arXiv subjects

Mehmet Turan

Publications and source records attributed to Mehmet Turan.

At least 19 recordsLinked to original sources

arXiv2024

The impact of the limit $q$-Durrmeyer operator on continuous functions

The limit $q$-Durrmeyer operator, $D_{\infty,q},$ was introduced and its approximation properties were investigated by V. Gupta in 2008 during a study of $q$-analogues for the Bernstein-Durrmeyer operator. In the present work, this operator is investigated from a different perspective. More precisely, the growth estimates are derived for the entire functions comprising the range of $D_{\infty,q}$. The interrelation between the analytic properties of a function $f$ and the rate of growth for $D_{\infty,q}f$ are established, and the sharpness of the obtained results are demonstrated.

math.CV↗

arXiv2021

Deep Learning-based Frozen Section to FFPE Translation

Frozen sectioning (FS) is the preparation method of choice for microscopic evaluation of tissues during surgical operations. The high speed of the procedure allows pathologists to rapidly assess the key microscopic features, such as tumour margins and malignant status to guide surgical decision-making and minimise disruptions to the course of the operation. However, FS is prone to introducing many misleading artificial structures (histological artefacts), such as nuclear ice crystals, compression, and cutting artefacts, hindering timely and accurate diagnostic judgement of the pathologist. Additional training and prolonged experience is often required to make highly effective and time-critical diagnosis on frozen sections. On the other hand, the gold standard tissue preparation technique of formalin-fixation and paraffin-embedding (FFPE) provides significantly superior image quality, but is a very time-consuming process (12-48 hours), making it unsuitable for intra-operative use. In this paper, we propose an artificial intelligence (AI) method that improves FS image quality by computationally transforming frozen-sectioned whole-slide images (FS-WSIs) into whole-slide FFPE-style images in minutes. AI-FFPE rectifies FS artefacts with the guidance of an attention mechanism that puts a particular emphasis on artefacts while utilising a self-regularization mechanism established between FS input image and synthesized FFPE-style image that preserves clinically relevant features. As a result, AI-FFPE method successfully generates FFPE-style images without significantly extending tissue processing time and consequently improves diagnostic accuracy. We demonstrate the efficacy of AI-FFPE on lung and brain frozen sections using a variety of different qualitative and quantitative metrics including visual Turing tests from 20 board certified pathologists.

eess.IV↗

arXiv2021

VR-Caps: A Virtual Environment for Capsule Endoscopy

Current capsule endoscopes and next-generation robotic capsules for diagnosis and treatment of gastrointestinal diseases are complex cyber-physical platforms that must orchestrate complex software and hardware functions. The desired tasks for these systems include visual localization, depth estimation, 3D mapping, disease detection and segmentation, automated navigation, active control, path realization and optional therapeutic modules such as targeted drug delivery and biopsy sampling. Data-driven algorithms promise to enable many advanced functionalities for capsule endoscopes, but real-world data is challenging to obtain. Physically-realistic simulations providing synthetic data have emerged as a solution to the development of data-driven algorithms. In this work, we present a comprehensive simulation platform for capsule endoscopy operations and introduce VR-Caps, a virtual active capsule environment that simulates a range of normal and abnormal tissue conditions (e.g., inflated, dry, wet etc.) and varied organ types, capsule endoscope designs (e.g., mono, stereo, dual and 360°camera), and the type, number, strength, and placement of internal and external magnetic sources that enable active locomotion. VR-Caps makes it possible to both independently or jointly develop, optimize, and test medical imaging and analysis software for the current and next-generation endoscopic capsule systems. To validate this approach, we train state-of-the-art deep neural networks to accomplish various medical image analysis tasks using simulated data from VR-Caps and evaluate the performance of these models on real medical data. Results demonstrate the usefulness and effectiveness of the proposed virtual platform in developing algorithms that quantify fractional coverage, camera trajectory, 3D map reconstruction, and disease classification.

cs.CV↗

arXiv2020

EndoSLAM Dataset and An Unsupervised Monocular Visual Odometry and Depth Estimation Approach for Endoscopic Videos: Endo-SfMLearner

Deep learning techniques hold promise to develop dense topography reconstruction and pose estimation methods for endoscopic videos. However, currently available datasets do not support effective quantitative benchmarking. In this paper, we introduce a comprehensive endoscopic SLAM dataset consisting of 3D point cloud data for six porcine organs, capsule and standard endoscopy recordings as well as synthetically generated data. A Panda robotic arm, two commercially available capsule endoscopes, two conventional endoscopes with different camera properties, and two high precision 3D scanners were employed to collect data from 8 ex-vivo porcine gastrointestinal (GI)-tract organs. In total, 35 sub-datasets are provided with 6D pose ground truth for the ex-vivo part: 18 sub-dataset for colon, 12 sub-datasets for stomach and 5 sub-datasets for small intestine, while four of these contain polyp-mimicking elevations carried out by an expert gastroenterologist. Synthetic capsule endoscopy frames from GI-tract with both depth and pose annotations are included to facilitate the study of simulation-to-real transfer learning algorithms. Additionally, we propound Endo-SfMLearner, an unsupervised monocular depth and pose estimation method that combines residual networks with spatial attention module in order to dictate the network to focus on distinguishable and highly textured tissue regions. The proposed approach makes use of a brightness-aware photometric loss to improve the robustness under fast frame-to-frame illumination changes. To exemplify the use-case of the EndoSLAM dataset, the performance of Endo-SfMLearner is extensively compared with the state-of-the-art. The codes and the link for the dataset are publicly available at https://github.com/CapsuleEndoscope/EndoSLAM. A video demonstrating the experimental setup and procedure is accessible through https://www.youtube.com/watch?v=G_LCe0aWWdQ.

cs.CV↗

arXiv2020

SelfVIO: Self-Supervised Deep Monocular Visual-Inertial Odometry and Depth Estimation

In the last decade, numerous supervised deep learning approaches requiring large amounts of labeled data have been proposed for visual-inertial odometry (VIO) and depth map estimation. To overcome the data limitation, self-supervised learning has emerged as a promising alternative, exploiting constraints such as geometric and photometric consistency in the scene. In this study, we introduce a novel self-supervised deep learning-based VIO and depth map recovery approach (SelfVIO) using adversarial training and self-adaptive visual-inertial sensor fusion. SelfVIO learns to jointly estimate 6 degrees-of-freedom (6-DoF) ego-motion and a depth map of the scene from unlabeled monocular RGB image sequences and inertial measurement unit (IMU) readings. The proposed approach is able to perform VIO without the need for IMU intrinsic parameters and/or the extrinsic calibration between the IMU and the camera. estimation and single-view depth recovery network. We provide comprehensive quantitative and qualitative evaluations of the proposed framework comparing its performance with state-of-the-art VIO, VO, and visual simultaneous localization and mapping (VSLAM) approaches on the KITTI, EuRoC and Cityscapes datasets. Detailed comparisons prove that SelfVIO outperforms state-of-the-art VIO approaches in terms of pose estimation and depth recovery, making it a promising approach among existing methods in the literature.

cs.CV↗

arXiv2020

EndoL2H: Deep Super-Resolution for Capsule Endoscopy

Although wireless capsule endoscopy is the preferred modality for diagnosis and assessment of small bowel diseases, the poor camera resolution is a substantial limitation for both subjective and automated diagnostics. Enhanced-resolution endoscopy has shown to improve adenoma detection rate for conventional endoscopy and is likely to do the same for capsule endoscopy. In this work, we propose and quantitatively validate a novel framework to learn a mapping from low-to-high resolution endoscopic images. We combine conditional adversarial networks with a spatial attention block to improve the resolution by up to factors of 8x, 10x, 12x, respectively. Quantitative and qualitative studies performed demonstrate the superiority of EndoL2H over state-of-the-art deep super-resolution methods DBPN, RCAN and SRGAN. MOS tests performed by 30 gastroenterologists qualitatively assess and confirm the clinical relevance of the approach. EndoL2H is generally applicable to any endoscopic capsule system and has the potential to improve diagnosis and better harness computational approaches for polyp detection and characterization. Our code and trained models are available at https://github.com/CapsuleEndoscope/EndoL2H.

cs.CV↗

arXiv2020

Milli-RIO: Ego-Motion Estimation with Low-Cost Millimetre-Wave Radar

Robust indoor ego-motion estimation has attracted significant interest in the last decades due to the fast-growing demand for location-based services in indoor environments. Among various solutions, frequency-modulated continuous-wave (FMCW) radar sensors in millimeter-wave (MMWave) spectrum are gaining more prominence due to their intrinsic advantages such as penetration capability and high accuracy. Single-chip low-cost MMWave radar as an emerging technology provides an alternative and complementary solution for robust ego-motion estimation, making it feasible in resource-constrained platforms thanks to low-power consumption and easy system integration. In this paper, we introduce Milli-RIO, an MMWave radar-based solution making use of a single-chip low-cost radar and inertial measurement unit sensor to estimate six-degrees-of-freedom ego-motion of a moving radar. Detailed quantitative and qualitative evaluations prove that the proposed method achieves precisions on the order of few centimeters for indoor localization tasks.

eess.SP↗

arXiv2019

ModelHub.AI: Dissemination Platform for Deep Learning Models

Recent advances in artificial intelligence research have led to a profusion of studies that apply deep learning to problems in image analysis and natural language processing among others. Additionally, the availability of open-source computational frameworks has lowered the barriers to implementing state-of-the-art methods across multiple domains. Albeit leading to major performance breakthroughs in some tasks, effective dissemination of deep learning algorithms remains challenging, inhibiting reproducibility and benchmarking studies, impeding further validation, and ultimately hindering their effectiveness in the cumulative scientific progress. In developing a platform for sharing research outputs, we present ModelHub.AI (www.modelhub.ai), a community-driven container-based software engine and platform for the structured dissemination of deep learning models. For contributors, the engine controls data flow throughout the inference cycle, while the contributor-facing standard template exposes model-specific functions including inference, as well as pre- and post-processing. Python and RESTful Application programming interfaces (APIs) enable users to interact with models hosted on ModelHub.AI and allows both researchers and developers to utilize models out-of-the-box. ModelHub.AI is domain-, data-, and framework-agnostic, catering to different workflows and contributors' preferences.

cs.LG↗

arXiv2019

On the q-moment determinacy of probability distributions

Given $0<q<1,$ every absolutely continuous distribution can be described in two different ways: in terms of a probability density function and also in terms of a $q$-density. Correspondingly, it has a sequence of moments and a sequence of $q$-moments if those exist. In this article, new conditions on the $q$-moment determinacy of probability distributions are derived. In addition, results related to the comparison of the properties of probability distributions with respect to the moment and $q$-moment determinacy are presented.

math.PR↗

arXiv2019

Discrete Stieltjes classes for log-Heine type distributions

The Stieltjes classes play a significant role in the moment problem since they permit to expose an infinite family of probability distributions all having equal moments of all orders. Given a moment-indeterminate distribution, it may not be easy to indicate another distribution with the same moments. Mostly, the Stieltjes classes have been considered for absolutely continuous distributions. In this work, a new approach for constructing them in the discrete case is presented. Examples for some widely used discrete distributions are provided.

math.PR↗

arXiv2019

Power Lindley distribution and software metrics

The Lindley distribution and its numerous generalizations are widely used in statistical and engineering practice. Recently, a power transformation of Lindley distribution, called the power Lindley distribution, has been introduced by M. E. Ghitany et al., who initiated the investigation of its properties and possible applications. In this article, new results on the power Lindley distribution are presented. The focus of this work is on the moment-(in)determinacy of the distribution for various values of the parameters. Afterwards, certain applications are provided to describe data sets of software metrics.

math.ST↗

arXiv2019

q-Stieltjes classes for some families of q-distributions

The Stieltjes classes play a significant role in the moment problem allowing to exhibit explicitly an infinite family of probability densities with the same sequence of moments. In this paper, the notion of $q$-moment determinacy/indeterminacy is proposed and some conditions for a distribution to be either $q$-moment determinate or indeterminate in terms of its $q$-density have been obtained. Also, a $q$-analogue of Stieltjes classes is defined for $q$-distributions and $q$-Stieltjes classes have been constructed for a family of $q$-densities of $q$-moment indeterminate distributions.

math.PR↗

arXiv2018

Uncorrelatedness sets of discrete uniform distributions via Vandermonde-type determinants

Given random variables $X$ and $Y$ having finite moments of all orders, their uncorrelatedness set is defined as the set of all pairs $(j,k)\in{\mathbb N}^2,$ for which $X^j$ and $Y^k$ are uncorrelated. It is known that, broadly put, any subset of ${\mathbb N}^2$ can serve as an uncorrelatedness set. This claim ceases to be true for random variables with prescribed distributions, in which case the need arises so as to identify the admissible uncorrelatedness sets. This paper studies the uncorrelatedness sets for positive random variables uniformly distributed on three points. Some general features of these sets are derived. Two related Vandermonde-type determinants are examined and applied to describe uncorrelatedness sets in specific cases.

math.PR↗

arXiv2018

On the invariant manifolds of the fixed point of a second order nonlinear difference equation

This paper addresses the asymptotic approximations of the stable and unstable manifolds for the saddle fixed point and the 2-periodic solutions of the difference equation $x_{n+1} = α+ βx_{n-1}+x_{n-1}/x_{n},$ where $α>0,$ $0\leqslant β<1$ and the initial conditions $x_{-1}$ and $x_0$ are positive numbers. These manifolds determine completely global dynamics of this equation. The theoretical results are supported by some numerical examples.

math.DS↗

arXiv2018

Unsupervised Odometry and Depth Learning for Endoscopic Capsule Robots

In the last decade, many medical companies and research groups have tried to convert passive capsule endoscopes as an emerging and minimally invasive diagnostic technology into actively steerable endoscopic capsule robots which will provide more intuitive disease detection, targeted drug delivery and biopsy-like operations in the gastrointestinal(GI) tract. In this study, we introduce a fully unsupervised, real-time odometry and depth learner for monocular endoscopic capsule robots. We establish the supervision by warping view sequences and assigning the re-projection minimization to the loss function, which we adopt in multi-view pose estimation and single-view depth estimation network. Detailed quantitative and qualitative analyses of the proposed framework performed on non-rigidly deformable ex-vivo porcine stomach datasets proves the effectiveness of the method in terms of motion estimation and depth recovery.

cs.RO↗

arXiv2018

Magnetic-Visual Sensor Fusion-based Dense 3D Reconstruction and Localization for Endoscopic Capsule Robots

Reliable and real-time 3D reconstruction and localization functionality is a crucial prerequisite for the navigation of actively controlled capsule endoscopic robots as an emerging, minimally invasive diagnostic and therapeutic technology for use in the gastrointestinal (GI) tract. In this study, we propose a fully dense, non-rigidly deformable, strictly real-time, intraoperative map fusion approach for actively controlled endoscopic capsule robot applications which combines magnetic and vision-based localization, with non-rigid deformations based frame-to-model map fusion. The performance of the proposed method is demonstrated using four different ex-vivo porcine stomach models. Across different trajectories of varying speed and complexity, and four different endoscopic cameras, the root mean square surface reconstruction errors 1.58 to 2.17 cm.

cs.RO↗

arXiv2018

The distance between two limit $q$-Bernstein operators

For $q\in(0,1),$ let $B_q$ denote the limit $q$-Bernstein operator. In this paper, the distance between $B_q$ and $B_r$ for distinct $q$ and $r$ in the operator norm on $C[0,1]$ is estimated, and it is proved that $1\leqslant \|B_q-B_r\|\leqslant 2,$ where both of the equalities can be attained. To elaborate more, the distance depends on whether or not $r$ and $q$ are rational powers of each other. For example, if $r^j\neq q^m$ for all $j,m\in \mathbb{N},$ then $\|B_q-B_r\|=2,$ and if $r=q^m, m\in \mathbb{N},$ then $\|B_q-B_r\|=2(m-1)/m.$

math.FA↗

arXiv2017

Magnetic-Visual Sensor Fusion based Medical SLAM for Endoscopic Capsule Robot

A reliable, real-time simultaneous localization and mapping (SLAM) method is crucial for the navigation of actively controlled capsule endoscopy robots. These robots are an emerging, minimally invasive diagnostic and therapeutic technology for use in the gastrointestinal (GI) tract. In this study, we propose a dense, non-rigidly deformable, and real-time map fusion approach for actively controlled endoscopic capsule robot applications. The method combines magnetic and vision based localization, and makes use of frame-to-model fusion and model-to-model loop closure. The performance of the method is demonstrated using an ex-vivo porcine stomach model. Across four trajectories of varying speed and complexity, and across three cameras, the root mean square localization errors range from 0.42 to 1.92 cm, and the root mean square surface reconstruction errors range from 1.23 to 2.39 cm.

cs.CV↗