Knowledge-Based Morphological Classification of Galaxies from Vision Features

Transcription

1 The AAAI-17 Workshop on Knowledge-Based Techniques for Problem Solving and Reasoning WS Knowledge-Based Morphological Classification of Galaxies from Vision Features Devendra Singh Dhami School of Informatics and Computing Indiana University David Leake School of Informatics and Computing Indiana University Sriraam Natarajan School of Informatics and Computing Indiana University Abstract This paper presents a knowledge-based approach to the task of learning and identifying galaxies from their images. To this effect, we propose a crowd-sourced pipeline approach that employs two systems - case based and rule based systems First, the approach extracts morphological features i.e. features describing the structure of the galaxy such as its shape, central characteristics e.g., has a bar or bulge at its center) etc., using computer vision techniques. Then it employs a case based reasoning system and a rule based system to perform the classification task. Our initial results show that this pipeline is effective in learning reasonably accurate models on this complex task. Introduction We consider the task of morphological classification of galaxies from images, i.e., identifying galaxies from astronomy images. This task has been classically addressed using the machinery of standard supervised learning methods (De La Calleja and Fuentes 2004b; Goderya and Lolling 2002). While reasonably successful, most of these methods made restrictive assumptions including but not limited to, rotational/scale invariance, availability of standardized features etc. In addition, they cannot provide explanations for their conclusions. Knowledge-based approaches are a step in the direction of overcoming this restriction, as rules can express the knowledge obtained from the features in a natural way. We take a knowledge-based approach for this task. Specifically, we design two systems - first is a case-based reasoning system (CBR) and the second is a rule-based system. These systems are then employed in a pipeline where the features are obtained from an automated computer vision system. Our hypothesis, that we verify empirically, is that such a computer vision feature extraction system when coupled with the knowledge-based systems for prediction would allow for effective and efficient extraction of the galaxies from the raw images. We compare our automated system Copyright c 2017, Association for the Advancement of Artificial Intelligence ( All rights reserved. with a human annotated data set called Galaxy Zoo and demonstrate the superiority of the proposed system in this challenging task. We first present the related work in the next section. We then outline the feature extraction component which identifies the computer vision features. Next, we discuss the two knowledge-based systems in greater detail. Finally, we present our initial empirical results before concluding the paper by discussing avenues for future research. Background and Related work De La Calleja and Fuentes (2004a) developed a three-state pipeline for galaxy classification image analysis, data compression, and machine learning. They applied three learning methods, Naive Bayes, C.4.5 and Random forests, on the New General Catalog (NGC) released by the Astronomical Society of the Pacific. Their results show that random forests performed better than Naive Bayes or C4.5. Banerji et al. (2010) applied neural networks to classify images into three classes: early types, spirals, and point sources/artifacts. Their results show that the color or the shape parameters, when taken individually, are not sufficient to capture the morphological features of the galaxy. However, combining those parameters increased the accuracy remarkably. Cui et al. (2014) developed a system, where a galaxy is queried by providing a galaxy image as an input, after which the system retrieves and ranks the most similar galaxies. They made the assumption that the input images must be invariant to rotation and scale. Kasivajhula, Raghavan, and Shah (2007) compare three classical machine learning algorithms, namely, Support vector machines, Random forests and Naive Bayes in the task of galaxy classification. The galaxies are classified into 3 categories, Elliptical, Spiral and Irregular and then subdivided into 7 classifications, although the dataset considered is different from the one we consider in this paper. Rule based systems (Hayes-Roth 1985) operate by using if-then rules that are generally defined by experts. Leake (1996) contrasts this process, in which reasoning draws conclusions by chaining together generalized rules, starting 719

2 from scratch, with the reasoning from prior cases in CBR and observes that it differs in two ways: first, the general rules are replaced by specific cases and second, chaining is replaced by retrieval and adaptation of cases. Mantaras et al. (2005) provide an overview of the foundations of CBR, including various aspects such as case retrievel, reuse etc., and standard methods. Our work can be seen as building on these early ideas for the task of morphological classification. To our knowledge, although rule based expert systems have been used for this task (Heck and Murtagh 1989), case based systems have not. Thus it becomes interesting to compare the two methods. We develop a pipeline and employ a knowledge based approach with an aim to perform a comprehensive analysis on this task. Morphological Classification using Knowledge-based systems We now outline our Morphological Classification of Galaxies using Knowledge-based systems (MCG-KB) algorithm. We first present the feature extraction process before presenting the knowledge based systems that we design for this task. Feature extraction We develop six unique features for determining the characteristics of a galaxy. The images we use are colored images of size 424 x 424. The center of the galaxies are located at the center of the image as thus the need of designing position invariant feature detectors is inessential. The images are pre-processed using the following steps: the color image is first converted into grayscale, and then to a binary image. Here, manually adjusting the binarization threshold was not practical due to the nature of the images as some galaxies have sparse patterns, which got neglected during the conversion. To handle this, we applied Otsu thresholding (Otsu 1975) which adaptively adjusts the threshold. We now list each set of the features and outline the procedure of feature extraction for each set. Detecting shape: Circularity A given galaxy can be either circular, elliptical, or spiral. We detect these shapes after converting the galaxy to a binary image. Although every galaxy image has noise due to the several stars in the galaxy, if we draw contours about every shape in the image, the galaxy will be the shape with the longest contour. This allows us to calculate the area of the galaxy. Given the length of the contour about the galaxy, i.e. the length of the perimeter L, as well as the area A, we plug these values into the isoperimetric inequality: 4 π A L 2 By using this equation, we calculate a value which tells us how similar a shape is to a circle i.e. the circularity of the shape. A value of 1.0 indicates the shape is a perfect circle. As the value approaches zero, the shape is less like a circle. Although a value close to zero could be any shape, there are a limited number of shapes in the domain of shapes a galaxy may take, and thus we may assume galaxies with low values are spiral galaxies. An interim threshold value indicates an elliptical galaxy. Detecting Viewing Angle Galaxies may be viewed as either being head-on or edge-on. To understand this, consider an analogy to a frisbee that may be viewed such that it appears to be a circle when held still (head-on), or may look like a thin bar, as when it is flying in the air (edge-on). After a galaxy has been reduced to a binary image, our approach is to compare the magnitudes of the gradients in two directions, the width and height of the galaxy. In a circular galaxy, since the width and the height are approximately the same, the two gradients will be approximately the same. In a galaxy viewed edge-on, the width of the galaxy is much greater than the height of the galaxy, or vice versa. Thus, a mismatch in the gradients can be expected and rather desired. To detect the two gradients of a circular galaxy, it is enough to take the gradients in the x and y direction. However, because an edge-on galaxy might be oriented at any degree, it is necessary to consider gradients in more than two directions. In addition, it was found that simply rotating the binary image 45, and taking the x and y gradients a second time was sufficient for determining the viewing angle of a galaxy. Thus, we take the magnitude of the gradient of the binary image in the x and y directions, rotate the binary image 45, and take the magnitude of the gradient in the x and y direction again. We then use the two sets of magnitudes (x and y in the normal image, x and y in the rotated image) to identify the one that yields the greatest difference between the two magnitudes. This set allows us to determine the difference between the height and width of a galaxy at any angle. In order to generate a value for thresholding, we use the ratio of the x magnitude over the y magnitude; higher values indicate a galaxy being viewed edge-on, whereas lower values indicate a galaxy being viewed head-on. This enables us to reliably determine the viewing angle of a galaxy, and produces an angle value that tells us the general orientation of the galaxy. Detecting existence of a bulge If a galaxy is being viewed edge-on, it is possible to see whether the galaxy has a bulge about the center or not as shown in figure 1. Thus we only Figure 1: An example image where bulge can be seen search for the presence of a bulge after detecting the viewing angle of the galaxy. Once we know the orientation of the galaxy, a one-pixel wide line along the width of the binary 720

3 Figure 2: Detecting spiral arms Figure 3: Detecting tightness of spiral arms image of the galaxy is passed. If the width of the galaxy is along the x-axis, a line going from the top of the image to the bottom of the image from left to right is passed. Likewise, if the width of the galaxy is along the y-axis, a line going from the left side of the image to the right, from top to bottom is passed. If the width of the galaxy is oriented at some other angle, we use the rotated image instead of the normal image. Since galaxies are typically symmetrical perpendicular to the galaxys width, it is sufficient and computationally efficient to only pass the line across half of the width of the galaxy. As we pass the bar over the galaxy we calculate the height of the galaxy by counting the number of white pixels along the line. Our method for detecting bulges is to look for the sudden increase in the height of the galaxy over a short distance towards the center of the galaxy. In a galaxy without a bulge, we can expect the height of the galaxy to stay consistent along the full width of the galaxy. Therefore, we score a galaxy by the derivative of the height of the galaxy, applying a weight towards the center of the galaxy, and use a threshold to determine the presence of a bulge. Detecting number of spiral arms Galaxies may possess two or more arms. It is only possible to detect spiral arms on galaxies which are being viewed head-on. We first calculate the pixels which belong to a series of lines radiating from the center of a galaxy. Each line is one pixel wide and extends a set length away from the center of the galaxy. The set length is a thresholded value that is sufficient to extend beyond the limits of the galaxy. A length extending just beyond the limits of the galaxy is used to avoid wasting computation time determining the pixel values of empty space. The lines are drawn at 10 intervals about the galaxy as shown in figure 2. Then, by examining the distribution of black and white pixels along an individual line, it can be determined whether the line intersects a spiral arm. If, beginning at the point which lies in the galaxy and going outwards to the point which lies in space, a large distribution of white pixels followed by a large distribution of black pixels is seen, it can be inferred that the line does not intersect a spiral arm. If, however, a large distribution of white pixels, followed by a small distribution of black pixels, a small distribution of white pixels, then a large distribution of black pixels is seen, it can be inferred that the line intersects a spiral arm. The small distribution of black pixels is the empty space in between the galaxy and the spiral arm, and the small distribution of white pixels is the spiral arm itself. At 10 intervals, multiple lines might intersect the same spiral arm; to avoid this, we use a flag which initially assumes that a spiral arm has not been detected. Beginning at the line at 0, we check for a spiral arm. If a spiral arm exists, we modify the flag, and do not change it back until we no longer detect a spiral arm as we move through each subsequent line. Detecting the tightness of the arms For spiral galaxies, the spiral arms may be tightly wound about the galaxy, loosely bound, or somewhere in between. Our approach for detecting how tightness of the arms is very simple. We fit the smallest bounding box around the binary image of a galaxy which does not intersect the arms of the galaxy; that is, the bounding box which best fits the galaxy as shown in figure 3. Then the ratio of black pixels over white pixels within the bounding box is taken. Galaxies with tightly bounded arms will tend to have smaller bounding boxes and have a lower ratio of black pixels to white pixels, whereas galaxies with loosely bounded arms tend to have bounding boxes which extend well beyond the center of the galaxy, and thus tend to have a high ratio of black pixels over white pixels. Also, the number of spiral arms present is taken into consideration, as it is possible that a spiral galaxy with four arms might have roughly the same bounding box as a galaxy with two arms. In such a situation, the bounding box of the galaxy with four arms would contain significantly more white pixels, although it does make it difficult to set a threshold value which would work across all galaxies. Detecting existence of a bar Galaxies may have bars in their center, which emit brighter light than the rest of the galaxy. The first step in exploiting the brightness of a potential bar, is to increase the contrast of the galaxy. We first convert the RGB image into an HSV color scale since we found that contrasting the image in the HSV color scale produced better results after applying thresholding. The threshold for the bar may be set very high; we used a threshold value of 255. We then extract from the contrasted image the pixels which satisfy the threshold. After constructing a contour around the mass of bright pixels, we determine the width and height of the shape bounded by the contour. If the width is much greater than the height, a bar is present in the galaxy. The process is shown in figure

4 (a) Original image (b) Contrasted image Figure 5: Examples of cases for case based reasoning system for human data (c) Extracted countor image (d) Rotated countor Figure 4: Detecting bar in an image Class Class 1.1 Class 1.2 Class 1.1 Class 2.1 Class 2.2 Class 3.1 Class 3.2 Class 4.1 Class 4.2 Class 9.1 Class 9.2 Class 9.3 Class 10.1 Class 10.2 Class 10.3 Class 11.1 Class 11.2 Class 11.3 Class 11.4 Class 11.5 Class 11.6 Description Is the galaxy smooth Is the galaxy a disk Is the galaxy a star/artifact The galaxy can be viewed edge on The galaxy cannot be viewed edge on (thus face-on) The galaxy has a bar structure in its center The galaxy does not have a bar structure in its center The galaxy has a spiral arm pattern The galaxy does not have a spiral arm pattern The galaxy has a rounded bulge at its center The galaxy has a boxy bulge at its center The galaxy has no rounded bulge at its center The galaxy has tightly bounded arms The galaxy has medium bounded arms The galaxy has loosely bounded arms The galaxy has 1 spiral arm The galaxy has 2 spiral arms The galaxy has 3 spiral arms The galaxy has 4 spiral arms The galaxy has more than 4 spiral arms The galaxy has no spiral arms Table 1: Class description With respect to the extracted features only few of the classes from the original human classification (Willett et al. 2013) remain relevant. These classes are shown in table 1. Knowledge-based systems We implement three systems in this work, two of which are case based reasoning systems and a rule based system. One of the CBR systems uses the human data obtained from the galaxy zoo project (Lintott et al. 2008) in which the human volunteers classified the galaxies into various classes (we denote this as CBH). The other case based and the rule based systems were implemented for the features obtained from our computer vision system. We denote these systems as CBCVF and RBCVF respectively. CBH system The format of the human classified data is static. The data provides us with the galaxy id and the class names with the probabilities as stated by humans of each galaxy belonging to the certain class. We make an assumption that the galaxies classified by the humans will belong to a single class. The class to which they belong will depend on the probabilities of their subclasses. Note that by subclasses we denote the classes for the CBCVF and RBCVF systems Figure 6: Examples of rules for rule based system because of the above assumption. A sample of the data is presented in table 2. We build the cases by converting the data to the appropriate case representation. Kolodner (1993) mentions that getting a case into a representation that works is more important than deciding on a single format for all systems. Our experimentation showed that the representation for the CBH system did not perform well with the CBCVF system and thus two representations were designed. For the CBH system our cases are of the format shown in figure 5. As can be seen, in the CBH system we have explicit probabilities for all subclasses for a galaxy class. In the CBCVH system, we employ the numerical values for the parameters of every features to construct a case as shown in figure 7. Our first goal is to find the class for which the probabilities of the subclasses sum up to 1 (or close enough due to inconsistencies with floating point numbers), as this indicates a 100% probability that the galaxy will belong to that specific class. If the above goal is not satisfied, then we take the approach of finding the nearest neighbor for the case in question. We determine the case for which the distance between the new case and the case is lowest. Then we obtain the class for which the distance is lowest. RBCVF System For the rule-based system we use the computer vision features extracted as explained above. An example output from the CV system is shown in table 3. The rules consist of the complete rule number as its first part (Rule-1, Rule-2 etc.). This is necessary to model the fact that Rule 1 is related to the Rule 2 and Rule 3 to Rule 9 etc. The second part of the rule has two components: (1) the antecedent that represents the feature of the galaxies in that subclass and, (2) the consequent which contains the class number and the rule which needs to fired next for that galaxy. 722

5 Galaxy ID Class 1.1 Class 1.2 Class 1.3 Class 2.1 Class 2.2 Class 3.1 Class Table 2: Example human annotated data Image ID Shape Arm tightness Disk arms smooth/disk Edge On Bar feature Bulge not-a-spiral no-arms smooth not-viewed-edge-on no-bar no-bulge not-a-spiral loose one smooth not-viewed-edge-on bar no-bulge not-a-spiral no-arms smooth not-viewed-edge-on no-bar no-bulge spiral loose one smooth viewed-edge-on bar no-bulge spiral tight one disk viewed-edge-on bar no-bulge spiral loose four disk not-viewed-edge-on no-bar no-bulge Table 3: Extracted features from the vision system for rule based system Image ID Circularity Bulge Viewing angle Bar feature Arm tightness number of arms Table 4: Extracted features from the vision system for case based system Next, all the values for that feature are normalized by dividing the feature values with the minimum value. Finally, the nearest case to the normalized value is found to obtain the feature. After the features are obtained we can map them to the corresponding class based on the corresponding case in the case base. Figure 7: Examples of training cases for case based reasoning system Our system includes a conflict resolution component that prevents the system from firing rules whose antecedents are false. CBCVF The extracted features for the CBR system differ from the rule-based system. As shown in table 4, in contrast to the RBCVF, we employ the numerical values for the parameters of every features. This is necessary to test the ability of the system to perform automatic feature extraction. We train our CBR system with selected cases which are not among the input cases. Some of the cases are shown in Figure 7. We take two different approaches for the first three features and the last three. For the first 3 features a weight matrix is used. This consists of weights that are assigned for each features for each case. These weights are assigned according to the intuition that the new case should be near to the one of the training cases. The weights are either 1 (very near to a case in the knowledge base), 0.5 ( neither very near nor very far to a case in the knowledge base) or -1 (very far from a case in the knowledge base). Then the best case is obtained according to the weights to determine the feature. For the last 3 features we find the minimum value for a feature from the new case and all cases in the knowledge base. Experiments We aim to explicitly ask the following questions: Q1: Does the choice between these knowledge based systems matter for the task of morphological classification? Q2: Do the features extracted from our computer vision system provide as much information for the task as the human labelled data? Q3: Finally, do knowledge based system techniques provide a potential tool for astronomy tasks, specifically, the task of classification of galaxies? To this effect, we employed a data set from the SDSS database (Lintott et al. 2008). This data set contains images of the galaxies and the crowd-sourced data. We test the systems on 32 images but claim that the system can be scaled up to any number of images with none or minor modification. The output obtained by using the case based reasoning approach on the crowd sourced human data is shown in table 5. The output obtained by using the rule based approach on the data obtained from our vision system is shown in table 6. The output obtained by using the case based reasoning approach on the the data obtained from our vision system is shown in table 7. As can be seen that both the rule-based system and the CBR system identify the galaxies correctly. We take the human annotated data as the baseline for evaluation of the systems. As an example, for the galaxy id case-based system gives the following classes: Class 1.1, Class 3.2, Class 4.2, Class 9.2, Class 723

6 CBR system output Knowledge Base is empty Adding the first case to knowledge base The galaxy belongs to [ Class 6 ] The galaxy belongs to [ Class 10 ] Appending the case to KB. The galaxy belongs to [ Class 5 ] Appending the case to KB. The galaxy belongs to [ Class 1 ] Appending the case to KB. Table 5: CBR system output for human annotated data Rule based system output Class-1.1 Class-2.2 Class-3.2 Class-4.2 Class-9.2 Class Class-1.1 Class-2.2 Class-3.2 Class-4.2 Class-9.2 Class Class-1.1 Class-2.2 Class-3.1 Class-4.2 Class-9.2 Class Class-1.1 Class-2.2 Class-3.2 Class-4.2 Class-9.2 Class Class-1.2 Class-2.1 Class-3.1 Class-4.1 Class-9.2 Class-10.3 Class Class-1.2 Class-2.2 Class-3.2 Class-4.1 Class-9.2 Class-10.3 Class Class-1.2 Class-2.2 Class-3.2 Class-4.1 Class-9.2 Class-10.2 Class Class-1.2 Class-2.1 Class-3.1 Class-4.1 Class-9.2 Class-10.1 Class Class-1.2 Class-2.1 Class-3.2 Class-4.1 Class-10.3 Class Class-1.1 Class-2.2 Class-3.1 Class-4.2 Class-9.2 Class Class-1.1 Class-2.2 Class-3.2 Class-4.2 Class-9.2 Class Class-1.1 Class-2.2 Class-3.2 Class-4.2 Class-9.2 Class Class-1.2 Class-2.1 Class-3.1 Class-4.1 Class-10.3 Class Class-1.1 Class-2.2 Class-3.2 Class-4.2 Class-9.2 Class Class-1.1 Class-2.2 Class-3.2 Class-4.2 Class-9.2 Class Class-1.2 Class-2.2 Class-3.2 Class-4.1 Class-9.2 Class-10.3 Class Class-1.2 Class-2.2 Class-3.2 Class-4.1 Class-9.2 Class-10.2 Class Class-1.2 Class-2.2 Class-3.2 Class-4.1 Class-9.2 Class-10.2 Class Class-1.1 Class-2.2 Class-3.2 Class-4.2 Class-9.2 Class Class-1.1 Class-2.2 Class-3.2 Class-4.2 Class-9.2 Class Class-1.1 Class-2.1 Class-3.2 Class-4.2 Class-9.2 Class Class-1.2 Class-2.2 Class-3.2 Class-4.1 Class-9.2 Class-10.3 Class Class-1.2 Class-2.1 Class-3.2 Class-4.1 Class-10.3 Class Class-1.2 Class-2.1 Class-3.1 Class-4.1 Class-10.3 Class Class-1.1 Class-2.1 Class-3.2 Class-4.2 Class Class-1.2 Class-2.1 Class-3.2 Class-4.1 Class-9.2 Class-10.3 Class Class-1.2 Class-2.1 Class-3.2 Class-4.1 Class-10.3 Class Class-1.2 Class-2.2 Class-3.1 Class-4.1 Class-9.2 Class-10.3 Class Class-1.2 Class-2.1 Class-3.2 Class-4.1 Class-10.3 Class Class-1.1 Class-2.2 Class-3.2 Class-4.2 Class-9.2 Class Class-1.2 Class-2.1 Class-3.2 Class-4.1 Class-9.2 Class-10.3 Class Class-1.2 Class-2.1 Class-3.2 Class-4.1 Class-9.2 Class-10.3 Class-11.1 Table 6: Rule based system output for extracted features data Case based system output Class 1.1, Class 3.2, Class 4.2, Class 9.2, Class 10.2, Class Class 1.1, Class 3.2, Class 4.2, Class 9.2, Class 10.1, Class Class 1.2, Class 3.1, Class 4.1, Class 9.1, Class 10.2, Class Class 1.1, Class 2.1, Class 3.2, Class 4.2, Class 9.2, Class 10.2, Class Class 1.2, Class 2.1, Class 3.1, Class 4.1, Class 9.2, Class 10.2, Class Class 1.2, Class 3.2, Class 4.1, Class 9.2, Class 10.2, Class Class 1.1, Class 3.2, Class 4.2, Class 9.2, Class 10.2, Class Class 1.1, Class 2.1, Class 3.1, Class 4.2, Class 9.2, Class 10.1, Class Class 1.2, Class 2.1, Class 3.1, Class 4.1, Class 9.1, Class 10.3, Class Class 1.1, Class 3.1, Class 4.2, Class 9.2, Class 10.1, Class Class 1.1, Class 3.2, Class 4.2, Class 9.2, Class 10.2, Class Class 1.1, Class 3.2, Class 4.2, Class 9.2, Class 10.1, Class Class 1.2, Class 2.1, Class 3.1, Class 4.1, Class 9.2, Class 10.3, Class Class 1.1, Class 3.2, Class 4.2, Class 9.2, Class 10.2, Class Class 1.1, Class 3.2, Class 4.2, Class 9.2, Class 10.2, Class Class 1.2, Class 3.2, Class 4.1, Class 9.2, Class 10.3, Class Class 1.1, Class 3.2, Class 4.2, Class 9.1, Class 10.2, Class Class 1.2, Class 3.2, Class 4.1, Class 9.2, Class 10.2, Class Class 1.1, Class 3.2, Class 4.2, Class 9.2, Class 10.2, Class Class 1.1, Class 2.1, Class 3.2, Class 4.2, Class 9.1, Class 10.2, Class Class 1.1, Class 2.1, Class 3.2, Class 4.2, Class 9.2, Class 10.3, Class Class 1.2, Class 3.2, Class 4.1, Class 9.1, Class 10.3, Class Class 1.2, Class 2.1, Class 3.2, Class 4.1, Class 9.1, Class 10.3, Class Class 1.2, Class 2.1, Class 3.1, Class 4.1, Class 9.1, Class 10.3, Class Class 1.1, Class 2.1, Class 3.2, Class 4.2, Class 9.1, Class 10.2, Class Class 1.2, Class 2.1, Class 3.2, Class 4.1, Class 9.2, Class 10.3, Class Class 1.2, Class 2.1, Class 3.2, Class 4.1, Class 9.1, Class 10.3, Class Class 1.2, Class 2.1, Class 3.1, Class 4.1, Class 9.2, Class 10.3, Class Class 1.2, Class 2.1, Class 3.2, Class 4.1, Class 9.2, Class 10.3, Class Class 1.1, Class 2.1, Class 3.2, Class 4.2, Class 9.1, Class 10.3, Class Class 1.2, Class 2.1, Class 3.1, Class 4.1, Class 9.2, Class 10.3, Class Class 1.2, Class 2.1, Class 3.2, Class 4.1, Class 9.2, Class 10.3, Class 11.1 Table 7: CBR system output for extracted features data 10.2, Class The rule-based system for the same galaxy gives the following result: Class-1.1, Class-2.2, Class-3.2, Class-4.2, Class- 9.2, Class It can be seen clearly the results are fairly close to each other with only the Class 10.2 missing from the rule-based system and Class 2.2 missing from the case-based system. The human data classifies the galaxy into the following classes Class 1.1, Class 3.2, Class 4.2, Class 10.2 It is easy to note that the case-based system is closer to the human classification than the rule-based system. Consider another example for galaxy id The case-based system classifies it into: Class 1.2, Class 2.1, Class 3.2, Class 4.1, Class 9.2, Class 10.3, Class whereas the rule-based system outputs: Class-1.2, Class-2.1, Class-3.2, Class-4.1, Class- 9.2, Class-10.3, Class The human data classifies the galaxy into the following classes Class 1.2, Class 2.1, Class 3.2, Class 4.1, Class 9.2, Class 10.3 As can be seen from the results, both the rule-based and the case-based systems perform almost the same. This helps us in answering Q1 clearly. The choice of the knowledge based system choice does not seem to matter for the task of morphological classification although we can see that the case based system performs slightly better. The results show that our knowledge based systems classify the galaxies into all the classes as the humans for all galaxies tested and some extra classes. Since human labellers cannot be considered perfect and the extra classes are related to the previous classification. Given that both systems exhibit similar performance to the human labelled data we can answer Q2 affirmatively, that is, the extracted vision features provide enough information to identify the galaxies correctly. Also the initial results helps us in answering Q3 positively. Knowledge based system techniques do provide a potential tool for astronomy tasks, and are worthy of additional study for such domains. Conculsion We considered the problem of classifying galaxy images and constructed three knowledge based systems. Our initial results show our MCG-KB algorithm can indeed identify the galaxies robustly and comparatively to the human classification. An interesting insight that we obtained from our experiments is that the choice of the knowledge based system did not significantly affect the performance. Extending these systems to a larger set of images remains an important research direction. Dhami (2015) has defined a larger set of features for the dataset. Using these features in the knowledge based systems remains a challenge. Marling et al. (2002) focuses primarily on systems that simultaneously use both case-based and rule-based methods (to mutu- 724

7 ally support a single process), and this integrated approach, or integrations with other methods, might be a potential future research area. References Banerji, M.; Lahav, O.; Lintott, C. J.; Abdalla, F. B.; Schawinski, K.; Bamford, S. P.; Andreescu, D.; Murray, P.; Raddick, M. J.; Slosar, A.; et al Galaxy zoo: reproducing galaxy morphologies via machine learning. Monthly Notices of the Royal Astronomical Society 406(1): Cui, Y.; Xiang, Y.; Rong, K.; Feris, R.; and Cao, L A spatial-color layout feature for content-based galaxy image retrieval. In IEEE Winter Conference on Applications of Computer Vision (WACV). De La Calleja, J., and Fuentes, O. 2004a. Automated classification of galaxy images. In International Conference on Knowledge-Based and Intelligent Information and Engineering Systems, Springer. De La Calleja, J., and Fuentes, O. 2004b. Machine learning and image analysis for morphological galaxy classification. Monthly Notices of the Royal Astronomical Society 349(1): De Mantaras, R. L.; McSherry, D.; Bridge, D.; Leake, D.; Smyth, B.; Craw, S.; Faltings, B.; Maher, M. L.; T COX, M.; Forbus, K.; et al Retrieval, reuse, revision and retention in case-based reasoning. The Knowledge Engineering Review 20(03): Dhami, D. S Morphological Classification of galaxies into spirals and non-spirals. Ph.D. Dissertation, Indiana University. Goderya, S. N., and Lolling, S. M Morphological classification of galaxies using computer vision and artificial neural networks: A computational scheme. Astrophysics and space science 279(4): Hayes-Roth, F Rule-based systems. Communications of the ACM 28(9): Heck, A., and Murtagh, F Knowledge-based systems in astronomy. In Knowledge Based Systems in Astronomy, volume 329. Kasivajhula, S.; Raghavan, N.; and Shah, H Morphological galaxy classification using machine learning. Monthly Notices of the Royal Astronomical Society 8:1 8. Kolodner, J Case-based reasoning. Morgan Kaufmann. Leake, D Cbr in context: the present and future. case based reasoning experiences-lessons and future experiences. d. leake. Lintott, C. J.; Schawinski, K.; Slosar, A.; Land, K.; Bamford, S.; Thomas, D.; Raddick, M. J.; Nichol, R. C.; Szalay, A.; Andreescu, D.; et al Galaxy zoo: morphologies derived from visual inspection of galaxies from the sloan digital sky survey. Monthly Notices of the Royal Astronomical Society 389(3): Marling, C.; Sqalli, M.; Rissland, E.; Muñoz-Avila, H.; and Aha, D Case-based reasoning integrations. AI magazine 23(1):69. Otsu, N A threshold selection method from graylevel histograms. Automatica 11( ): Willett, K. W.; Lintott, C. J.; Bamford, S. P.; Masters, K. L.; Simmons, B. D.; Casteels, K. R.; Edmondson, E. M.; Fortson, L. F.; Kaviraj, S.; Keel, W. C.; et al Galaxy zoo 2: detailed morphological classifications for galaxies from the sloan digital sky survey. Monthly Notices of the Royal Astronomical Society stt