﻿ 一种基于模板匹配的线性特征混合像元的亚像元定位的新方法 New Template Matching Method for Subpixel Mapping of Linear Feature Mixed Pixels

Journal of Image and Signal Processing
Vol. 08  No. 03 ( 2019 ), Article ID: 31517 , 14 pages
10.12677/JISP.2019.83024

New Template Matching Method for Subpixel Mapping of Linear Feature Mixed Pixels

Haiqiang Lu1, Zhaoxin Liu2*, Wei Zhu1

1Hengchuang Power Equipment Co., Ltd., Jiaxing Zhejiang

2College of Computer Science, Hangzhou Dianzi University, Hangzhou Zhejiang

Received: Jul. 4th, 2019; accepted: Jul. 22nd, 2019; published: Jul. 29th, 2019

ABSTRACT

By analyzing the problems of subpixel mapping algorithm based on template matching, a linear feature sub-pixel mapping algorithm based on improved template matching is proposed. Based on the correlation coefficient selection template, two new template selection methods are proposed: 1) Further determining the template by fitting a line with linear feature mixed pixels eight neighborhood, to some extent, reduces the scope of template selection; 2) In order to avoid the uncertainty of template selection, the best template is obtained through line fitting on the mixed pixels eight neighborhoods and the template and calculating the linear correlation. Furthermore, combined with pixel gravity, the sub-pixel mapping problem of linear feature pixel containing three or more ground objects is solved. The experiment results show that the proposed method can improve the sub-pixel mapping accuracy.

Keywords:Mixed Pixel, Subpixel Mapping, Template Matching, Correlation Coefficient, Line Fitting

1嘉兴市恒创电力设备有限公司，浙江 嘉兴

2杭州电子科技大学计算机学院，浙江 杭州

1. 引言

2. 含线特征混合像元亚像元定位的模板匹配法

2.1. 含线特征混合像元

Figure 1. Four different types of mixed pixels. (a) Sub-pixel target; (b) Dense mixed pixels; (c) Boundary mixed pixel; (d) Linear target

2.2. 亚像元定位的模板匹配法

1) 对每个混合像元，确定像元尺度下最佳匹配的线状模板。

Figure 2. 3 × 3 template

${T}_{k}=\left[\begin{array}{ccc}t\left(-1,-1\right)& t\left(-1,0\right)& t\left(-1,1\right)\\ t\left(0,-1\right)& t\left(0,0\right)& t\left(0,1\right)\\ t\left(1,-1\right)& t\left(1,0\right)& t\left(1,1\right)\end{array}\right]$ (1)

${r}_{i,j,k}=\frac{{\sum }_{m=-w}^{w}{\sum }_{n=-w}^{w}\text{ }{T}_{k}\left(m,n\right)\cdot {S}_{c}\left(i+m,j+n\right)}{\sqrt{{\sum }_{m=-w}^{w}{\sum }_{n=-w}^{w}\text{ }\text{ }{S}_{c}{\left(i+m,j+n\right)}^{2}\cdot {\sum }_{m=-w}^{w}{\sum }_{n=-w}^{w}\text{ }{T}_{k}{\left(m,n\right)}^{2}}}$ (2)

2) 利用最优模板 ${T}_{k}$ 对混合像元Pij中第c类地物进行定位。

3) 像元内其他亚像元类别确定

2.3. 存在的问题

1) 直接根据相关系数ri,j,k进行模板选择时最大ri,j,k对应的模板可能不唯一，如何从多个匹配的模板中选出唯一的最优模板仍是个问题；

2) 当混合像元内包含三种及以上地物时，用随机方法确定像元内其他亚像元类别不够准确。

3. 两种最佳匹配模板确定的新方法

3.1. 基于拟合直线的最佳匹配模板确定

Figure 3. Schematic diagram of line fitting. (a) Eight neighborhood abundance map of mixed pixels of class c; (b) Linear fitting after binarization

Figure 4. 4 results of line fitting

$d\left({P}_{mn},{L}_{a}\right)=|\frac{A{x}_{mn}+B{y}_{mn}+C}{\sqrt{{A}^{2}+{B}^{2}}}|$ (3)

NT值最大的模板为最优模板。图4给出了图2中部分模板的直线拟合结果，其中各模板中直线所经过的灰色区域个数NT分别为1，3，2，1，图4(b)所示模板为最优模板。

3.2. 标准相关匹配结合直线拟合相关性选择最佳模板

SC-PLF方法虽然进一步缩小了模板选择的范围，但是对于模板唯一性仍无法保证。为此本节提出了标准相关匹配结合直线拟合相关性(Line Fitting Correlation after Standard Correlation, SC-LFC)的方法，在基于标准相关性的模板匹配选择方法选择出的若干模板基础上，分别对所选的模板和含线特征混合像元邻域进行直线拟合，并计算各模板和像元拟合直线间的相关性，可以保证模板选择的唯一性，算法主要思想是：

1) 对混合像元Pi,j及其邻域像元根据地物 的丰度进行二值化，拟合直线 ${L}_{a}=k1\cdot x+b1$

2) 对经过SC算法选择出的各模板，根据 $t\left(m,n\right)=1$ 的位置拟合直线 ${L}_{i}=k2\cdot x+b2,i=1,2,\cdots ,k$

3) 利用式(4)计算La和直线 ${L}_{1},{L}_{2},\cdots ,{L}_{k}$ 的相关性：

$L{C}_{i}=w1\left(k1-ki\right)+w2\left(b1-bi\right),\text{\hspace{0.17em}}\text{\hspace{0.17em}}i=1,2,\cdots ,k$ (4)

Figure 5. Result of line fitting

4. 改进的含线特征混合像元亚像元定位流程

$N\left({P}_{ab}\right)=\left\{{P}_{ij}|\left(\frac{a}{s}\ne i\vee \frac{b}{s}\ne j\right)\wedge \left(|\frac{a}{s}-i|\le 1\wedge |\frac{b}{s}-j|\le 1\right)\right\}$ (5)

${P}_{ab}\left(c\right)=\text{avg}\left\{\frac{{S}_{c}\left(x,y\right)}{d\left({P}_{ij},{P}_{ab}\right)}|{P}_{ij}\in N\left({P}_{ab}\right)\right\}$ (6)

$d\left({P}_{ab},{P}_{ij}\right)=\sqrt{{\left[a+0.5-s×\left(i+0.5\right)\right]}^{2}+{\left[b+0.5-s×\left(j+0.5\right)\right]}^{2}}$ (7)

Figure 6. Schematic diagram of the subpixels mapping process of linear feature mixed pixels

5. 实验与分析

Table 1. Description of the subpixel mapping algorithm of linear feature mixed pixels

5.1. 实验数据

5.1.1. 仿真数据

Figure 7. Synthetic dataset. (a) 7 kinds of ground spectrum; (b) Ground truth; (c) 90 × 60 synthetic map; (d) 54 × 36 synthetic map

5.1.2. 真实数据

Figure 8. Real hyperspectral dataset. (a) Grayscale map of the 37th band; (b) Ground truth

5.2. 混合像元内线状地物亚像元定位实验

Figure 9. Experimental data. (a) Schematic diagram of subgraph capture; (b) Scaled subgraph; (c) Line feature detection result of graph (a); (d) Detection result of graph (b)

Figure 10. Result of line feature mixed pixels mapping

Figure 11. Result of line detection (a) and result of line future mixed pixels mapping (b) - (e)

Table 2. Comparison of mixed pixels mapping results of each line feature algorithm (without optimization)

Figure 12. Result of subpixel mapping of Figure 9(b)

Table 3. Subpixel mapping result of each algorithm

5.3. 亚像元定位实验

5.3.1. 仿真数据实验

Figure 13. Subpixel mapping result of reconstruction scale of 3

Figure 14. Subpixel mapping result with reconstruction scale of 5

Table 4. Experiment result with reconstruction scale of 3

Table 5. Experiment result with reconstruction scale of 5

5.3.2. 真实数据实验

Figure 15. Result of subpixel mapping

Table 6. Experiment result with reconstruction scale of 3

6. 结论

New Template Matching Method for Subpixel Mapping of Linear Feature Mixed Pixels[J]. 图像与信号处理, 2019, 08(03): 180-193. https://doi.org/10.12677/JISP.2019.83024

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24. NOTES

*通讯作者。