On an hypercomplex generalization of Gould-Hopper and related Chebyshev polynomials

An operational approach introduced by Gould and Hopper to the construction of generalized Hermite polynomials is followed in the hypercomplex context to build multidimensional generalized Hermite polynomials by the consideration of an appropriate basic set of monogenic polynomials. Directly related functions, like Chebyshev polynomials of first and second kind are constructed

Segal-Bargmann-Fock modules of monogenic functions

In this paper we introduce the classical Segal-Bargmann transform starting from the basis of Hermite polynomials and extend it to Clifford algebra-valued functions. Then we apply the results to monogenic functions and prove that the Segal-Bargmann kernel corresponds to the kernel of the Fourier-Borel transform for monogenic functionals. This kernel is also the reproducing kernel for the monogenic Bargmann module.Comment: 11 page

Towards real-time 6D pose estimation of objects in single-view cone-beam X-ray

Deep learning-based pose estimation algorithms can successfully estimate the pose of objects in an image, especially in the field of color images. 6D Object pose estimation based on deep learning models for X-ray images often use custom architectures that employ extensive CAD models and simulated data for training purposes. Recent RGB-based methods opt to solve pose estimation problems using small datasets, making them more attractive for the X-ray domain where medical data is scarcely available. We refine an existing RGB-based model (SingleShotPose) to estimate the 6D pose of a marked cube from grayscale X-ray images by creating a generic solution trained on only real X-ray data and adjusted for X-ray acquisition geometry. The model regresses 2D control points and calculates the pose through 2D/3D correspondences using Perspective-n-Point(PnP), allowing a single trained model to be used across all supporting cone-beam-based X-ray geometries. Since modern X-ray systems continuously adjust acquisition parameters during a procedure, it is essential for such a pose estimation network to consider these parameters in order to be deployed successfully and find a real use case. With a 5-cm/5-degree accuracy of 93% and an average 3D rotation error of 2.2 degrees, the results of the proposed approach are comparable with state-of-the-art alternatives, while requiring significantly less real training examples and being applicable in real-time applications.Comment: Published at SPIE Medical Imaging 202

Investigating and Improving Latent Density Segmentation Models for Aleatoric Uncertainty Quantification in Medical Imaging

Data uncertainties, such as sensor noise or occlusions, can introduce irreducible ambiguities in images, which result in varying, yet plausible, semantic hypotheses. In Machine Learning, this ambiguity is commonly referred to as aleatoric uncertainty. Latent density models can be utilized to address this problem in image segmentation. The most popular approach is the Probabilistic U-Net (PU-Net), which uses latent Normal densities to optimize the conditional data log-likelihood Evidence Lower Bound. In this work, we demonstrate that the PU- Net latent space is severely inhomogenous. As a result, the effectiveness of gradient descent is inhibited and the model becomes extremely sensitive to the localization of the latent space samples, resulting in defective predictions. To address this, we present the Sinkhorn PU-Net (SPU-Net), which uses the Sinkhorn Divergence to promote homogeneity across all latent dimensions, effectively improving gradient-descent updates and model robustness. Our results show that by applying this on public datasets of various clinical segmentation problems, the SPU-Net receives up to 11% performance gains compared against preceding latent variable models for probabilistic segmentation on the Hungarian-Matched metric. The results indicate that by encouraging a homogeneous latent space, one can significantly improve latent density modeling for medical image segmentation.Comment: 12 pages incl. references, 11 figure

q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials

We define a q-deformation of the Dirac operator, inspired by the one dimensional q-derivative. This implies a q-deformation of the partial derivatives. By taking the square of this Dirac operator we find a q-deformation of the Laplace operator. This allows to construct q-deformed Schroedinger equations in higher dimensions. The equivalence of these Schroedinger equations with those defined on q-Euclidean space in quantum variables is shown. We also define the m-dimensional q-Clifford-Hermite polynomials and show their connection with the q-Laguerre polynomials. These polynomials are orthogonal with respect to an m-dimensional q-integration, which is related to integration on q-Euclidean space. The q-Laguerre polynomials are the eigenvectors of an su_q(1|1)-representation

Aanvullend waardplantenonderzoek van Meloidogyne fallax Karssen, 1996

De wortelknobbelaaltjes Meloidogyne chitwoodi en M.fallax staan op de quarantainelijsten van de EU en de EPPO.De levenswijze van deze nematoden, hun potentiële schade en hun schaarse verspreiding in Europa waren aanleiding voor de quarantaine status. Beide nematoden zijn in Nederland aanwezig. Voor enkele gewassen is waardplantgeschiktheid voor M. chitiwoodi bekend, maar ontbreekt die van M.fallax. Om de uitbrekende gegevens aan te vullen is een aantal gewassen getoetst op hun waardplantgeschikthei

Early esophageal adenocarcinoma detection using deep learning methods

Purpose This study aims to adapt and evaluate the performance of different state-of-the-art deep learning object detection methods to automatically identify esophageal adenocarcinoma (EAC) regions from high-definition white light endoscopy (HD-WLE) images. Method Several state-of-the-art object detection methods using Convolutional Neural Networks (CNNs) were adapted to automatically detect abnormal regions in the esophagus HD-WLE images, utilizing VGG’16 as the backbone architecture for feature extraction. Those methods are Regional-based Convolutional Neural Network (R-CNN), Fast R-CNN, Faster R-CNN and Single-Shot Multibox Detector (SSD). For the evaluation of the different methods, 100 images from 39 patients that have been manually annotated by five experienced clinicians as ground truth have been tested. Results Experimental results illustrate that the SSD and Faster R-CNN networks show promising results, and the SSD outperforms other methods achieving a sensitivity of 0.96, specificity of 0.92 and F-measure of 0.94. Additionally, the Average Recall Rate of the Faster R-CNN in locating the EAC region accurately is 0.83. Conclusion In this paper, recent deep learning object detection methods are adapted to detect esophageal abnormalities automatically. The evaluation of the methods proved its ability to locate abnormal regions in the esophagus from endoscopic images. The automatic detection is a crucial step that may help early detection and treatment of EAC and also can improve automatic tumor segmentation to monitor its growth and treatment outcome

HIV in hiding: methods and data requirements for the estimation of the number of people living with undiagnosed HIV

Many people who are HIV positive are unaware of their infection status. Estimation of the number of people with undiagnosed HIV within a country or region is vital for understanding future need for treatment and for motivating testing programs. We review the available estimation approaches which are in current use. They can be broadly classified into those based on prevalence surveys and those based on reported HIV and AIDS cases. Estimation based on prevalence data requires data from regular prevalence surveys in different population groups together with estimates of the size of these groups. The recommended minimal case reporting data needed to estimate the number of patients with undiagnosed HIV are HIV diagnoses, including CD4 count at diagnosis and whether there has been an AIDS diagnosis in the 3 months before or after HIV diagnosis, and data on deaths in people with HIV. We would encourage all countries to implement several methods that will help develop our understanding of strengths and weaknesses of the various methods

A deep learning system for detection of early Barrett's neoplasia:a model development and validation study

BACKGROUND: Computer-aided detection (CADe) systems could assist endoscopists in detecting early neoplasia in Barrett's oesophagus, which could be difficult to detect in endoscopic images. The aim of this study was to develop, test, and benchmark a CADe system for early neoplasia in Barrett's oesophagus.METHODS: The CADe system was first pretrained with ImageNet followed by domain-specific pretraining with GastroNet. We trained the CADe system on a dataset of 14 046 images (2506 patients) of confirmed Barrett's oesophagus neoplasia and non-dysplastic Barrett's oesophagus from 15 centres. Neoplasia was delineated by 14 Barrett's oesophagus experts for all datasets. We tested the performance of the CADe system on two independent test sets. The all-comers test set comprised 327 (73 patients) non-dysplastic Barrett's oesophagus images, 82 (46 patients) neoplastic images, 180 (66 of the same patients) non-dysplastic Barrett's oesophagus videos, and 71 (45 of the same patients) neoplastic videos. The benchmarking test set comprised 100 (50 patients) neoplastic images, 300 (125 patients) non-dysplastic images, 47 (47 of the same patients) neoplastic videos, and 141 (82 of the same patients) non-dysplastic videos, and was enriched with subtle neoplasia cases. The benchmarking test set was evaluated by 112 endoscopists from six countries (first without CADe and, after 6 weeks, with CADe) and by 28 external international Barrett's oesophagus experts. The primary outcome was the sensitivity of Barrett's neoplasia detection by general endoscopists without CADe assistance versus with CADe assistance on the benchmarking test set. We compared sensitivity using a mixed-effects logistic regression model with conditional odds ratios (ORs; likelihood profile 95% CIs).FINDINGS: Sensitivity for neoplasia detection among endoscopists increased from 74% to 88% with CADe assistance (OR 2·04; 95% CI 1·73-2·42; p&lt;0·0001 for images and from 67% to 79% [2·35; 1·90-2·94; p&lt;0·0001] for video) without compromising specificity (from 89% to 90% [1·07; 0·96-1·19; p=0·20] for images and from 96% to 94% [0·94; 0·79-1·11; ] for video; p=0·46). In the all-comers test set, CADe detected neoplastic lesions in 95% (88-98) of images and 97% (90-99) of videos. In the benchmarking test set, the CADe system was superior to endoscopists in detecting neoplasia (90% vs 74% [OR 3·75; 95% CI 1·93-8·05; p=0·0002] for images and 91% vs 67% [11·68; 3·85-47·53; p&lt;0·0001] for video) and non-inferior to Barrett's oesophagus experts (90% vs 87% [OR 1·74; 95% CI 0·83-3·65] for images and 91% vs 86% [2·94; 0·99-11·40] for video).INTERPRETATION: CADe outperformed endoscopists in detecting Barrett's oesophagus neoplasia and, when used as an assistive tool, it improved their detection rate. CADe detected virtually all neoplasia in a test set of consecutive cases.FUNDING: Olympus.</p