Elsevier

Optik

Volume 124, Issue 13, July 2013, Pages 1614-1619
Optik

A unified form of multi-scale top-hat transform based algorithms for image processing

https://doi.org/10.1016/j.ijleo.2012.06.016Get rights and content

Abstract

Top-hat transform is one important operation of mathematical morphology and widely used in different applications. However, the image processing ability of top-hat transform is not very efficient. Multi-scale operation has been one efficient way to improve the performance of top-hat transform. The key of multi-scale top-hat transform is appropriately organizing and using multi-scale top-hat transform to extract the multi-scale image features. If a unified form of multi-scale top-hat transform could be proposed, the application of multi-scale top-hat transform would be focused on the decision of some functions of the unified form. This would simplify the algorithm design. In this paper, a unified form of multi-scale top-hat transform based algorithms is given through reviewing and analyzing the existed multi-scale top-hat transform based algorithms. To verify the unified form, some applications of multi-scale top-hat transform based algorithms are integrated into the unified form by specifying the key functions of the unified form. These examples not only verify the unified form, but also provide the way of how to determine the key functions of the unified form for different applications. The given unified form is important for the further research and application of multi-scale top-hat transform.

Introduction

Top-hat transform [1] is one important operation of mathematical morphology. It has been widely used in different applications, such as target detection, objection recognition, biomedical engineering and so on [1]. But, because of image detail smoothing and using only one structuring element, the image processing ability of top-hat transform is inefficient. Many algorithms have been proposed to improve the performance of top-hat transform [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13]. Among them, the multi-scale based methods [10], [11], [12], [13] are one active research area. Top-hat transform based multi-scale operation [10], [11], [12], [13] is one kind of important multi-scale morphological operations [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21]. Top-hat transform extracts protruding regions of image at the scale specified by the used structuring element [2], [3], [4], [5], [6], [7], [8], [9], and multi-scale top-hat transform could extract protruding regions of image at different scales [10], [11], [12], [13]. So, multi-scale top-hat transform would be more efficient for different applications of image processing [10], [11], [12], [13].

Because multi-scale top-hat transform extracts protruding regions at different scales, the image features at different scales could be expressed and used through multi-scale top-hat transform for impulsive noise removal [10], image fusion [11], [12], image enhancement [13] and so on. Impulsive noises are protruding pixels comparing with the real content of image. So, top-hat transform could be used to extract impulsive noises and restore the original image without impulsive noises. Usually, impulsive noises may exist at different scales of image. Then, appropriately organizing and using multi-scale top-hat transform would be very efficient for the application of impulsive noise removal [10]. In multi-focus images, focused regions and un-focused regions in one image have different features. Through appropriately organizing and using multi-scale top-hat transform to extract the different features could identify the focused regions of image. Then, all the focused regions in multi-focus images could be combined to form a fused multi-focus image in which all the regions of image are focused [11]. Also, the useful features of the same region in multi-modal images could be extracted through appropriately organizing and using multi-scale top-hat transform, and then combined to form a fused image in which the useful features of all the regions of fused image are clear [12]. Bright and black features of image at different scales could be extracted by multi-scale top-hat transform. These bright and black features could be organized and used to enhance the contrast between them, and thus enhance the contrast of image [13]. Based on the analysis above, the key of multi-scale top-hat transform is appropriately organizing and using multi-scale top-hat transform to extract the multi-scale image features.

In all, most of the multi-scale top-hat transform based algorithms need to calculate the multi-scale operations of top-hat transform and appropriately use them for different applications [10], [11], [12], [13]. Then, if a unified form of multi-scale top-hat transform based algorithms could be proposed, the application of multi-scale top-hat transform would be focused on the decision of some functions of the unified form. This would simplify the algorithm design. Moreover, the unified form may provide a general hardware implementation for most of multi-scale top-hat transform based algorithms. Therefore, it is important to give a unified form of multi-scale top-hat transform based algorithms.

In this paper, a unified form of multi-scale top-hat transform based algorithms is given through reviewing and analyzing the existed multi-scale top-hat transform based algorithms. To verify the unified form, some applications of multi-scale top-hat transform based algorithms are integrated into the unified form by specifying the key functions of the unified form. These examples not only verify the unified form, but also provide the way of determining the key functions of the unified form for different applications. Section 2 shows the definition of multi-scale top-hat transform. Section 3 reviews some multi-scale top-hat transform based algorithms. Section 4 gives the unified form and discusses the properties. Section 5 illustrates examples of integrating multi-scale top-hat transform based algorithms into the unified form. Section 6 concludes the paper.

Section snippets

Multi-scale top-hat transform

Mathematical morphology has been an important image analysis tool after being proposed. Basic morphological operations work with two sets: the original image (f) and structuring element (B), which are defined as follows:fB=(fB)B,fB=(fB)B,fB=maxu,v(f(xu,yv)),fB=minu,v(f(x+u,y+v)),○, ●, ⊕ and ⊖ are opening, closing, dilation and erosion operations, respectively. (x,y) and (u,v) are the pixel coordinates of f and B, respectively.

Top-hat transform includes white top-hat transform (WTH)

Local contrast enhancement

Local contrast enhancement is an important technique for low contrast image enhancement. The crucial point of local contrast enhancement is finding useful bright and black features and enlarging the contrast between them. Ref. [13] proposed a multi-scale top-hat transform based algorithm for local contrast enhancement.

The useful bright features at the ith scale are extracted as:FiO(x,y)=f(i1)BfiB.

The useful bright features at all of n scales are:SO=i=1nFiO.

The useful black features at the i

Unified form of multi-scale top-hat transform

Based on the reviewing of some multi-scale top-hat transform based algorithms, all the algorithms could be divided into three parts. Firstly, the multi-scale top-hat transform is calculated. Secondly, the useful features of each scale are extracted following different applications. Finally, the final image is reconstructed. So, all the algorithms could be integrated into a unified form as Fig. 1 shown.

According to Fig. 1, the design of all the multi-scale top-hat transform based algorithms

Local contrast enhancement

One efficient way of local contrast enhancement is finding bright regions and black regions, and then enlarging the contrast between them. According to the unified form, the bright and black regions at each scale are calculated through the multi-scale top-hat transform in part 1. Then, the bright regions at all the scales could be combined as:Fs=i=1n(ni+1) WTHi,where WTHi = f○(i  1)B  fiB.

The black regions at all the scales could be combined as:Gs=i=1n(ni+1) BTHi,where BTHi = fiB  f●(i  1)B.

Then,

Conclusions

Top-hat transform has been widely used for different applications. And, multi-scale operation is one efficient way to improve the performance of top-hat transform. The key of multi-scale top-hat transform is appropriately organizing and using multi-scale features extracted by top-hat transform. If a unified form of multi-scale top-hat transform based algorithms could be proposed, the application of multi-scale top-hat transform would be focused on the setting of some functions of the unified

Acknowledgements

We are grateful to Dr. Yan Li at Peking University, Beijing, China, for many helpful discussions and comments. Part of this paper has been presented at an international conference [20]. This work is partly supported by the National Natural Science Foundation of China (Grant No. 60902056), open funding project of State Key Laboratory of Virtual Reality Technology and Systems, Beihang University (Grant No. BUAA-VR-12KF-04), Civil Aviation United Foundation of National Natural Science Foundation

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