLD 算法的匹配结果和前者的对比。

对比结果发现对于未变形的图像,文章中介绍的算法较MLD 算法没有很明显的优势,但对于变形的图像如透视,旋转和照度不均,结果明显要好很多。结果表明文章中介绍的HSD 算法在抗变形和稳定性上有更好的性能。

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