Classification of Clouds in Satellite Imagery Using Adaptive Fuzzy Sparse Representation

Meteorological satellites have advantages such as a wide range of spatial observations, high temporal resolution, all-weather observation, etc. Satellite cloud imagery has become one of the important means for weather forecasting and climate analysis [1,2,3], especially for forecasting and monitoring some natural disasters, such as typhoons, floods, snowstorms, forest fires, etc. Cloud classification is one of the fundamental works of satellite cloud image processing. The current commonly used methods for cloud classification are threshold based methods (including simple threshold method and histogram based method mainly), statistical based methods, and artificial intelligence based methods [4]. Simple threshold methods [5,6] analyze the spectral characteristics of different channels to inverse the brightness temperature for each pixel, then take the gray value and brightness temperature of each pixel with the difference of brightness temperature between channels to determine a series of thresholds as comprehensive criterion, but it is very difficult to determine the series of thresholds. Histogram based method [7] improves the simple threshold method by taking advantage of statistical properties of the partial or global histograms of satellite cloud images, but for complex weather systems, it is still hard to obtain adaptive thresholds. As for the statistical-based methods—such as C-means, fuzzy C-means clustering [8], etc.—based on the cluster analysis of sample set, these methods classify the pixels into different types of clouds by computing the distance between samples and cluster centers. The performance of cloud classification could be improved, but in case that different clouds superimposed each other, their clustering results is poor, thus they cannot achieve reasonable classification performance. In recent years, artificial intelligence based methods, such as artificial neural networks [9] and support vector machine (SVM) [10,11,12,13,14,15], have been applied to cloud classification. These methods improved the accuracy of cloud classification by using machine learning to extract the inherent features of training samples. In particular, support vector machine, which is based on the principle of structural risk minimization and Vapnik-Chervonenkis (VC) dimension, can find the best compromise between learning ability and model complexity, thus it can obtain good generalization ability for cloud identification. However, actual weather systems are really intricate; the distributions of clouds are very perplexing. For example, in transition regions of different cloud types, and in regions where the clouds are just in developing or extinction phases, there are not only clouds with distinctive features, but also some clouds with fuzzy properties. Even worse, satellite cloud imagery may easily be deteriorated by noises, atmospheric turbulence, fluctuation of undulating surface or drift of satellite orbit, etc. So it is inevitable that cloud images possess the characteristics of fuzzy, non-uniform, complex, and changeable cloud types. Thus, introducing fuzzy theory into satellite image processing may improve the accuracy of cloud classification. Based on traditional SVM, using linear fuzzy membership to optimize the sample set, Lin et al. constructed a fuzzy support vector machine (FSVM), experiments showed that FSVM can reduce the sensitivity to noises and outliers of traditional SVM [12]. Fu et al. applied a modified FSVM to the detection of cumulus cloud, which achieves good performance [13], but it cannot detect other cloud types effectively, and its generalization is relatively poor. To handle the deficiency of traditional FSVM, Zhang et al. defined affinity among samples and proposed an affinity based FSVM [14]. According to the affinity among samples, the modified FSVM assigns each sample a proper fuzzy membership to suppress the impact caused by noises and outliers during the training of SVM, and presents an effective scheme to identify valid or invalid samples. However, the definition of the fuzzy membership function based on affinity cannot accurately depict the changing trends of different samples; moreover, the function parameters are not very adaptable or flexible.

Due to the successful application of sparse representation for pattern classification problem [16,17,18], our research team proposed a cloud classification method using over-complete dictionary via sparse representation [19], which improved the classification accuracy in most weather systems, but this method did not take the fuzziness of cloud samples into consideration. By introducing the fuzziness into sparse representation, a cloud classification method using adaptive fuzzy sparse representation-based classification (AFSRC) is proposed, this method defines some adaptive parameters which relate to the attenuation rate and critical value of fuzzy membership, then constructs an adaptive membership function to alleviate the problem that the traditional fuzzy membership function is ineffective in depicting the distribution characteristics of training samples. Finally, the proposed fuzzy membership function is combined with sparse representation to design an adaptive classifier. The motivation of this method lies in that a single pixel of cloud image is usually the comprehensive reflection of different clouds and surface features; it implies that a single pixel is a linear combination of several components of cloud systems in a picture, which exactly coincide with the idea of sparse representation [16], so sparse representation has some promising applicability for cloud classification. Moreover, by introducing an adaptive fuzzy membership function into sparse representation to optimize the sample set, the adaptive dictionary with stronger discriminative capability can be obtained, which is expected to improve the accuracy of cloud classification.

The rest of the paper is organized as follows: Section 2 briefly introduces the cloud feature extracting and cloud classification system for satellite imagery; Section 3 introduces the traditional fuzzy membership theory for cloud classification; Section 4 presents the proposed adaptive fuzzy membership function, and combines it with sparse representation classifier, providing the proposed scheme for cloud classification; Section 5 gives the experiment results; the conclusion is presented in Section 6.

In actual weather systems, apart from the clouds with distinguishing characteristics, there are also some clouds with fuzzy characteristics; thus, it is difficult to classify cloud into a specific cloud type arbitrarily. Establishing a fuzzy membership to describe the relation between samples and specific cloud types is a helpful scheme. In fact, in the application of machine learning, fuzzy membership plays an important role in depicting the relations among training samples and specific classes. If training sample ${\mathbf{x}}_i$ is assigned a fuzzy membership $p_i\in [0,1]$, which denotes its specific belonging class, a soft classification model can be established and the classification performance of machine learning algorithms can be improved. Since traditional SVM is sensitive to noises or outliers, Lin et al., by assigning smaller membership to noises or outliers to eliminate their impact on hyperplane of classification, proposed the fuzzy support vector machine (FSVM) and improved the performance of SVM classifier effectively [12]. So, constructing a reasonable fuzzy membership function is the key to building a soft classification model.

The traditional linear and sigmoid membership functions cannot depict the distribution characteristic of invalid samples such as noises and outliers effectively, and they cannot reflect the uncertainty of samples. To solve the problem, Ref. [14,15] proposed a membership function based on affinity. A minimum hypersphere is constructed, which contains most of the valid samples, and the affinity among samples, defined by support vector data description (SVDD) [20], is represented by the radius of the minimum hypersphere. The membership function is then constructed as follows [14]: here, $d({\mathbf{x}}_i)(i=1,2,\dots ,l)$ is the distance between training samples ${\mathbf{x}}_i$ and its class center, R is the radius of the minimum hypersphere. If $d({\mathbf{x}}_i)\le R$, which means that ${\mathbf{x}}_i$ lies inside the hypersphere, or ${\mathbf{x}}_i$ is more likely to be a valid sample, the corresponding membership of the sample is calculated using the upper formula of Equation (1). Otherwise, if $d({\mathbf{x}}_i)\ge R$, which means that ${\mathbf{x}}_i$ lies outside the hypersphere, the corresponding membership of the sample is calculated using the lower formula of Equation (1). According to the definition of membership function as Equation (1), the membership is larger than 0.4 for samples inside the hypersphere, and is less than 0.4 for samples outside the hypersphere; here, 0.4 acts as a critical membership. By calculating membership with different formula for samples inside or outside the hypersphere, the membership function could distinguish valid and invalid samples better and decrease the membership for noises and outliers, so as to eliminate their adverse impact on the classification hyperplane. Figure 2 shows a set of membership function curves of Equation (1) for different R.

Figure 2 shows that the critical membership depicts the boundary between the inner and outer samples of the minimum hypersphere, and the fuzzy memberships vary differently for different radius R. As R increases, the membership attenuation rate for samples outside the hypersphere (where ${\mu }_i<0.4$ in Figure 2) accelerates a bit, while that slows down for samples inside the hypersphere (where ${\mu }_i>0.4$ in Figure 2). If R is too small ($R<3$), the membership attenuation rate for samples outside the hypersphere is smaller than that for samples inside the hypersphere. In this paper, a 14-dimensional feature vector is extracted and then normalized. After normalization, for real data, the radius R of the minimum hypersphere for different cloud type sample sets are all less than 3. In practice, samples inside or outside the hypersphere are treated as valid or invalid samples, respectively. To show the different importance of valid or invalid samples in designing a classifier, the membership should attenuate slowly for valid samples, and should attenuate far more quickly for invalid samples. Hence, the membership function defined by Equation (1) is not consistent with the distribution characteristics of satellite cloud images, which will degrade the performance of cloud type identification. In addition, the critical membership in Equation (1) is fixed to 0.4, which is not good enough. In fact, different sample sets might have different distribution characteristics, and their corresponding critical membership should be different, too. In the following section, membership function with adaptive parameters will be defined, and an adaptive fuzzy sparse representation classifier for cloud type identification will be constructed.

In actual weather systems, cloud distribution is very complex; clouds may overlap each other and are changing all the time; noises and data errors in acquisition and transmission make it more difficult to conduct satellite cloud image processing. In order to achieve better classification performance, it is necessary to utilize the distribution characteristics of training samples. After analyzing the distribution characteristics of training samples for cloud classification, by eliminating the influence of outliers and noises, an adaptive fuzzy membership function is designed to improve the capability of affinity-based fuzzy membership function. Combining the improved fuzzy membership function with the sparse representation classifier, an adaptive fuzzy sparse representation classifier is constructed for cloud type identification.

In this section, the performance of the proposed cloud classification system with some existing methods is compared. Experiments are conducted on a computer with 2.4 GHz Intel CPU and 4 GB RAM. The cloud image data come from the FY-2G satellite that carries five channel sensors (IR1, IR2, IR3, IR4, VIS) for a period of 10 days (from 28 June to 7 July 2016). From 28 June to 6 July 2016, the satellite data were collected at 8 a.m., 10 a.m., 12 p.m., 2 p.m., 4 p.m., and 6 p.m. Beijing time each day, so 9 × 6 = 54 times satellite data were collected. From these cloud images, three meteorologists examine the cloud images carefully, then manually identify and select 300 pixels (samples) for each of the six predefined cloud types as mentioned in Section 2.2. Totally, 1800 samples are used in experiments in Section 5.1 and Section 5.2. Satellite data collected at 2 p.m. Beijing time, on 7 July 2016, is used for experiment of visual comparison in Section 5.3. All experiments in Section 5.1, Section 5.2 and Section 5.3 use the same training samples. In order to effectively represent spectral information, feature vectors for each selected sample are extracted and normalized by ${\ell }_2$-norm. In the proposed AFSRC, the centers and radius R of hyperspheres for the membership value calculations were determined by SVDD, and Gaussian kernel function was used in SVDD. Constant C, as a penalty factor, which controls the trade-off between the volume and the errors in SVDD, is set to be C = 1.0. The classification accuracy of the proposed method is evaluated; several existing methods—including affinity based FSVM [14], SRC [16], and CCSI-ODSR [19]—are compared with the proposed method, the computation efficiency of the different methods is provided, and training time for training SVDD is listed in Section 5.4.

Since traditional fuzzy membership has poor flexibility and is inconsistent with the distribution characteristics of samples for cloud classification, by defining adaptive parameters related to attenuation rate and critical membership, an adaptive fuzzy membership function is constructed and then combined with sparse representation classifier. The newly proposed adaptive fuzzy sparse representation-based classification (AFSRC) method for satellite cloud classification can eliminate the impact of noises and outliers for cloud classification. Experiments results on FY-2G satellite cloud images show that the proposed AFSRC not only improves the accuracy of cloud classification with acceptable time efficiency, but it also has strong stability and adaptability. How to find a more reasonable way to determine the parameters in AFSRC, and how to apply the AFSRC method in other satellite cloud classification, will be presented in future work.