1.

Introduction

Top-hat transformation¹ has been widely used to enhance and detect the infrared small target.^{2, 3, 4, 5} But, the ability of target enhancement of top-hat transformation is weak. If the SNR of the image is low or the image has heavy clutter, then the top-hat transformation may decrease the SNR of the image, leading to losing target and increasing false alarm. One way of improving the enhancement ability of the top-hat transformation is using some preprocessing methods, such as energy cumulating² and structuring element selection.³ Although they can perform well in some cases, these methods do not really improve the enhancement ability of the top-hat transformation. Another way is constructing the structuring elements with the purpose of the target recognition applications.⁴ But, the improvement of the existing method is very limited. To apparently improve the enhancement ability of the top-hat transformation, a new class of top-hat transformation through structuring element construction and operation reorganization is proposed. Experiments verified that the new top-hat transformation performed better than the classical top-hat transformation^{1, 2, 3} and other widely used methods for infrared small target enhancement.^{5, 6, 7}

2.

Classical Top-Hat Transformation

The classical white and black top-hat transformations (WTH and BTH) are defined as follows.¹

3.

New Class of Top-Hat Transformation

3.1.

Definitions

The small target usually can be recognized as a small bright region embedded in the infrared clutter background.² Thus, the gray intensity of the surrounding regions will be much different from that of the target region.

But, in classical top-hat transformation, the use of the two same structuring elements cannot differentiate the target region and the surrounding region very well through the relationship of the structuring elements, and thus, cannot utilize the gray intensity difference between the target region and the surrounding region very well for the purpose of small target enhancement. Also, because of the use of the two same structuring elements, all the pixels in the target region and the surrounding region are used for the top-hat transformation calculation. Then, the noises in these regions will affect the performance of top-hat transformation for small target enhancement, leading to losing target or increasing false alarm.

Therefore, to greatly improve the performance of top-hat transformation, the two structuring elements can be reconstructed so that the top-hat transformation can greatly suppress the effect of the noises and utilize the gray intensity difference between the target region and the surrounding region well. In light of this, a new class of top-hat transformation [new WTH (NWTH) and new BTH (NBTH)] is defined as follows:

Eq. 5

$$\mathrm{NWTH}(x,y)=f(x,y)-f◼B_{oi}(x,y),$$

Eq. 6

$$\mathrm{NBTH}(x,y)=f◻B_{oi}(x,y)-f(x,y),$$

Eq. 7

$$f◼B_{oi}(x,y)=(f\oplus \Delta B)\Theta B_b,$$

Eq. 8

$$f◻B_{oi}(x,y)=\left(f\Theta \Delta B\right)\oplus B_b.$$

$B_{oi}$ represents two structuring elements $B_o$ and $B_i$ . The relationship of the structuring elements $B_o$ , $B_i$ , $B_b$ , and $\Delta B$ is demonstrated in Fig. 1 , in which $O$ is the origin of all the structuring elements. $S_{\Delta }$ , $S_i$ , $S_b$ , and $S_o$ are the size of the structuring elements $\Delta B$ , $B_i$ , $B_b$ , and $B_o$ , separately.

Fig. 1

Relationship of the structuring elements in NWTH and NBTH.

4.

Extension for Infrared Small Target Enhancement

5.

Experimental Results

To verify the performance of NWTH for infrared small target enhancement, some infrared images with size $720\times 576$ obtained from the forward-looking infrared (FLIR) system are used. One image that is cut from the original image with an appropriate size is demonstrated in Fig. 2 . The target is an aircraft and is labeled by a rectangle. In Fig. 2 the noises and clutter are heavy. In addition, the target is dim as illustrated in the 3-D plot of the gray intensity [Fig. 2]. But, NWTH can greatly enhance the small target as shown in Fig. 2. In Fig. 2, the noises and clutter are well suppressed and the target is much enhanced, leading to easy detection of the target.

Fig. 2

Infrared small target enhancement: (a) the original image; (b) 3-D plot of the gray intensity of the target region and the surrounding region in (a); and (c) 3-D plot of the gray intensity of the target region and the surrounding region after NWTH.

To prove the improved performance of NWTH for infrared small target enhancement, some widely used methods [U-kernel,⁷ E-kernel,⁷ Max-mean,⁶ Max-median,⁶ WTH (Refs. 1, 2, 3)] as well as NWTH are applied on the images. The measure local signal to background ratio⁵ (LSBR) is adopted here to compare their performances, and the result is shown in Table 1 ,

Table 1

Comparison of target enhancement (LSBR).

Another measure named probability of false alarms (PFA) per pixel versus the input LSBR (Ref. 5) is also adopted to describe the performances of the methods, and the result is shown in Fig. 3 . In Fig. 3, the number of false alarms caused by NWTH is much smaller than other methods at any LSBR, which also verifies that the performance of NWTH is efficient.

Fig. 3

PFA-LSBR curves.

6.

Conclusions

A new class of top-hat transformation through structuring element construction and operation reorganization is proposed to improve the performance of top-hat transformation for infrared small targe enhancement. The experiments verify that the new class of top-hat transformation can be well used for infrared small target enhancement and performs better than other widely used methods. Moreover, the appropriate selection of $B_i$ , $B_b$ , and $B_o$ will result in good performance of NWTH and NBTH for different application purposes.