# Evaluation of Metamorphic Testing for Edge Detection in MRI Brain Diagnostics
## 1 Introduction  
In the medical field, ultrasound, X-ray, computed tomography (CT) scans, positron emission tomography (PET) scans, and magnetic resonance imaging (MRI) are the important sources of digital images used in diagnostic decision-support systems. MRI is one of the most powerful diagnostic tools among modern-day clinical testing devices, while offering highly sophisticated research prospects and studies of physiological processes. However, it is also perceived as a not-so-accurate and cost-intensive method which is an important driver of the errors in diagnostics [1]. The contrast configuration is one the most lethal contributing factor of radiology error (MRI related misdiagnosis) for identifying abnormalities or to correctly interpret them [2]. Thus, there is a crucial need to improve its effectiveness in terms of clinical outcomes, within the context of noninvasive diagnosis and minimally invasive therapy. Nowadays, machine learning and, in particular, deep learning approaches are frequently used for automated diagnosis from medical images (MRI, CT Scan, ultrasound, etc.). This process involves an important step of edge detection in the images. Edge detection is a very meticulous process that serves as a chief tool for the detection of edges in the image with variations in its luminosity or incoherence [3]. There are different conventional edge detection algorithms such as Canny, Sobel, Prewitt, Robert, etc. for the detection of edges. A review of the literature shows that deep learning approaches have been used primarily in image-based diagnosis, and not for edge detection. However, in a few approaches, deep learning has been used as a preprocessing step prior to edge detection to improve the accuracy of edge detection. In this paper, our focus is on evaluation of metamorphic testingfor edge detection algorithm. For this purpose, we have selected enhanced Canny edge detection algorithm given in [4]. In general, error-prone software systems can cause massive disaster. Software system testing is a fundamental approach to identify the bugs in implementation under test (IUT) to check whether the system meets its specification or not [5]. Therefore, it is imperative to reckon the reliability and consistency of these systems through dependable testing [6]. More complex software systems such as IPAs are playing a vital role in our daily lives in various areas such as medical imaging, surveillance, biometrics, etc. These IPAs are handling large amounts of data to produce multifaceted outputs [7]. As compared to the conventional software-testing, the software-testing of IPA is very resource intensive because IPA is tested manually. Many complex images, used as inputs for testing, must be generated and the expected outputs of the testing must be determined to gauge the conclusions of the testing of IPA [8]. Complex visual semantics of the images used make the testing of IPA quite challenging, such as sometimes it is difficult to produce the expected output from the selected test case [7] called the _test oracle problem_, which is a mechanism to determine the ability to distinguish between correct and incorrect behavior of the system under test for a given input [9]. Usually, the testers use input images that can be handcrafted or have well-defined expected output results [10]. The results of testing using handcrafted images are easily predictable and limited to the selection of input images made. There are different methods to alleviate the test oracle problem in IPAs such as Pseudo-Oracle, Partial-Oracle, and metamorphic testing (MT). Among these three methods, MT is widely used to deal with the applications that have the test oracle problem for which it is very difficult to predict the output correctly when an arbitrary input has been given to the system [11]. In MT, source test cases are generated through traditional test case generation techniques. New test cases known as follow-up test cases are generated from source test cases using metamorphic relations.