Average Euclidean Distance Research Articles

Towards a massive sentinel-2 LAI time-series production using 2-D convolutional networks

Biophysical parameters and more specifically the leaf area index provide an absolute quantification of the biomass of vegetation allowing an overview of the development status of a plant. However, the estimation of the leaf area index requires sophisticated and complex algorithms. This paper proposes a new procedure to estimate the leaf area index using Sentinel-2 data. The proposed procedure relies on the 2-D convolutional network known as the UNet algorithm for regression. The architecture of the UNet algorithm is adapted to account for the processing of large chunks of Sentinel-2 data. Moreover, the adopted procedure makes use of the dropout as a Bayesian approximation at the inference step in order to allow estimating the algorithm confidence interval, which is a very important quality indicator for the production of biophysical parameters. The proposed procedure is validated on multiple Sentinel-2 tiles and years and compared to the multilayer perceptron algorithm and the Sentinel Application Platform of the European Space Agency, also known as SNAP. The UNet and multilayer perceptron algorithms provide coherent results when compared to the results obtained using the SNAP software with an average correlation of 0.99 for both algorithms. However, the UNet algorithm provides better results in terms of average Euclidean distance, mean squared error and R2 score. One main advantage of the UNet algorithm is the vast reduction of inference time when compared to the SNAP software and the multilayer perceptron regressor. The estimation of the leaf area index of a Sentinel-2 tile at 20 m requires 18 s, 13.5 min and 15 min using the UNet, multilayer perceptron and SNAP, respectively. This advantage allows a massive production of temporal sequences of leaf area index based on Sentinel-2 images. Furthermore, experiments conducted on multiple crop types prove that the proposed approach can serve as a generic procedure to estimate the leaf area index regardless of the crop type.

An Efficient Estimation of the Number of Optimal Iterations for GS Pre-coding in Downlink Massive MIMO Systems

This paper proposes an estimation scheme of the number iterations for optimal Gauss–Seidel (GS) pre-coding in the downlink massive multiple input multiple output (MIMO) systems for the first time. The number of iterations in GS pre-coding is one of the key parameters and should be estimated accurately prior to signal transmission in the downlink systems. For efficient estimation without presentations of the closed-form solution for the GS pre-coding symbols, the proposed estimation scheme uses the relative method which calculates the normalized Euclidean distance (NED) between consecutive GS solutions by using the property of the monotonic decrease function of the GS solutions. Additionally, an efficient initial solution for the GS pre-coding is proposed as a two term Neumann series (NS) based on the stair matrix for improving the accuracy of estimation and accelerating the convergence rate of the GS solution. The evaluated estimation performances verify high accuracy in the downlink massive MIMO systems even in low loading factors. In addition, an additional complexity for estimating the number of the optimal iterations is nearly negligible.

Highly Accurate Scale Estimation from Multiple Keyframes Using RANSAC Plane Fitting With a Novel Scoring Method

Due to the projective nature of a single camera, monocular visual simultaneous localization and mapping (vSLAM) algorithms suffer from scale drift. Recent studies have addressed the scale drift by estimating the height of the camera from the fitted ground plane. However, the low accuracy of 3D ground point (3DGP) reconstruction and the insufficient number of 3DGPs from the textureless ground region make the fitted plane inaccurate for scale estimation. In this paper, we introduce a novel accuracy measure of the fitted plane. From the previous keyframe, we first obtain the 3D points from the intersection of the fitted plane with a ray passing through the camera center and the 2D feature points on the ground region. We then transform the 3D points and 2D feature points to the current keyframe using their respective planar homography. Finally, we project the transformed 3D points onto the image plane of the current keyframe and measure the average Euclidean distance between the projected points and the transformed feature points. The proposed method achieves the average translation error of 1.03% on the KITTI dataset, which outperforms the state-of-the-art monocular vSLAM methods.

Condition Monitoring Method for Automatic Transmission Clutches

This paper presents the development of a condition monitoring method for wet friction clutches which might be useful for automatic transmission applications. The method is developedbased on quantifying the change of the relative rotational velocity signal measured between the input and output shaft of a clutch. Prior to quantifying the change, the raw velocity signal is preprocessed to capture the relative velocity signal of interest. Three dimensionless parameters, namely the normalized engagement duration, the normalized Euclidean distance and the spectral angle mapper distance, that can be easily extracted from the signal of interest are proposed in this paper to quantify the change. In order to experimentally evaluate and verify the potential of the proposed method, clutches’ life data obtained by conducting accelerated life tests on some commercial clutches with different lining friction materials using a fully instrumented SAE#2 test setup, are utilized for this purpose. The aforementioned parameters extracted from the experimental data clearly exhibit progressive changes during the clutch service life and are well correlated with the evolution of the mean coefficient of friction (COF), which can be seen as a reference feature. Hence, the quantities proposed in this paper can therefore be seen as principle features that may enable us to monitor and assess the condition of wet friction clutches.

A low-density SNP genotyping panel for the accurate prediction of cattle breeds

Genomic tools to better define breed composition in agriculturally important species have sparked scientific and commercial industry interest. Knowledge of breed composition can inform multiple scientifically important decisions of industry application including DNA marker-assisted selection, identification of signatures of selection, and inference of product provenance to improve supply chain integrity. Genomic tools are expensive but can be economized by deploying a relatively small number of highly informative single-nucleotide polymorphisms (SNP) scattered evenly across the genome. Using resources from the 1000 Bull Genomes Project we established calibration (more stringent quality criteria; N = 1,243 cattle) and validation (less stringent; N = 864) data sets representing 17 breeds derived from both taurine and indicine bovine subspecies. Fifteen successively smaller panels (from 500,000 to 50 SNP) were built from those SNP in the calibration data that increasingly satisfied 2 criteria, high differential allele frequencies across the breeds as measured by average Euclidean distance (AED) and high uniformity (even spacing) across the physical genome. Those SNP awarded the highest AED were in or near genes previously identified as important signatures of selection in cattle such as LCORL, NCAPG, KITLG, and PLAG1. For each panel, the genomic breed composition (GBC) of each animal in the validation dataset was estimated using a linear regression model. A systematic exploration of the predictive accuracy of the various sized panels was then undertaken on the validation population using 3 benchmarking approaches: (1) % error (expressed relative to the estimated GBC made from over 1 million SNP), (2) % breed misassignment (expressed relative to each individual's breed recorded), and (3) Shannon's entropy of estimated GBC across the 17 target breeds. Our analyses suggest that a panel of just 250 SNP represents an adequate balance between accuracy and cost-only modest gains in accuracy are made as one increases panel density beyond this point.

Inspection by exception: A new machine learning-based approach for multistage manufacturing

Manufacturing processes usually consist of multiple different stages, each of which is influenced by a multitude of factors. Therefore, variations in product quality at a certain stage are contributed to by the errors generated at the current, as well as preceding, stages. The high cost of each production stage in the manufacture of high-quality products has stimulated a drive towards decreasing the volume of non-added value processes such as inspection. This paper presents a new method for what the authors have referred to as ‘inspection by exception’ – the principle of actively detecting and then inspecting only the parts that cannot be categorized as healthy or unhealthy with a high degree of certainty. The key idea is that by inspecting only those parts that are in the corridor of uncertainty, the volume of inspections are considerably reduced. This possibility is explored using multistage manufacturing data and both unsupervised and supervised learning algorithms. A case study is presented whereby material conditions and time domain features for force, vibration and tempering temperature are used as input data. Fuzzy C-Means (FCM) clustering is implemented to achieve inspection by exception in an unsupervised manner based on the normalized Euclidean distances between the principal components and cluster centres. Also, deviation vectors for product health are obtained using a comparator system to train neural networks for supervised learning-based inspection by exception. It is shown that the volume of inspections can be reduced by as much as 82% and 93% using the unsupervised and supervised learning approaches, respectively.

AGE challenge: Angle Closure Glaucoma Evaluation in Anterior Segment Optical Coherence Tomography.

Angle closure glaucoma (ACG) is a more aggressive disease than open-angle glaucoma, where the abnormal anatomical structures of the anterior chamber angle (ACA) may cause an elevated intraocular pressure and gradually lead to glaucomatous optic neuropathy and eventually to visual impairment and blindness. Anterior Segment Optical Coherence Tomography (AS-OCT) imaging provides a fast and contactless way to discriminate angle closure from open angle. Although many medical image analysis algorithms have been developed for glaucoma diagnosis, only a few studies have focused on AS-OCT imaging. In particular, there is no public AS-OCT dataset available for evaluating the existing methods in a uniform way, which limits progress in the development of automated techniques for angle closure detection and assessment. To address this, we organized the Angle closure Glaucoma Evaluation challenge (AGE), held in conjunction with MICCAI 2019. The AGE challenge consisted of two tasks: scleral spur localization and angle closure classification. For this challenge, we released a large dataset of 4800 annotated AS-OCT images from 199 patients, and also proposed an evaluation framework to benchmark and compare different models. During the AGE challenge, over 200 teams registered online, and more than 1100 results were submitted for online evaluation. Finally, eight teams participated in the onsite challenge. In this paper, we summarize these eight onsite challenge methods and analyze their corresponding results for the two tasks. We further discuss limitations and future directions. In the AGE challenge, the top-performing approach had an average Euclidean Distance of 10 pixels (10µm) in scleral spur localization, while in the task of angle closure classification, all the algorithms achieved satisfactory performances, with two best obtaining an accuracy rate of 100%. These artificial intelligence techniques have the potential to promote new developments in AS-OCT image analysis and image-based angle closure glaucoma assessment in particular.

Accuracy assessment of a novel optical image guided system for trans-nasal sinus and skull base surgeries

Purpose: Many studies have been conducted on assessment of navigation accuracy on cadaver head using pre-installed CT fiducials. However, there are fewer studies on assessing accuracy on real patient due to its complexity in measuring Target Registration Error (TRE). In this paper we propose a new approach for quantifying navigation accuracy on the real patients. This paper summarizes the results of navigation accuracy of a novel optical image guided navigation system evaluated on over 20 patients. Method: Commercially available optical navigation system (Navient Image guided navigation system - ClaroNav Kolahi Inc., Toronto, Canada) was used on over 20 patients from 2017 to 2019. Navient employs both landmarks based and trace based registration. Since mounting CT fiducials on the real patients is invasive and impractical, we developed a new approach to measure the distance from the navigation probe to the patient’s skin as a new metric to quantify navigation accuracy. The measurement was conducted in dozens of locations including patient’s forehead, temples and base of the nose. These anatomical locations were chosen very carefully to represent navigation accuracy in coronal, sagittal and axial directions respectively. Furthermore, our method also eliminates human errors involved in the TRE measurements which is the main source of error in TRE studies. Results: The average Euclidian distance from skin on 23 patients were 1.47(mm). the standard deviation of the accuracy was 0.28(mm). Low STD demonstrates consistent accuracy during the two year course of the study. Conclusion: A new noninvasive approach for accuracy assessment of image guided navigation systems on real patient was proposed and validated using a novel optical navigation system. The low STD of navigation accuracy indicates its reliable accuracy.

Optimized Design for NB-LDPC-Coded High-Order CPM: Power and Iterative Efficiencies

In this paper, a non-binary low-density parity-check (NB-LDPC) coded high-order continuous phase modulation (CPM) system is designed and optimized to improve power and iterative efficiencies. Firstly, the minimum squared normalized Euclidean distance and the 99% double-sided power bandwidth are introduced to design a competitive CPM, improving its power efficiency under a given code rate and spectral efficiency. Secondly, a three-step method based on extrinsic information transfer (EXIT) and entropy theory is used to design NB-LDPC codes, which reduces the convergence threshold approximately 0.42 and 0.58 dB compared with the candidate schemes. Thirdly, an extrinsic information operation is proposed to address the positive feedback issue in iterative detection and decoding and the value of bit error rate (BER) can approximately be reduced by 5×10−3. Finally, iteration optimization employing the EXIT chart and mutual information between demodulation and decoding is performed to achieve a suitable tradeoff for the communication reliability and iterative decoding delay. Simulation results show that the resulting scheme provides an approximately 3.95 dB coding gain compared to the uncoded CPM and achieves approximately 0.5 and 0.7 dB advantages compared with the candidate schemes. The resulting NB-LDPC-coded high-order CPM for a given code rate and spectral efficiency converges earlier into a turbo cliff region compared with other competitors and significantly improves power and iterative efficiencies.

Noise modeling of offshore platform using progressive normalized distance from worst-case error for optimal neuron numbers in deep belief network

Noise prediction is important for crew comfort in an offshore platform such as oil drilling rig. A deep neural network learning on the oil drilling rig is not widely studied. In this paper, a deep belief network (DBN) with the last layer initialized with trained DBN (named DBN-DNN) is used to model the sound pressure level (SPL) in the compartments of the oil drilling rig. The method finds an optimal number of the hidden neurons in restricted Boltzmann machine by using a normalized Euclidean distance from the worst possible error for each hidden layer progressively. The dataset used for experimental results is obtained via vibroacoustics simulation software such as VA-One and actual site measurements. The results show that output parameters such as spatial SPL, average spatial SPL, structure-borne SPL and airborne SPL improve the testing root mean square error to around 20% as compared to randomly assigning the number of neurons for each hidden layer. The testing RMSE in the output parameters has improved when compared with a multi-layer perceptron, sparse autoencoder, Softmax, self-taught learning and extreme learning machine.

Brain Tumor Segmentation of T1w MRI Images Based on Clustering Using Dimensionality Reduction Random Projection Technique.

Early diagnosis of a brain tumor may increase life expectancy. Magnetic resonance imaging (MRI) accompanied by several segmentation algorithms is preferred as a reliable method for assessment. The availability of high-dimensional medical image data during diagnosis places a heavy computational burden and a suitable pre-processing step is required for lower- dimensional representation. The storage requirement and complexity of image data are also a concern. To address this concern, the random projection technique (RPT) is widely used as a multivariate approach for data reduction. This study mainly focuses on T1-weighted MRI image clustering for brain tumor segmentation with dimension reduction by using the conventional principal component analysis (PCA) and RPT. Two clustering algorithms, K-means and fuzzy c-means (FCM) were used for brain tumor detection. The primary study objective was to present a comparison of the two clustering methods between MRI images subjected to PCA and RPT. In addition to the original dimension of 512 × 512, three other image sizes, 256 × 256, 128 × 128, and 64 × 64, were used to determine the effect of the methods. In terms of average reconstruction, Euclidean distance, and segmentation distance errors, the RPT produced better results than the PCA method for all the clustered images from clustering techniques. According to the values of performance metrics, RPT supported fuzzy c-means in achieving the best clustering performance and provided significant results for each new size of the MRI images.

Caracterização biométrica de frutos e sementes de cagaita (Eugenia dysenterica DC.) na região sul do Piauí, Brasil

Objetivou-se neste estudo caracterizar a diversidade genética de uma população natural Eugenia dysenterica DC, no sul do Piauí, a partir das características morfológicas dos frutos e sementes. Foram avaliadas sete características fenotípicas para 200 frutos e estimada a diversidade de 10 indivíduos adultos. Os dados biométricos foram analisados por meio de estatísticas univariadas e os desvios da normalidade dos dados foram confirmados pelo teste de Lilliefors, para uso da correlação não paramétrica de Spearman. A divergência genética entre os indivíduos observada foi baseada no dendrograma, por meio da matriz de distância euclidiana média, que foi obtida a partir dos valores das variáveis biométricas. Em relação à assimetria, ocorreu distribuição à esquerda para as variáveis: peso dos frutos, da polpa e casca. As demais variáveis apresentaram valores positivos. O número de sementes por fruto e o peso da polpa e casca evidenciaram uma medida de curtose menor que a da distribuição normal, sendo K < 3. De acordo com o dendrograma que avaliou a semelhança entre os indivíduos quanto às características biométricas, observou-se maior similaridade entre os indivíduos 1 e 3, com máxima dissimilaridade entre os indivíduos 7 e 8. A maioria das correlações entre as variáveis biométricas não foi significativa, exceto entre o peso do fruto e peso da semente; peso do fruto e peso da polpa e casca; peso da semente e número da semente. Os resultados obtidos neste estudo foram relevantes, pois servirão de subsídios para estudos relacionados ao pré-melhoramento e conservação genética da espécie.

A novel piracy protection scheme for videos using force-induced pixels

In this paper, a novel reversible keyless invisible authentication method is proposed for video piracy protection which uses randomized pixel at Red color channel for hiding information with locations of such modified pixels being stored in an immediate next frame. Each pair of these frames is identified with an embedded random number and an alphabet “A” or “B” based on hidden information frame and location information frame respectively. Such randomization at two different levels is not considered in any of the existing methods. Videos with this proposed embedding of copyright information ensure minimum distortions and maximum resistance to the removal of authentication information thereby providing an effective control of the rampant piracy menace. Keyless invisible embedding process increases the security and reduces the cost. Modified Least Significant Bit (LSB) based mechanism is used for achieving cost effectiveness and simplicity. The extracted information will be compared to assure the authenticity of videos. The average Euclidean distance between original and authenticated frames’ histogram is 2.5902e-10 that implies high similarity and thereby increasing its ability to withstand visual attacks. The proposed method results in PSNR greater than 50 dB with MSE less than 0.001 leading to high resultant image quality after embedding. High level of robustness is achieved due to the inherent mechanism of storing authentication information across all pairs of frame as well as complete randomization of the authentication storing pixels. In case of eavesdropping, using Bit-tolerance and Frame-tolerance we can confirm whether the corrupted video is acceptable or not.

A Case-Based Reasoning Model for Depression Based on Three-Electrode EEG Data

Depression, threatening the well-being of millions, has become one of the major diseases in the past decade. However, the current method of diagnosing depression is questionnaire-based interviews, which is labor-intensive and highly dependent on doctors' experience. Thus, objective and cost-efficient methods are needed. In this paper, we present a case-based reasoning model for identifying depression. Electroencephalography data were collected using a portable three-electrode EEG device, and then processed to remove artifacts and extract features. We applied multiple classifiers. The best performing k-Nearest Neighbor (KNN) was selected as the evaluation function to select the effective features which were then used to create the case base. Based on the weight set of standard deviations, the similarity was calculated using normalized Euclidean distance to get the optimal recognition rate of depression. The accuracy of optimal similarity identification of patients with depression was 91.25 percent, which was improved compared to the accuracy using KNN classifier (81.44 percent) or previously reported classifiers. Thus, we provide a novel pervasive and effective method for automatic detection of depression.

Bazı Soya Fasulyesi [Glycine Max (L.) Merr.] Genotipleri Arasında Agronomik Özelliklerin ve ISSR Yönteminin Karşılaştırmalı Analizi

In this study, the genetic diversity was investigated among 12 soybeans genotypes using inter simple sequence repeats (ISSR) and agronomic traits. DNA was isolated from the leaves of the genotypes. For molecular characterization, a total of 26 primers of ISSRs and eight agronomic characteristics were evaluated. ISSR analysis revealed 88 polymorphic bands. The genetic diversity among the genotypes according to ISSR analysis and agronomic traits were estimated based on Nei homology and Euclidian distance, respectively, and dendrograms reflecting genetic similarity were constructed using UPGMA and NTSYSpc, respectively. Nei’s homology coefficient values used for ISSR analysis ranged from 78%-84%, and the average Euclidean distance used for agronomic data ranged from 1.96-9.77. Although soybean genotypes evaluated in this study were highly similar, dendrograms showed that these genotypes could be distinguished both morphologically and genetically.

Superior accuracy and precision of SEEG electrode insertion with frame-based vs. frameless stereotaxy methods

Stereotactic electroencephalography (SEEG) has largely become the preferred method for intracranial seizure localization in epileptic patients due to its low morbidity and minimally invasive approach. While robotic placement is gaining popularity, many centers continue to use manual frame-based and frameless methods for electrode insertion. However, it is unclear how these methods compare in regard to accuracy, precision, and safety. Here, we aim to compare frame-based insertion using a CRW frame (Integra®) and frameless insertion using the StealthStation™ S7 (Medtronic®) navigation system for common temporal SEEG targets. We retrospectively examined electrode targets in SEEG patients that were implanted with either frame-based or frameless methods at a level 4 epilepsy center. We focused on two commonly used targets: amygdala and hippocampal head. Stealth station software was used to merge pre-operative MR with post-operative CT images for each patient, and coordinates for each electrode tip were calculated in relation to the midcommissural point. These were compared to predetermined ideal coordinates in regard to error and directional bias. A total of 81 SEEG electrodes were identified in 23 patients (40 amygdala and 41 hippocampal head). Eight of 45 electrodes (18%) placed with the frameless technique and 0 of 36 electrodes (0%) placed with the frame-based technique missed their target and were not clinically useful. The average Euclidean distance comparing actual to ideal electrode tip coordinates for frameless vs. frame-based techniques was 11.0mm vs. 7.1mm (p< 0.001) for the amygdala and 12.4mm vs. 8.5mm (p< 0.001) for the hippocampal head, respectively. There were no hemorrhages or clinical complications in either group. Based on this series, frame-based SEEG insertion is significantly more accurate and precise and results in more clinically useful electrode contacts, compared to frameless insertion using a navigation guidance system. This has important implications for centers not currently using robotic insertion.

EyesGAN: Synthesize human face from human eyes

Face recognition recently has achieved remarkable success in many fields, especially in mobile payment, authentication, criminal investigation, and city management. However, face occlusion is still the key problem in person identification, such as in the field of anti-terrorism, criminal cases and public security. To solve this problem, an improved end-to-end deep generative adversarial network (named EyesGAN) has been proposed to synthesize human face from human eyes in this paper, which can be used as a potential scheme for masked face recognition. BicycleGAN is chosen as the baseline and effective improvements have been achieved. First, the self-attentional mechanism is introduced so that the improved model can more effectively learn about the internal mapping between human eyes and face. Second, the perceptual loss is applied to guide the model cyclic training and help with updating the network parameters so that the synthesized face can be of higher-similarity to the ground truth face. Third, EyesGAN has been designed by getting the utmost out of the performance of the perceptual loss and the self-attentional mechanism in GANs. A dataset of eyes-to-face synthesis has been reconstructed based on the public face datasets for training and testing. Finally, the faces synthesized by EyesGAN have been quantitatively and qualitatively compared with the results of existing methods. Extensive experiments demenstrate that our proposed method has performed better than the state-of-the-art methods in terms of Average Euclidean Distance, Average Cosine Similarity, Synthesis Accuracy Percentage, Fréchet Inception Distance, and Baidu face recognition rate (the accuracy achieved 96.1% on 615 test data of CelebA database). In this paper, the feasibility of synthesizing human face from human eyes has been explored, and the attention map shows that our network can predict other parts of the face from eyes.

A Phantom Study of the Spatial Precision and Accuracy of Stereotactic Localization Using Computed Tomography Imaging with the Leksell Stereotactic System

Stereotactic localization of neurosurgical targets traditionally relies on computed tomography (CT), which is considered the optimal imaging modality for geometric accuracy. However, in-depth investigations that characterize the precision and accuracy of CT images are lacking. We used a CT phantom to examine interscanner precision and interprotocol accuracy in coordinate localization. A polymethylacrylate phantom was scanned with Toshiba Aquilion 64 and GE Healthcare LightSpeed 16 CT scanners, using both helical and incremental single-slice (SS) image acquisition protocols. The X, Y, and Z coordinates of 94 points across 6 surfaces of the phantom were physically measured. The CT scan-derived coordinates were compared with the phantom coordinates and with each other to determine accuracy and precision, respectively. Using the SS imaging protocol, the mean (SD) interscanner disparity in localization was 0.93 (0.39) mm, given by the average Euclidean distance between the coordinates of the 2 scanners. This discrepancy significantly varied by axis and surface, with the greatest discrepancy in the Z-axis of 0.30 mm (95% confidence interval, 0.25-0.35; P= 0.05) and on the superior surface of 1.30 mm (95% confidence interval, 1.15-1.45; P= 0.05). SS acquisition was significantly more accurate than the helical protocol. We found evidence of clinically relevant inconsistency between 2 CT scanners used for stereotactic localization. SS image acquisition was superior to helical scanning with respect to localization accuracy. Interscanner consistency cannot be assumed. Institutions would benefit from identifying the errors inherent in their CT scanners.

Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

SummaryThis paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group with the tracking error of the normalized Euclidean distance meeting predefined transient and steady‐state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low‐cost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form.

Towards fully automated third molar development staging in panoramic radiographs.

Staging third molar development is commonly used for age assessment in sub-adults. Current staging techniques are, at most, semi-automated and rely on manual interactions prone to operator variability. The aim of this study was to fully automate the staging process by employing the full potential of deep learning, using convolutional neural networks (CNNs) in every step of the procedure. The dataset used to train the CNNs consisted of 400 panoramic radiographs (OPGs), with 20 OPGs per developmental stage per sex, staged in consensus between three observers. The concepts of transfer learning, using pre-trained CNNs, and data augmentation were used to mitigate the issues when dealing with a limited dataset. In this work, a three-step procedure was proposed and the results were validated using fivefold cross-validation. First, a CNN localized the geometrical center of the lower left third molar, around which a square region of interest (ROI) was extracted. Second, another CNN segmented the third molar within the ROI. Third, a final CNN used both the ROI and the segmentation to classify the third molar into its developmental stage. The geometrical center of the third molar was found with an average Euclidean distance of 63 pixels. Third molars were segmented with an average Dice score of 93%. Finally, the developmental stages were classified with an accuracy of 54%, a mean absolute error of 0.69 stages, and a linear weighted Cohen's kappa coefficient of 0.79. The entire automated workflow on average took 2.72 s to compute, which is substantially faster than manual staging starting from the OPG. Taking into account the limited dataset size, this pilot study shows that the proposed fully automated approach shows promising results compared with manual staging.