Elsevier

Pattern Recognition

Volume 43, Issue 6, June 2010, Pages 2145-2156
Pattern Recognition

Analysis of new top-hat transformation and the application for infrared dim small target detection

https://doi.org/10.1016/j.patcog.2009.12.023Get rights and content

Abstract

To improve the performance of top-hat transformation for infrared dim small target detection in a simple and effective way, the definition, properties, multi-scale operations of new top-hat transformation and the application for infrared dim small target detection are addressed in this paper. The definition of new top-hat transformation uses two different but correlated structuring elements to reorganize the classical top-hat transformation, and takes into account of the difference information between the target and surrounding regions. Given this definition, the new top-hat transformation has some special properties and three types of multi-scale operations, which are discussed in detail. Subsequently, one application case of multi-scale operation for noise suppression is given. Good performance of the application for infrared dim small target detection is obtained, which could be ascribed to the proper selection of structuring elements based on the properties. The experimental results of the application demonstrate that new top-hat transformation can detect infrared dim small target more efficiently than classical top-hat transformation and some other widely used methods.

Introduction

Mathematical morphology was firstly proposed and extended for image analysis by Matheron and Serra [1]. Mathematical morphology is based on geometry and set theory. It has been well used and developed in different applications [2], [3], [4], [5], [6], [7], [8], [9]. Small target detection is one of the important applications of mathematical morphology, and the top-hat transformation is an important operation in this application [7], [8], [9], [10].

Although the top-hat transformation has been used for small target detection, the ability of target detection is weak. When the signal to noise ratio (SNR) of image is high, top-hat transformation can be directly used for small target detection [7]. But, when SNR is low, the target is dim, and the noises and clutter are heavy, which heavily affect the performance of top-hat transformation. In this situation, top-hat transformation cannot detect small target well, and may even decrease the SNR of original image and cause target losing. To enhance the adaptability of top-hat transformation to noises, heavy clutter and dim target intensity, and thus to improve the performance of top-hat transformation for small target detection, many improved algorithms are proposed [8], [9], [10]. Increasing SNR of image through energy cumulating before target detection can suppress the effect of noises and heavy clutter [8], but this algorithm does not solve the problem of top-hat transformation. Structuring element is one of the crucial parts of top-hat transformation, and is also the crucial part of the performance improvement of top-hat transformation. To find an appropriate structuring element for target detection, algorithms based on neural network and genetic algorithm are proposed [9]. Although these algorithms perform well in some cases, they do not directly improve the top-hat transformation. Constructing new top-hat transformation through changing the structuring elements to suppress the effect of noises is a direct way to improve the performance of top-hat transformation [10]. However, it has not been used for infrared small target detection as far as we know. A new top-hat transformation has been defined and well used in our previous work [11]. In this paper, the definition, properties, multi-scale operations of new top-hat transformation and its application for infrared dim small target detection are discussed in detail. Comparing with the new top-hat transformation, the original top-hat transformation is called classical top-hat transformation. Firstly, some shortcomings of classical top-hat transformation are given. Then, the definition of new top-hat transformation is given through importing two different but correlated structuring elements into top-hat transformation and reorganizing classical top-hat transformation. This definition is based on suppressing the shortcomings of classical top-hat transformation. The properties and three types of multi-scale operations of new top-hat transformation are analyzed, which shows the superiority of new top-hat transformation. To ensure that the new top-hat transformation can be used well in the application of infrared small target detection, the selection of structuring elements is studied following the properties. Various experiments of the application of infrared dim small target detection verified that new top-hat transformation was better than classical top-hat transformation and other widely used methods.

This paper is organized as follows. Section 2 presents the definitions of classical top-hat transformation. Section 3 gives the shortcomings of classical top-hat transformation and defines new top-hat transformation. Section 4 studies the properties of new top-hat transformation. Section 5 discusses the multi-scale operations of new top-hat transformation. Section 6 demonstrates the application of new top-hat transformation for infrared small target detection. And, Section 7 is a conclusion.

Section snippets

Classical top-hat transformation

All the mathematical morphology operations are based on two basic operations: dilation and erosion. They work with two sets. One set is the original image to be analyzed and the other set is structuring element. Let f and B represent the gray-scale image and structuring element, respectively. The dilation and erosion of f(x, y) by B(u, v), denoted by fB and fB, are defined by (fB)(x,y)=maxu,v(f(xu,yv)+B(u,v)),(fB)(x,y)=minu,v(f(x+u,y+v)B(u,v)),where the domain of fB and fB are the

Shortcomings of classical top-hat transformation

Structuring element is the crucial part of mathematical morphology operations. Small target is usually different from the surrounding background regions. So, there are difference information between the small target and the surrounding regions. The difference information is the reason of top-hat transformation being used for small target detection. So, top-hat transformation can detect target by using this difference information. But, classical top-hat transformation uses two same structuring

Properties

The definitions indicate that new top-hat transformations are different from classical top-hat transformations, and new top-hat transformations form new operations through the two different but correlated structuring elements. Then, new top-hat transformations possess some new properties.

(1) If MB)≠0, new top-hat transformations do not satisfy: ffBoi and ffBoi.

Classical opening operation fB in WTH smoothes bright region of image, then it satisfies: ffB. Similarly, there is ffB. But,

Definitions

Multi-scale operation of mathematical morphology could apparently increase the adaptability of mathematical morphological operations for image processing. So, the theory of multi-scale mathematical morphology is widely researched [12], [13]. New top-hat transformations are derived from mathematical morphology. Then, the theory of multi-scale operation of new top-hat transformation can also be derived from the basic theory of multi-scale mathematical operation [12], [13].

Two different

Application for infrared dim small target detection

One of the most important applications of top-hat transformation is infrared dim small target detection. This paper will demonstrate how to use new top-hat transformation to detect infrared dim small target under the conditions of heavy clutter background and noises. MNWTH and MNBTH not only possess the superiority of new top-hat transformations, but also avoid the negative values in the result image. So, this paper will mainly use MNWTH to detect infrared small targets.

New top-hat

Conclusions

Classical top-hat transformation has been widely used in image processing. However, the noises and heavy clutter heavily affect the performance of classical top-hat transformation. Especially, when the classical top-hat transformation is used for infrared dim small target detection, the heavy clutter, noises and dim intensity of target usually make it an ineffective way. The reason is classical top-hat transformation does not well utilize the difference information between the target and

Acknowledgments

The authors would like to thank the anonymous reviewers for their very constructive comments and suggestions. This work is partly supported by the National Natural Science Foundation of China (60902056), Aeronautical Science Foundation of China (20090151007), and Innovation Foundation of Beijing University of Aeronautics and Astronautics for Ph.D. Students. The authors also would like to thank Dr. Yan Li at the School of Geology and Space Science in Peking University, Beijing, China for many

About the Author—XIANGZHI BAI received his B.S. degree from Beijing University of Aeronautics and Astronautics (BUAA) in 2003 and his Ph.D. from BUAA in 2009. He is currently a lecture of image processing center of BUAA. From 2007 to 2008, he was with the CSIRO Mathematical and Information Sciences, Sydney, Australia. His research interests include computer vision, image analysis, pattern recognition, and bioinformatics.

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About the Author—XIANGZHI BAI received his B.S. degree from Beijing University of Aeronautics and Astronautics (BUAA) in 2003 and his Ph.D. from BUAA in 2009. He is currently a lecture of image processing center of BUAA. From 2007 to 2008, he was with the CSIRO Mathematical and Information Sciences, Sydney, Australia. His research interests include computer vision, image analysis, pattern recognition, and bioinformatics.

About the Author—FUGEN ZHOU received his B.S. degree from Beijing University of Aeronautics and Astronautics (BUAA) in 1986 and his Ph.D. from BUAA in 2006. He is the director of image processing center of BUAA. His research interests include object recognition, image compressing and restoration.

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