发布时间: 2018-11-16 摘要点击次数: 全文下载次数: DOI: 10.11834/jig.180258 2018 | Volume 23 | Number 11 NCIG 2018会议专栏

Facet方向导数特征与稀疏表示相结合的红外弱小目标检测算法

 收稿日期: 2018-04-17; 修回日期: 2018-06-05 基金项目: 国家自然科学基金项目（U1736217） 第一作者简介: 荣楚君, 1994年生, 男, 硕士研究生, 主要研究方向为红外小目标检测与跟踪。E-mail:459187614@qq.com;曹晓光, 男, 副教授, 主要研究方向为图像模式识别应用。E-mail:xgcao@buaa.edu.cn. 中图法分类号: TP391 文献标识码: A 文章编号: 1006-8961(2018)11-1768-09

# 关键词

Infrared small target detection algorithm based on derivative characteristics of Facet combined with sparse representation
Rong Chujun, Cao Xiaoguang, Bai Xiangzhi
School of Astronautics, Beihang University, Beijing 100191, China
Supported by: National Natural Science Foundation of China(U1736217)

# Abstract

Objective Infrared dim and small target detection is a research interest in the field of infrared image processing, which is difficult but practical. It plays a crucial role in reconnaissance and warning, aircraft tracking, and missile guidance systems. The process of detecting infrared small targets in natural scenes is characterized by the fact that the target area can frequently be expressed as a small, uniform, compact area with a significant discontinuity or contrast compared with the surrounding background. The detection of a small target in an infrared image is affected by many factors, such as the small number of target pixels, low contrast between a target and a background, dim edges of the targets, complex image background, and lack of texture information of the small targets, thereby resulting in the difficulty of infrared small target detections. The existing methods have achieved effective results in detecting small targets in infrared images; however, drawbacks, such as low adaptability to complex background, low detection rate, and high false alarm rate, still remain. In addition, methods related to sparse representation have the following shortcomings:the construction of a dictionary directly from the original images ignores the feature extraction of the target, or does not establish the target and the background dictionaries simultaneously, thus resulting in a weak representation capability of the entire dictionary. Thus, an infrared small target detection algorithm that combines facet directional derivative features with sparse representation is proposed. Method A dictionary must initially be constructed. A background dictionary is constructed by intercepting 1 000 small blocks and then obtaining their derivatives in a certain direction. K-SVD algorithm is used to train the blocks after merging them into column vectors. A background dictionary with 500 atoms is achieved. The construction method of the target dictionary is as follows:325 small blocks containing small targets are generated in accordance with the characteristics of the small target. The first-order derivative in one direction is calculated for these small blocks containing small targets, and then the columns are converted into column vectors. The target dictionary containing 325 atoms is obtained in that direction after normalizing. We combine the target and the background dictionaries into one large dictionary with 825 atoms, which will be used in the subsequent sparse solution section. The facet model is utilized to extract the first-order derivative features of the original infrared image in four directions, that is 0°, 90°, 45°, and -45°. Then, the blocks separated from the image are processed from top to bottom and left to right on the basis of the directional derivative information through the sparse representation method. The detection result map is constructed using the sparse coefficients and reconstruction residuals of the derivative image blocks. Finally, a threshold is calculated from the detection result map to separate the target from the background. Result The classical max-mean and max-median algorithms are selected as the algorithms for comparison. Comparative results show that the max-mean and max-median algorithms are sensitive to the edges in the infrared image. The traditional algorithms perform ineffectively in removing these clusters when the infrared image has clusters due to distance, atmospheric refraction, lens aberration, and optical defocus. A 3D image of the detection result shows that our method has better performance, is insensitive to noise, and can achieve an excellent target detection effect. Therefore, our algorithm has certain advantages over the traditional algorithms. Receiver operating characteristic (ROC) curves of detection and false alarm rates are plotted through experimental verification of four infrared image sequences. The results evidently show that the proposed algorithm has a higher detection rate and lower false alarm rate in a small target detection than other algorithms. Conclusion Our algorithm extracts image directional derivative information through the facet model, combines the directional derivative features of infrared imagery with sparse representation theory, analyzes the characteristics of the small target in a single direction in detail, and extends it to feature information presented in multiple directions. The difference between the target and the background is discussed. The final test results of the small target are obtained using sparse representation theory as a medium. Experiments show that the proposed algorithm has a high detection accuracy and strong anti-noise capability. The proposed algorithm has certain advantages, improves detection rate, and reduces false alarm rate over the traditional detection algorithms. Another important advantage of our algorithm is that it can generate different background dictionaries in accordance with a certain background under different conditions to obtain improved detection results and perform an effective pertinence in practical applications.

# Key words

infrared image; object detection; small target; directional derivative; sparse representation

# 1 Facet模型

Haralick提出[9]:一个图像中任意一个像素点某一个邻域所有像素点灰度值所形成的灰度强度表面，都可以被一个空间的二元三次多项式拟合，现在假定这个映射函数为$f$，可以通过计算两组1维离散多项式的张量积，来构建2维离散正交多项式基组。又由于现在要得到一个三次函数，就可以忽略高于三阶的多项式。根据Haralick模型，针对一个像素所在5×5邻域进行具体地阐述，现定义一组离散1维数组$\mathit{\boldsymbol{R}}$={-2 -1 0 1 2}，和另一个离散1维数组$\mathit{\boldsymbol{L}}$={-2 -1 0 1 2}，这两组1维离散数组的张量积$\mathit{\boldsymbol{R}} \times \mathit{\boldsymbol{C}}$

 $\mathit{\boldsymbol{R}} \times \mathit{\boldsymbol{C}} = \left\{ \begin{array}{l} 1,r,c,{r^2} - 2,rc,{c^2} - 2,\\ {r^3} - 17/5r,\left( {{r^2} - 2} \right)c,\\ r\left( {{c^2} - 2} \right),{c^3} - 17/5c \end{array} \right\}$ (1)

$\mathit{\boldsymbol{S}}$为图像的某一像素点$(x, y)$的5×5邻域，对于这个5×5邻域中有${\rm{(}}\mathit{r}{\rm{, }}\mathit{c}{\rm{)}} \in \mathit{\boldsymbol{S}}$, 其中$(r, c)$为一个像素点坐标，$r$$c取值都是{-2, -1, 0, 1, 2}，像素点 (x, y)在这个5×5邻域中对应坐标为中心点(0, 0)，以此类推。那么，之前所述用于拟合一个图像中任意一个像素点5×5邻域二元三次多项式 f(r, c)就可以表示为  \begin{array}{*{20}{c}} {f\left( {r,c} \right) = {K_1} + {K_2}r + {K_3}c + {K_4}\left( {{r^2} - 2} \right) + }\\ {{K_5}rc + {K_6}\left( {{c^2} - 2} \right) + {K_7}\left( {{r^3} - 17/5r} \right) + }\\ {{K_8}\left( {{r^2} - 2} \right)c + {K_9}r\left( {{c^2} - 2} \right) + }\\ {{K_{10}}\left( {{c^3} - 17/5c} \right)} \end{array} (2) 式中， {\mathit{K}_\mathit{i}}\left( {i = 1, \cdots , 10} \right)是该二元三次多项式的拟合系数，它是由最小二乘法表面拟合而成。这种方法在对图像灰度强度表面进行拟合的同时，能够将一些椒盐噪声去除，因此，这种方法不仅能计算导数，还具有一定程度的滤波效果。 在本文方法中需要求解图像中任意一个像素点0°、90°、45°和-45°方向的一阶导数，如图 1所示。  {{f'}_0}\left| {_{\left( {0,0} \right)}} \right. = {K_3} - 2{K_8} - 3.4{K_{10}} (3)  {{f'}_{90}}\left| {_{\left( {0,0} \right)}} \right. = {K_2} - 2{K_9} - 3.4{K_7} (4)  \begin{array}{*{20}{c}} {{{f'}_{45}}\left| {_{\left( {0,0} \right)}} \right. = {{f'}_0}\left| {_{\left( {0,0} \right)}} \right. \times \cos \left( {{{45}^ \circ }} \right) + }\\ {{{f'}_{90}}\left| {_{\left( {0,0} \right)}} \right. \times \sin \left( {{{45}^ \circ }} \right)} \end{array} (5)  \begin{array}{*{20}{c}} {{{f'}_{ - 45}}\left| {_{\left( {0,0} \right)}} \right. = {{f'}_0}\left| {_{\left( {0,0} \right)}} \right. \times \cos \left( { - {{45}^ \circ }} \right) + }\\ {{{f'}_{90}}\left| {_{\left( {0,0} \right)}} \right. \times \sin \left( { - {{45}^ \circ }} \right)} \end{array} (6) 利用式(3)—(6)求出原图像的4个方向上的方向导数特征。 # 2 目标检测算法 # 2.1 单一方向目标检测 在自然场景中，目标区域通常可以表述为一个小尺寸、均匀、紧凑的区域，没有明显形状尺寸和纹理信息，与周围背景相比，具有显著不连续性或者强烈对比性。在通常情况下，一幅灰度图中小目标可以看做一个2维高斯函数模型[10]  I\left( {x,y} \right) = A\exp \left\{ { - \frac{1}{2}\left[ {{{\left( {\frac{x}{{{\sigma _1}}}} \right)}^2} + {{\left( {\frac{y}{{{\sigma _2}}}} \right)}^2}} \right]} \right\} (7) 式中， I(x, y)表示 (x, y)坐标处灰度值， A表示函数幅值， {\sigma _1}$$ {\sigma _2}$表示对应标准差。理想情况下，目标在某一个方向上呈现图 2(a)中曲线分布，其一阶导数呈现如图 2(b)中曲线分布，而背景区域在理想情况下某一个方向上一阶导数曲线近似于曲线$y$=0型分布，利用目标和背景在一阶导数上呈现出分布差异这一特点，就可以对它们加以区分。

 $\begin{array}{*{20}{c}} {\min {{\left\| {{\mathit{\boldsymbol{X}}_t}} \right\|}_0} + {{\left\| {{\mathit{\boldsymbol{X}}_b}} \right\|}_0}}\\ {{\rm{s}}.\;{\rm{t}}.\;\;{\mathit{\boldsymbol{D}}_{\rm{t}}}{\mathit{\boldsymbol{X}}_{\rm{t}}} + {\mathit{\boldsymbol{D}}_{\rm{b}}}{\mathit{\boldsymbol{X}}_{\rm{b}}} = \mathit{\boldsymbol{Y}}} \end{array}$ (8)

 $\mathit{\boldsymbol{P}} = \frac{1}{n}\sum\limits_{i = 1}^n {{\gamma _i} \cdot {\mathit{\boldsymbol{G}}_i}}$ (15)

# 2.2.4 目标检测

 $T = \bar I + q \cdot {\sigma _r}$ (16)

# 3.1 ROC曲线

ROC(receiver operating characteristic)曲线是衡量目标检测结果的一个常用指标，能够反映检测率$DR$和虚警率$FA$之间的动态关系[17]。记总目标数为$T_{\rm NT}$，检测到目标数为$T_{\rm NC}$，误检像素数为$P_{\rm NF}$，图像总像素数为$P_{\rm NA}$，分别计算检测率和虚警率

 $DR = \frac{{{T_{{\rm{NC}}}}}}{{{T_{{\rm{NT}}}}}};FA = \frac{{{P_{{\rm{NF}}}}}}{{{P_{{\rm{NA}}}}}}$ (17)

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