Segmenting of the Sonar Image from an Undersea Goal Using Two Dimensional THC Entropy

Abstract

Sonar image segmentation is the basis of undersea goal detection and recognition. The THC (Tsallis-Havrda-Charvát) entropy can describe the statistical properties of the non-extensive systems and has a wider range of applications. There are multiple choices for the two features of the two-dimensional histograms, such as the gray value, the average gray value within a neighborhood, the median gray value within a neighborhood, the mode of gray values within a neighborhood, and so on. This paper investigates the segmentation results of a sonar image from an undersea goal using THC entropies of a variety of two-dimensional histograms, and gives the evaluation indexes for the segmentation results.

1 Introduction

A sonar is common equipment for undersea measurement, and in some cases it is irreplaceable. Undersea goal finding, undersea rescue, undersea manufacture, undersea robot movement, seabed treasure finding, ocean exploitation, and sea warfares often contain the goal recognition with the help of the sonar images of undersea goals [1]. In order to recognize the sonar images, segmenting the image first is usually essential. The sonar image of an undersea goal usually contains three areas: the goal light area, the goal dark one, and the seabed reverberation one. The sonar image segmentation is to obtain the above goal light area and goal dark one.

The thresholding is a well-known image segmentation method, and widely used because of its simple and fast calculation [2, 3]. There are some thresholding methods based on entropies [4]. There is a the entropy based method which uses the THC (Tsallis-Havrda-Charvát) entropy [3, 5]. The THC entropy can describe the statistical properties of the non-extensive systems and has a wider range of applications [3, 6]. The THC entropy based method in the reference [3] uses the gray value and the average gray value within a neighborhood as the features of the pixel to form the two-dimensional histogram for image segmentation. Not only the gray value and the average gray value within a neighborhood are used to form the two-dimensional histogram in this paper, but other features are also used. That is, this paper investigates the segmentation results using a variety of two-dimensional histograms.

2 Dual-Threshold Method Using the Two-Dimensional THC Entropy

There are multiple choices for the two features of the two-dimensional histograms, such as gray value, the average gray value within a neighborhood, the median gray value within a neighborhood, the mode of gray values within a neighborhood, and so on. Let f₁(m, n) and f₂(m, n) represent the two features of the pixel in an image, and the two-dimensional histogram is prescribed as

$$ p(i,j) = \frac{n(i,j)}{{M \times N}} $$

(1)

where n(i, j) denotes the pixel number when f₁(m, n) = i and f₂(m, n) = j, M × N represents the size of the sonar image. Suppose i = 0, 1, ···, i_max where i_max is the maximum value of f₁(m, n) while (m, n) traveling across the whole image and j = 0, 1, ···, j_max where j_max is the minimum value of f₂(m, n) while (m, n) traveling across the whole image. Suppose that a sonar image of an undersea goal is divided into three areas using (t₁, s₁) and (t₂, s₂): the goal light area, the goal dark one, and the seabed reverberation one. Here t₁ and t₂ denote the thresholds of the feature f₁(m, n) in the image, and s₁ and s₂ are the thresholds of the feature f₂(m, n) in the image.

THC entropy with the order α related to the goal dark area is prescribed by

$$ H_d^\alpha (t_1 ,s_1 ) = \frac{1}{\alpha - 1}[1 - \sum_{i = 0}^{t_1 } {\sum_{j = 0}^{s_1 } ( \frac{p(i,j)}{{p_d (t_1 ,s_1 )}}} )^\alpha ] $$

(2)

where

$$ P_d (t_1 ,s_1 ) = \sum_{i = 0}^{t_1 } {\sum_{j = 0}^{s_1 } {p(i,j)} } $$

(3)

THC entropy with the order α related to the goal light area is prescribed by

$$ H_l^\alpha (t_2 ,s_2 ) = \frac{1}{\alpha - 1}[1 - \sum_{i = t_2 + 1}^{i_{\max } } {\sum_{j = s_2 + 1}^{j_{\max } } ( \frac{p(i,j)}{{p_l (t_2 ,s_2 )}}} )^\alpha ] $$

(4)

where

$$ P_l (t_2 ,s_2 ) = \sum_{i = t_2 + 1}^{i_{\max } } {\sum_{j = s_2 + 1}^{j_{\max } } {p(i,j)} } $$

(5)

THC entropy with the order α related to the seabed reverberation area is prescribed by

$$ H_r^\alpha (t_1 ,s_1 ,t_2 ,s_2 ) = \frac{1}{\alpha - 1}[1 - \sum_{i = t_1 + 1}^{t_{2} } {\sum_{j = s_1 + 1}^{s_2 } ( \frac{p(i,j)}{{p_r (t_1 ,s_1 ,t_2 ,s_2 )}}} )^\alpha ] $$

(6)

where

$$ P_r (t_1 ,s_1 ,t_2 ,s_2 ) = 1 - P_d (t_1 ,s_1 ) - P_l (t_2 ,s_2 ) $$

(7)

The total THC entropy is given by

$$ H^\alpha (t_1 ,s_1 ,t_2 ,s_2 ) = H_d^\alpha (t_1 ,s_1 ) + H_r^\alpha (t_1 ,s_1 ,t_2 ,s_2 ) + H_l^\alpha (t_2 ,s_2 ) $$

(8)

Receive the value $(t_1^\ast ,s_1^\ast ,t_2^\ast ,s_2^\ast )$ corresponding to the maximum value of the total THC entropy by means of maximizing the total THC entropy, that is

$$ (t_1^\ast ,s_1^\ast ,t_2^\ast ,s_2^\ast ) = Arg\mathop {\max }\limits_{t_1 ,s_1 ,t_2 ,s_2 } [H^\alpha (t_1 ,s_1 ,t_2 ,s_2 )] $$

(9)

Here $(t_1^\ast ,s_1^\ast )$ and $(t_2^\ast ,s_2^\ast )$ are two thresholds which are used for the thresholding (segmentation) of an image.

3 Segmentation Results for the Sonar Image from an Undersea Goal

3.1 Introduction to the Sonar Image from an Undersea Goal

Figure 1(a) is a sonar image from an undersea man-made goal. The lighter part is the goal light area and the darker part is the goal dark area in the image. The goal dark area is on the goal light area and close to the goal light area. The reverberation area is around the goal light area and the goal dark one.

3.2 Segmentation Procedures and Results for the Sonar Image from an Undersea Goal

The segmentation procedures are as follows.

• (1) Input the sonar image from an undersea goal.

• (2) Filter the image using Wiener filter with a window size of 5 × 5.

• (3) Calculate the two-dimensional histogram.

• (4) Let α = 0.8 [3], and calculate $H_d^\alpha (t_1 ,s_1 )$, $H_l^\alpha (t_2 ,s_2 )$ and $H_r^\alpha (t_1 ,s_1 ,t_2 ,s_2 )$ using the formulas (2), (4) and (6).

• (5) Calculate $(t_1^\ast ,s_1^\ast ,t_2^\ast ,s_2^\ast )$ using the formula (9).

• (6) Receive two pair of thresholds $(t_1^\ast ,s_1^\ast )$ and $(t_2^\ast ,s_2^\ast )$.

• (7) Receive the thresholded image containing three gray values with the help of the thresholds $(t_1^\ast ,s_1^\ast )$ and $(t_2^\ast ,s_2^\ast )$.

In Fig. 1, Fig. 1(b) is the images after Wiener filtering, Fig. 1(c) is the image after manual segmentation which is regarded as the best segmentation result. Figure 1(d)-1(i) are the segmented images by means of the two-dimensional THC entropy. Figure 1(d)-1(i) are the segmented images corresponding to the feature combinations 1 (the gray value and the average gray value within a neighborhood), 2 (the gray value and the median gray value within a neighborhood), 3 (the gray value and the mode of gray values within a neighborhood), 4 (the average gray value within a neighborhood and the mode of gray values within a neighborhood), 5 (the average gray value within a neighborhood and the median gray value within a neighborhood), and 6(the median gray value within a neighborhood and the mode of gray values within a neighborhood). The thresholds for image segmentation corresponding to Fig. 1(d)-1(i) are (38,43), (94,86); (38,42), (96,91); (39,43), (101,81); (38,41), (133,117); (40,42), (91,82); (38,40), (105,83).

It can be found out from Fig. 1 that the sonar image of an undersea man-made goal is roughly divided into a goal dark area, a reverberation one and a goal light one. However, the parts of the reverberation area are wrongly divided into the goal light area or the goal dark one. The reason for this phenomenon is that the values of the two features of each feature combination in the parts of the reverberation area are actually equal to the values of the two features of each feature combination in the goal light area or the goal dark one. Visually, although there are errors in segmentation, in comparison, Fig. 1(g), namely feature combination 4, has the best segmentation effect.

This paper attempts to give the evaluation indexes IOU (intersection over union) and FPR (false positive rate) for the above segmentation results. Table 1 gives the evaluation indexes IOU and FPR of the goal light area. Table 2 gives the evaluation indexes IOU and FPR of the goal dark area [6]. In terms of the evaluation indexes IOU and FPR, for the segmentation of the goal light area, Fig. 1(g), namely feature combination 4, has the best segmentation effect; and for the segmentation of the goal dark area, Fig. 1(i), namely feature combination 6, has the best segmentation effect. In general, the evaluation using indexes IOU and FPR is roughly the same as the visual effect.

Fig. 1.

Segmentation results based on the two-dimensional THC entropies.

Table 1. Evaluation indexes for the segmentation of the goal light area.

Table 2. Evaluation indexes for the segmentation of the goal dark area.

4 Conclusion

This paper investigates the application of the THC entropies of 6 kinds two-dimensional histograms to the sonar image segmentation. The segmentation results with different two-dimensional histograms are different. In practical applications, we can determine which two-dimensional histogram is more appropriate based on experiments. But we should also know that for a sonar image from an undersea goal, there may be mis-segmentation with any two-dimensional histogram given in the paper. That is because, for a sonar image from an undersea goal, any two-dimensional histogram given in the paper is not an ideal shape of the three peaks and two valleys.

This work is supported by Hainan Provincial Natural Science Foundation of China (No. 420CXTD439) and the National Science Foundation of China (No. 61661038).