Tropical Cyclone Center Determination Algorithm by Texture and Gradient of Infrared Satellite Image Tropical Cyclone Center Determination Algorithm by Texture and Gradient of Infrared Satellite Image

A novel algorithm for tropical cyclone (TC) center determination is presented by using texture and gradient of infrared satellite image from geostationary satellite. Except those latter disappearing TC satellite images that are little valuable to a TC center determina - tion, generally other periods of TC, all have an inner core. And the centers are generally determined in the inner core. Based on this, an efficient TC center determination algo - rithm is designed. First, the inner core of a TC is obtained. Then, according to the texture and gradient information of the inner core, the center location of the TC is determined. The effectiveness of the proposed TC center determination algorithm is verified by using Chinese FY-2C stationary infrared satellite image. And the location result is compared with that of the “tropical cyclone yearbook,” which was compiled by Shanghai Typhoon Institute of China Meteorological Administration. Experimental results show that the proposed algorithm can provide a new technique that can automatically determine the center location for a TC based on infrared satellite image.


Introduction
Tropical cyclone (TC) is one of the most serious natural disasters in the world. Satellite remote sensing technology can not only observe the whole situation but also the structural characteristics and center information of a TC. It is the current main method of the TC center location.
Dvorak technique (DT) is widely used to TC center location. DT, which was proposed by [1,2] in the 1970s was the most important method for TC analysis in the world. Nowadays, based on the DT, advanced Dvorak technologies [3][4][5] were developed to determine the TC center location. Li et al. [6] put forward a new artificial intelligence algorithm for the eye TC center location. First, the image segmentation technique was used to extract the TC cloud features. And then, the mathematic morphology opening operation and the filling operation are used to obtain the contour of the TC eye. The gravity calculation method is applied to locate the TC center. Comparing the data to the Central Meteorological Observatory of China, the experimental results show that the deviation is smaller. Li et al. [7] proposed an improved genetic algorithm to determine the TC center location. The theoretical analysis and experimental results show that this method is reasonable and effective. Yang et al. [8] combined pattern matching with the vector field analysis to determine the TC center position. The proposed method is very efficient for the TCs, which have clear spiral structure. Fan et al. [9] used 85 GHz vertical polarization channels in specail sensor microwave/imager (SSM/I) for TC center location. According to the distributed characteristics of brightness and temperature, the TC of its band is analyzed and classified. The average gap of the best route in the test results of TC is smaller. Wei et al. [10] presented a novel spiral band model to automatically locate the TC center. And particle swarm optimization was used to optimize the model parameters.
Experimental results show that this model can achieve the best average error in both latitude and longitude in comparison with the best track data. Zhang et al. [11] proposed a novel intelligent automatic system framework, which was based on the image process technology to locate the TC center. According to the symmetry shape and spiral movement feature of TC, a rotation matching methodology is used to catch the track of TC. Compared with the data of Shanghai Meteorology Center, experimental results show that this system is efficient and the performance errors are acceptable for practical applications. Zheng et al. [12] established the TC forecast service production system based on geographic information system (GIS) technology and realized the function construction. It had met the requirements of the TC center forecast service production in the Central Meteorological Observatory. Recently, some researchers used deviation angle variance [13] and pattern matching algorithm [14] for TC center detection.
Although there are some advantages in the above methods, some defects are existing. The subjectivity of DT is stronger, and the degree of automation is limited. The location effect for the smaller intensity cyclone is poorer. The method based on mathematical morphology is suitable for tropical cyclone whose morphology characteristic can be identified easily. If it is applied to the weak or atypical morphology cyclone, a big deviation will be resulted. Intelligent learning method requires a lot of experimental data and experience accumulation. It is suitable for recognizing the particular structures. Wind field analysis method is applicable to locate the tropical cyclone center, which is weak and whose circulation center is not clear. When the intensity level of tropical cyclone is higher, the center location is not accurate because it is easily affected by the resolution and heavy rain [11]. The temperature/ humidity structure retrieval method is also only applied to locate the tropical cyclone center whose intensity is strong. The tempo-spatial movement matching method applied movement information of adjacent satellite images to determine the TC center position [11]. But the computation burden of the method is large. Generally, center location for eye TCs has good results. But it is not very satisfying for non-eye TCs due to some reasons. Therefore, it is very important to improve the accuracy of automatic TC center location.
Here, we extract the inner core region from an infrared satellite image, which contains a TC initially. Then, according to the characteristic of the position of TC center, which is the intersection of the ambient airflow and the different textures between the inner core region and other cloud area, we determine the TC center further. And the texture is uniform and smooth in the inner core region. The gray values of the inner core region are higher than those which are on the edge of the TC. So, we calculate the fractal dimension and 3-s order statistical parameters of a gray-gradient co-occurrence matrix to determine the inner core region of the TC. Then, according to the gradient information of the inner core region, the center location of the TC is determined.

Extract the inner core region
In general, the TC cloud consists of spiral cloud band, inner core region, and TC center area. If the inner core region is extracted from the TC cloud, it will reduce the area, which contains the TC center. The average gray values of the inner core region in an infrared satellite image are high and the difference between the gray values of pixels is small. The gray-gradient cooccurrence matrix (GGCOM) can be used to measure the gray value difference in an infrared satellite image. The fractal dimension is a useful to represent texture characteristics of the infrared satellite image. The inner core region of a TC is extracted by combining the fractal dimension with GGCOM.

GGCOM
The analysis method of the gray-gradient co-occurrence matrix is to extract the texture feature by the comprehensive information about the gray values and gradient of the images. Because the scales of different characteristic parameters are different, we normalize the gray values and gradient values of the image. Details for GGCOM computation refer to our previous work [15].

Fractal dimension
According to the characteristics of the satellite cloud image, we use the method by Sarkar and Chaudhuri [16] to calculate the box fractal dimension.
If the size of image is N × N , we shrink the image into an value S n by the plotting scale, 1 < S n ≤ N / 2 , and S n ( 1 ≤ n ≤ N ) is an integer. So, we have an estimate of the scale r , which is r = N / S n .
Let an image be considered as a three-dimensional space ( x, y, z ) . Here, ( x, y ) means two-dimensional coordinate, and z means the gray value of the image element. So, ( x, y ) plane is divided into S n × S n grid. There is a series of boxes, whose bottom is S n × S n in each grid. The height h of box can be calculated by the gray level L of the whole image, namely [ . Each box is labeled from down to up as 1, 2, 3, ⋯ , and in which box the maximum and minimum image gray values of the (m, n) grid ( 1 ≤ m ≤ N ) fall is checked. If the maximum value falls into a and the minimum value falls into b , then n r = a − b + 1 . N r , which is the number of the boxes that cover the entire image can be described as: In this way, N r is calculated by each r . r changes as the change of s . The minimum linear fit is used for log ( N r ) and log (1 / r) , and then the slope is calculated, namely Q , which is the fractal dimension.
It is necessary to consider how to select the window of subimage and r calculates the scale of fractal dimension. The window size of subimage is too small to lose the important texture or is too large to mix the edge pixels with other pixels of the image area. It affects the selection of the texture feature. Choosing different scales will also affect the correctness of the linear fitting,that is, it affects the fractal dimension Q .

Extraction of inner core region
Through a large number of experimental satellite cloud images, we select the parameters, which can reflect the characteristic of TC cloud image clearly. The specific standard for choosing is as follows: the difference of this characteristic in different TC cloud images, inner core region, and other cloud regions is the biggest. And this characteristic is not sensitive for the inner core region or other cloud region, that is, it is consistent between different samples. In this chapter, average gray scale, small gradient advantage, and gradient uniformity of the GGCOM are used as features to locate the center of the TC [15]. Then, the inner core region of TC is determined by combining GGCOM with fractal dimension.
The scales of the above four characteristic parameters vary widely because the physical significance and scope of the different characteristic parameters are different. We test 10 groups of the main cloud region of the satellite cloud images whose size is 512 × 512: (1)  shown in Figure 1. The corresponding main bodies of the satellite cloud images are shown in Figure 2. Here, the fractal dimension Q , the average gray scale G ¯ , the small gradient S ¯ , and the inhomogeneity of the gradient distribution D ¯ are the characteristics of the main cloud of images. The four characteristics parameter values of these 10 test cloud images are shown in Table 1.
From Table 1, we can see that the range of the fractal dimension Q is from 1 to 3; the range of S ¯ is from 0 to 1; the range of D ¯ is on the amount of 10 5 ; and the range of G ¯ is from 0 to 200.
The difference between small and big components is large. The small component is easy to be ignored when the Euclidean distance is measured. The aforementioned four parameters should be normalized so that the same weight is used to compute the Euclidean distance.
The steps of determining the inner core region are as follows: Step 1. Separate main body of the TC from an infrared satellite image based on our previous work [17]; Step 2. Because the size of the selection of the test cloud images is 512 × 512 or 256 × 256, we use 39 × 39 window, which is determined by the experiments to compute fractal dimension and GGCOM; Step 3. Normalize four parameters to compute the difference value Δ D w ( w = 1, 2, ⋯ , 39 ) of the fractal dimension and GGCOM; Step 4. Get the values of Δ D w in each window; Step 5. Compare with each Δ D w , the window, which Δ D w is the biggest is determined as the inner core region of TC. Extracting the inner core region not only can reduce the region of TC center but also can eliminate the influence of the outer spirals. It can make the foundation for extracting the small gradient information. Based on these two purposes, it is not important whether to completely extract the inner core region. The key is to extract the main part of the inner core region. So a rough estimation by the size of TC cloud is feasible. The experiments also prove that the size of window can satisfy the need as per the above algorithm.

Determine the center of TC
It is assumed that whatever the type of the bending cloud, strong wind, eye cloud region, or type of center closed clod cloud region, the center of TC is almost located in the inner core   Table 1. Characteristic parameters of the main cloud in 10 groups of satellite cloud images.

Understanding of Atmospheric Systems with Efficient Numerical Methods for Observation and Prediction
region. After extracting the inner core region, we can determine the center of TC by the inner core region. The region near TC center has obviously the warm structure. The infrared brightness temperature gradient of the inner core region is small compared with the TC eye. The richest gradient region can be considered as the TC center region.

Compute the gradient information of inner core region
Before computing the gradient of the inner core region, Gaussian filter reduces the noise of the main body of the TC. The image and Gaussian smoothing filter are convolved as follows: where S (i, j; σ 2 ) represents the Gaussian function and σ 2 indicates variance. How to choose proper σ 2 is very important. I (i, j) shows TC main body image.
Different variance σ 2 will be used to extract different gradient information from the main body cloud of a TC. The infrared channel 2 cloud image of the No. 0601 TC "Chanchu," which was obtained at 12 o'clock on May 12, 2006 is an example (see in Figure 3(a)).
The image in which the variance is chosen as σ 2 = 0.5 is shown in Figure 3(b). The image in which the variance is chosen as σ 2 = 1.0 is shown in Figure 3(c). The image in which the variance is chosen as σ 2 = 1.5 is shown in Figure 3(d). The image in which the variance is chosen as σ 2 = 2.0 is shown in Figure 3(e). The image in which the variance is chosen as σ 2 = 2.5 is shown in Figure 3(f).
From Figure 3, we can see that the influence of σ 2 for extracting the gradient information is big. When the value of σ 2 is small, the accuracy of the edge position is high. But edge details change a lot. When the value of σ 2 is small, the effect of the smooth is large and the details lose a lot. The accuracy of the edge position is low. And the gradient information is rich. Based on it, we choose the variance σ 2 is 2.0. For this condition, the gradient image of the inner core is obvious.
In order to further enhance the gradient in the inner core region. A constant 5 is multiplied to the gradient image. Canny operator is used to determine the concentrated gradient region. This region should contain the TC center. The effect of the gradient information extracted from the inner core region is shown in Figure 4. Figure 4(a) is the gradient information of the inner core region when σ 2 = 2.0. Figure 4(b) is the gradient information of the enhanced image. Figure 4(c) is the result of the edge detection by Canny operator.
We can see from Figure 4(a) that the gradient information of the image is not obvious. In Figure 4(b), the gradient information after enhancing the image is clearer. It is convenient to do the edge detection by the Canny operator. The gradient and texture information of the inner core region is very obvious in Figure 4(c).

Determine the center of TC
The region whose gradient information is the most abundant in the inner core region is the region which contains the TC center. The gradient information, which is extracted from the clear eye TC is the obvious characteristic. According to edge information of the image in Section 3.1, which is the gradient information and expresses the texture feature of the image, the region whose texture is the most abundant in the inner core region, which is called the region of interest (ROI), is the region, which contains the TC center. The geometric center of the ROI is defined as the TC center.
Generally, the average diameter for a TC eye is 45 km or so. The spatial resolution for FY-2C satellite image is 5 km. Therefore, a 9 × 9 mask is used to search the inner core region. If a closed curve is found in the inner core region, the centroid of the curve is determined as TC center. Otherwise, the region whose intersection lines are the most is chosen as the ROI.

Results and discussion
Infrared satellite images from Chinese geostationary satellite FY-2C are used to verify the performance of the proposed algorithm in this paper. The TC center location is used to test the  We can see from above figures that the location results by the proposed TC center location algorithm are very close to the reference positions. Namely, the results are very close to the real center of TC. After the extraction of the main body cloud of a TC, the selected inner core region almost contains the cloud area of the eye of TC. And the texture of the inner core region is clear. The distance of the center location by the proposed algorithm and the reference position is so little. So it is difficult to identify the difference between them by the naked eye. Since   Table 2.
In Table 2, we can find that the error of the TC center location by the proposed algorithm is below 40 km. And it is suitable for the infrared channel 1 and the infrared channel 2 cloud images. We can see from the figures that the located results by the proposed TC center location algorithm are very close to the reference positions. The effect of the non-eye TC center location is good. In order to get the more accurate location error, we calculate the distance error of the TC center position by the longitude and latitude errors. The center position errors of the six experimental groups of the non-eye TC center location are shown in Table 3.

Experimental group of non-eye TC center location
In Table 3, we can find that the error of five groups of the non-eye TC center location by the proposed algorithm is below 70 km. Only the error of one group is more than 70 km, but it is below 100 km. In all, the proposed algorithm is suitable to be used to determine the center position for a TC by using the infrared channel 1 and the infrared channel 2 cloud images. Although the accuracy of the non-eye TC center location is slightly less than that of the eye TC center location, the error is small for the non-eye TC in which the texture is not prominent.

Conclusions
An effective TC center location algorithm, which is based on the fractal feature features and gradient of the infrared satellite cloud images, is proposed. The proposed algorithm is based on the assumption that the centers of a TC, which belongs to different development stages are mostly located in the inner core region. The inner core region is determined firstly. Then special gradient information and texture of the TC center are used to determine the center of TC. The proposed algorithm can be applied in the eye TC center location and the non-eye TC center location. The accuracy of the location by this proposed algorithm is higher. Moreover, the calculation of the proposed algorithm is simpler than that of the existing TC center location methods, such as the wind field analysis method, intelligent learning method based on the spiral fitting, tempo-spatial movement matching method, and so on. The proposed method is not proper to disorganized or weak TCs. Further work is needed to improve the location accuracy of TCs by using new features or techniques.