CLASSIFICATION OF HIGH-RESOLUTION SATELLITE IMAGES USING FUZZY LOGICS INTO DECISION TREE

Received 05 December 2019 Accepted 12 January 2020 Available online 05 February 2020 In this paper, DTFL an image classifier based on Decision Tree and Fuzzy Logics is proposed. At the beginning of classification using DTFL, each pixel is located at the highest level of a decision tree where it belongs to the combination of all classes. DTFL transfers a pixel to a lower level of the decision tree where the pixel belongs to a combination of fewer classes. Decision-making about transfers is based on fuzzy logic with seven different membership functions including triangular-shaped, trapezoidal-shaped, π-shaped, bell-shaped, Gaussian, differential S-shaped and multiplicative S-shaped. Eventually, pixels will reach the lowest level of the decision tree where it belongs to only one class. For accuracy assessment, DTFL was used to classify a GeoEye-1 image. The overall accuracy of 96.14% and a kappa coefficient of 96.06% were reached by DTFL. In comparison, the overall accuracy of 89.91% and a kappa coefficient of 89.77% were reached by a Maximum Likelihood Classifier, MLC. In the case of applying a threshold in MLC to reach the same accuracy as DTFL, 8.73% of pixels take the non-classified label while using DTFL all the pixels get a proper label. The results indicate that the proposed classifier extracts more information from images.


INTRODUCTION
During the last decades, a wide range of pattern recognition techniques has been invented to extract information from remotely sensed data such as satellite images. Meanwhile, the flexibility and performance of image classifiers make them one of the main recognition techniques for extracting information from satellite images. Image classification is defined as a decision-making process in which a label of a class (or more classes) is assigned to each pixel of an image with the maximum confidence of assignment (Gomez et al., 2016;Momeni, 2011). Traditional image classification methods carry out a hard classification output based on the fundamental law of "one pixel-one class". The fundamental law clears that a pixel is either a full member of a class or not. Consequently, traditional image classification methods are not considered as the best method for classifying mixed or imprecise pixels in an image (Momeni, 2011). On the other hand, advanced image classification methods, such as genetic algorithms and expert systems, have many issues with image classification, such as no general standards for defining the architecture, training requirements and time-consuming training (Gomez et al., 2016;Ghosh et al., 2014).
In recent decades, fuzzy logic has been implemented in various fields of study such as control systems, image processing and classification of remotely sensed data (Momeni, 2011;Zimmermann, 2011). A fuzzy classifier estimates the contribution of each class in each pixel. In other words, a fuzzy classifier assumes that each pixel in the image is a decomposable unit and, accordingly, works on a new fundamental law of "one pixel-several class" to extract more information about pixels (Momeni, 2011;Ghosh et al., 2010;Dutta, 2009). A group researchers, provided a survey on different image classification methods and concluded fuzzy logic as one of the most reliable image classification methods (Akgun et al., 2004;Weng and Lu, 2007). In addition, some other scholars have investigated applications of fuzzy image classification and claimed that fuzzy classifiers are among the most powerful tools for the classification of satellite images (Bai et al., 2014;Xu et al., 2019;Joseph and Chockalingam, 2017). Pixel-based classification is still among the most practical classification approaches due to simplicity, low computational cost and high reliability (Gonzalez et al., 2016). However, pixel-based classification is not accurate to classify mixed pixels with overlapped spectral characteristics. Even though applying thresholds can increase the accuracy and reliability in the labeling of pixels, but thresholds omit some of the mixed pixels from the classification process. In that case, omitted pixels get a non-classified label (Momeni, 2011;Joseph and Chockalingam, 2017). This paper is aimed to introduce a novel satellite images classifier, called DTFL, based on a Decision-Tree and Fuzzy Logic. DTFL is able to classify all the pixels in an image and avoids non-classified labeling. It also takes the advantages of fuzzy concepts to increases the accuracy of classification in comparison with traditional classifiers such as Maximum Likelihood (ML). In order to assess the performance of the proposed classifier, DTFL was used in the classification of a high-resolution GeoEye-1 satellite image of the Azadi Complex, Iran, and the results were compared with the results of image classification using the ML classifier. Using an advanced image classifier such as DTFL helps the city and regional planners to understand their surroundings more precisely to offer a more reliable plan for the future of the region. In particular, regional farm managers can estimate the amount of different agricultural products more precisely and will make key strategic plans based on more accurate knowledge. The rest of this paper is organized as the following: Section Two describes the proposed DTFL classifier. The principal of the decision tree approach and different fuzzy membership functions, as well as different reasoning rules, are discussed in the same section. A brief description of datasets and results of using DTFL for classification is discussed in Section Three. Section Four is dedicated to discussions and lastly, the concluding remarks are given in Section Five.

METHODOLOGY
DTFL is a sub-pixel supervised classification method based on the tree method and fuzzy logic. At the beginning of the image classification using DTFL, each pixel is located at the highest level of a decision tree. Each level represents the number of confusions in the classification. Each pixel belongs to the combination of all the initial classes at the highest level of the decision tree. DTFL classifies each pixel in a smaller combination of classes by defining a hypothesis. The hypothesis is based on the transfer of each pixel from a higher level to a lower level and needs validation. Decision making about the transfer of each pixel to a lower level is based on fuzzy logic. Using an iterative process, each pixel is transferred from the higher level to the lower one ( Figure 1). The iterative process continues until either of the two following conditions is satisfied: A) A state having a single class (called a leaf) is reached

B) No new state is reached after the iteration
In the first case, the pixel is classified as a pure pixel and get a single label while in the latter case, the pixel is classified as a mixed pixel and get a label according to its level on the tree (avoids non-classified label).

Decision Tree
Decision Tree (DT) classification is a hierarchical process where at each level, a test is applied to one or more attribute values and makes one or more outcomes. The outcome(s) may be either a leaf resembling a class (or more classes) or a decision node (or more decision nodes) describing a further test on the attribute values which creates a branch or sub-tree of the tree (Al-Obeidat et al., 2015). The classification process is completed by passing the pixel down the tree until either a leaf is reached or no new state is reached after the iteration. In the latter case, the pixel is classified as a mixed pixel and get a proper label according to its level. The structure of a decision tree classifier is shown in Figure 1 (Momeni, 2011).

Schematic presentation of a decision tree
Consider a multispectral image of an area whose pixels have to be classified. Let's assume CL as the set of all k possible classes. Each pixel in the image has to be classified into one or more (for mixture pixels) of the k possible classes in CL. Figure 2 shows the outline of interpreting a pixel in a four-classes problem (k=4) where CL= {C1, C2, C3, C4}. For instance, the node {C1, C2} indicates the state: "The pixel may belong unconditionally to the C1 or unconditionally to the C2 or to a combination of C1 and C2". The connector lines in Figure 2 represent hypotheses through which state transfers can occur. For instance, the connector line between {C1, C2, C3} and {C1,C2} indicates the hypothesis that: "The pixel belongs to one or more classes in the set of {C1, C2} with the assumption that it belongs to one or more of classes in the set of {C1, C2, C3}". The inference mechanism chooses appropriate hypotheses to test. Each hypothesis is either true or false. According to the results of those tests, the inference mechanism infers the new state of the pixel.

Inference mechanism
The interpretation of a pixel is an iterative process of inference. Each iteration includes three steps: Step1: selecting appropriate hypothesis for the test; Step2: testing the validity of the selected hypothesis; Step3: analyzing the passed hypothesis in order to infer the next state.
The iterative process continues until either of the following conditions is satisfied: A) A state with a single class (a leaf) is reached (e.g., states {C1} or {C2}). In such cases, a solid decision is reached and the pixel gets a single label of the class; or B) No new state is reached after iteration. In such cases, a solid decision could not be reached either due to lack of knowledge or due to the case of a mixed pixel (e.g., pixel covering more than one land cover classes). In such cases, the pixel is considered as a mixed pixel and get a proper label of classes.
The decision in the latter case assigns a set of possible classes to the pixel and avoids the non-classified label. For example, assigning {C1, C2} to a pixel means the pixel is a mixture of class {C1} and {C2} and other classes (such as {C3} or {C4}) have no contributions in the pixel. In comparison, traditional classifiers such as MLC, omit mixed pixels and simply assign a non-classified label to them.

Selecting appropriate hypotheses
As Figure 2 shows, classification schema is separated into different levels based on the number of classes each level contains. In other words, the level of a state indicates the degree of uncertainty. For instance, four possible states are available at the level-3, where each of them is a unique combination of three land cover classes. Consequently, at any given state such as S, the set of possible hypotheses is in the form of D S → , where D⊂ S. The sublevel of a hypothesis D S → is defined as d where d is the level of D (e.g., the number of classes in D). The process of inferring always starts at the maximum uncertainty and the first sublevel. The process then continues iteratively. At the end of each iteration, the new states and sublevels are deduced for the next iteration.

Testing chosen hypotheses
For testing the chosen hypotheses, appropriate rules must be selected and their validity should be verified. The basic representation of rules is as the following (Equ. 1): Where CLi is logical constraints on one or more attributes of pixels. In a real classification problem usually more than one rule is defined. In that case, if R1,…, Rm is a set of rules which leads to a hypothesis Hk , then Hk is satisfactory if all of R1,… , Rm is satisfied. To analyze a rule, each of its components, e.g. CLi, is validated. If all the components are true then the rule is valid.

Analysis of the passed hypotheses to choose the next state
Suppose the state T of level-t and the hypothesis sublevel-d in an iteration. Then two possibilities for the rule are: A) The rule is not passed: which indicates that all the hypotheses of sublevel-d are rejected. Therefore, the decision is transferred to the next sublevel (e.g. d=d+1). If d is equal to t, then the pixel belongs to one or more of the classes in T. Otherwise, the next iteration continues with d and the same state T. B) The rule is passed: Suppose the hypothesis was T ⟶ D. Then, the new state is T = D. If the level of this new state is one, the pixel is classified into a class in new-S and the analysis of the pixel is terminated. Otherwise, the new sublevel is new-d=1. The progress to the next iteration with new-T and new-d is continued.

Fuzzy Logic
There are three steps in a fuzzy method for the classification of remote sensing images. In the first step, the contribution of each class in each pixel is estimated using a fuzzification process with a proper membership function (MF). In this step, each pixel is converted to a matrix of membership degrees. In the second step, proper reasoning rules are applied to the fuzzy inputs (e.g. to the matrix of membership degrees) to achieve a fuzzy classification of pixels. In this step, normalization of data may be required. Lastly, in the third step, a defuzzification process is applied to create a hard classification output (Ghosh et al., 2014;Ghosh et al., 2010;Dutta, 2009;Xu et al., 2019;Al-Obeidat et al., 2015;Melgani et al., 2000;Zhao, 2008).

Fuzzification
The fuzzy domain includes several fuzzy sets representing the bands. Each fuzzy set (band) contains fuzzy subsets that indicate the land cover classes. Each fuzzy subset (e.g. land cover c), in a given fuzzy set (e.g. band b) is defined by a membership function, x is the value of the spectral pixel of X in the band b and land cover c.
In the proposed classifier, DTFL, seven different fuzzy membership functions were used for fuzzification including triangular shape, trapezoidal shape, π shape, bell shape, Gaussian, differential S shape and multiplicative S shape. The mathematical expression of each membership function is as the following (Momeni, 2011;Zhao, 2008;Matlab, 2017):

Reasoning rule
According to literature, a low fuzzy membership value MIN rule (so-called intersection rule) is a simple, fast and effective reasoning rule for many fuzzy problems (Ghosh et al., 2014;Ghosh et al., 2010;Melgani et al., 2000). In addition to the MIN rule, a high fuzzy membership value MAX rule (so-called union rule) is also considered as an effective reasoning rule (Ghosh et al., 2014;Ghosh et al., 2010;Melgani et al., 2000). However, intersection and union rules are generally not powerful enough for sophisticated classification processes where there are highly overlapped classes. In the current work, 12 different reasoning rules were used including minimum, maximum, multiplicative, collective, collective second power, mathematical mean, geometric mean, harmonic mean, minimum/ maximum, mathematical mean× minimum/ maximum, geometric mean × minimum/ maximum and harmonic mean ×minimum/ maximum. The mathematical expression of each reasoning rule is shown in the following (Momeni, 2011):

Defuzzification
In the proposed classifier, DTFL, the last step is a hard classification using MAX or MIN operations as the simplest defuzzifiers. Other defuzzification methods, such as centroid of the area or mean of maximum, are used in other problems such as control systems (Momeni, 2011;Ghosh et al., 2014;Ghosh et al., 2010). However, in the proposed approach, DTFL, each pixel is assigned to the class c with the highest membership value using the MAX operator. The mathematical expression of the MAX operator is as: where ) (x F j is the membership value for the j th class (Momeni, 2011). Figure 3 illustrates the flowchart of classification using DTFL. In that flowchart, two parts of DTFL, the decision tree and the fuzzy logic, are shown simultaneously.

EXPERIMENTAL RESULTS
In order to evaluate the accuracy and performance of the proposed method, a GeoEye-1 satellite image of Azadi Stadium, Iran, (Figure 4) was classified using DTFL. In the study area nine different dominant classes were determined as "blue-seats" and "white-seats" from the first floor of the stadium, "lawn" and "soil" and "pedestrian-gravel" from the playing fields, "concrete-seats" from second floor of the stadium, "asphalt-road" and "cement-wall" from the surrounding of the stadium, and "water" from northern lake of the stadium. The GeoEye-1 image was taken on Jan 07, 2009 with GSD of 16 inches (0.41 m) in panchromatic mode and GSD of 65 inches (1.65 m) in a multispectral mode with 11 bits per pixel as radiometric resolution (Momeni et al., 2018;Bagheri et al., 2011). Even though GeoEye-1 is able to acquire images with a resolution of 41 cm, but under the company's current operating license from the National Oceanographic and Atmospheric Agency (NOAA) images must be resampled down to half a meter for commercial customers (Momeni et al., 2018). This resampling will mix up some pixels and classes and decreases the accuracy of classification.
A set of training data were used to estimate the statistical parameters of each class for each reasoning rule. In this study, training data were collected based on 1:2000 topographic maps and ground surveying. Finally, the satellite image of the study area was classified using DTFL with seven different fuzzy membership functions and 12 different decision rules. Membership functions included triangular shape, trapezoidal shape, π shape, bell shape, Gaussian, differential S shape and multiplicative S shape. Decision rules included Minimum, Maximum, Multiplicative, Collective, Collective second power, mathematical mean, geometric mean, harmonic mean, minimum/ maximum, mathematical mean × minimum/ maximum, geometric mean × minimum/ maximum and harmonic mean × minimum/ maximum. Table 1 and Table 2 summarize the Kappa coefficients and overall accuracies of image classification using DTFL.

DISCUSSION
To prove the performance of image classification using DTFL, the results were compared with the results of the Maximum Likelihood classification. The best result of DTFL (using triangulation shape membership function and harmonic mean as reasoning rule) is compared with the result of the Maximum Likelihood (ML) in Table 3.  Table 3, it is concluded that the results of classification by DTFL in the best mode (using a triangular-shaped membership function and harmonic-mean as reasoning rule) is better than the results of ML classifier. DTFL improves the accuracy of the classification for more than 6% in comparison with ML. In practice, it is common to use a threshold in the ML classifier to increase the accuracy and precision of the classification (Momeni, 2011). In this case, low-reliability pixels are excluded from the classification process and get a non-classified label. Therefore, the accuracy of the rest of the pixels in the classification will be improved. By defining a threshold in the ML method to achieve the same accuracy of the DTFL in this case study, 8.73% of the pixels took the non-classified label. Therefore, using ML 8.73% of pixels are excluded in the future decision makings as there is no idea about their mixed contents. However, as it already mentioned in Section Two, DTFL is able to classify all the pixels and avoids non-classification labels. Therefore, using DTFL, we have more knowledge about mixed pixels and their contents. The confusion matrix resulted from DTFL (using triangulation shape membership function and harmonic mean as reasoning rule) is shown in Table 4.   Truth pixels  181  298  5162  576  324  486  302  330  5965  13624 No. Non-classified pixels 0 0 0 0 0 0 0 0 0 0 Where C1 to C9 are "blue-seats", "white-seats", "lawn", "soil", "pedestrian-gravel", "concrete-seats", "asphalt-road", "cement-wall" and "Water", respectively. Also, the confusion matrix resulted from an ML classifier is shown in Table 5.