# Positron Emission Tomography Image Segmentation Based on [PERSON]'s Intuitionistic Fuzzy Sets
## 1 Introduction  
Segmentation of digital images is the procedure of partitioning an image into disjoint parts, regions, classes, or subsets so that every part must fulfill an unmistakable and very characterized property and attribute. Image segmentation is an essential step towards the analysis of image information. Image segmentation plays an important role in digital image processing and is used in almost every field of science; for example, digital image processing, satellite imaging, computer vision, biometrics, medical images and other [1, 2, 3, 4, 5, 6, 7].  
In this work, we use image segmentation to detect and delineate tumors in PET images.  
Positron emission tomography, or PET, is a technique for the imaging of physiological processes in humans. This technique presents the distribution of a radioactive emitter monitored by surrounding detectors. With the aid of mathematical algorithms, the image is constructed based on the distribution of the marker. PET has become an indispensable tool to ensure more accurate treatment of patients and early diagnosis for the treatment of cancer [8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. PET is heavily used in medicine, biology, neurology, and pharmaceutical research of brain activity, blood, or glucose.  
PET images are known for their high sensitivity and low spatial resolution. Furthermore, PET images have low signal-to-noise ratios and suffer from noise caused by random and scattered coincidences. With these conditions, the difficulties for a successful image segmentation increase [9, 18, 19, 20, 21, 22, 23, 24, 25]. The delineation of tumors in PET images is a crucial step because the determination of this boundary should be kept as small as possible to minimizedamage to healthy tissue by future treatments, but the boundary must ensure the inclusion of the entire extent of the diseased tissue. Different methods have been proposed using several segmentation techniques [26; 27; 28; 29; 30]. Fixed threshold methods do not find a consensus value to correctly delineate the tumor [3; 11]; adaptive threshold methods have better results, but most of the times the results depend on standardized uptake values (SUV) [20; 31; 32; 33] or source-to-background ratio (SBR) [23; 34; 35] values, and these values are not always available; the iterative threshold methods depend on knowing ground truth metrics or limiting the number of iterations, which can change the output values [23; 36]. The best region-based methods are region of interest (ROI)- or seed-dependent, and edge-based methods do not have good results because of the faded image edges, caused by the noisy characteristic of PET images. Stochastic-based methods with very different approaches presented several results [22; 37; 38; 39; 40]. The use of deep learning-based methods is limited both by the problem's nature (precision of the delineation) and the number of labeled samples needed. Nevertheless, some deep learning-based methods have also been recently proposed [41; 42; 43].  
We will introduce a new approach to PET image segmentation, using an iterative thresholding method based on [PERSON]'s intuitionistic fuzzy sets (A-IFSs). Hereupon, the presented algorithm finds and delineates tumors in PET images in a non-supervised way. The method is invariant to the images size, seeds position, region shape, and SUV or SBR values, resulting in a better and more efficient tumor delineation procedure.