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This paper introduces Spectral U-Net, a novel deep learning network based on spectral decomposition, by exploiting Dual Tree Complex Wavelet Transform (DTCWT) for down-sampling and inverse Dual Tree Complex Wavelet Transform (iDTCWT) for up-sampling. We devise the corresponding Wave-Block and iWave-Block, integrated into the U-Net architecture, aiming at mitigating information loss during down-sampling and enhancing detail reconstruction during up-sampling. In the encoder, we first decompose the feature map into high and low-frequency components using DTCWT, enabling down-sampling while mitigating information loss. In the decoder, we utilize iDTCWT to reconstruct higher-resolution feature maps from down-sampled features. Evaluations on the Retina Fluid, Brain Tumor, and Liver Tumor segmentation datasets with the nnU-Net framework demonstrate the superiority of the proposed Spectral U-Net.

Diffusion models (DPMs) have demonstrated remarkable performance in image generation, often times outperforming other generative models. Since their introduction, the powerful noise-to-image denoising pipeline has been extended to various discriminative tasks, including image segmentation. In case of medical imaging, often times the images are large 3D scans, where segmenting one image using DPMs become extremely inefficient due to large memory consumption and time consuming iterative sampling process. In this work, we propose a novel conditional generative modeling framework (LDSeg) that performs diffusion in latent space for medical image segmentation. Our proposed framework leverages the learned inherent low-dimensional latent distribution of the target object shapes and source image embeddings. The conditional diffusion in latent space not only ensures accurate n-D image segmentation for multi-label objects, but also mitigates the major underlying problems of the traditional DPM based segmentation: (1) large memory consumption, (2) time consuming sampling process and (3) unnatural noise injection in forward/reverse process. LDSeg achieved state-of-the-art segmentation accuracy on three medical image datasets with different imaging modalities. Furthermore, we show that our proposed model is significantly more robust to noises, compared to the traditional deterministic segmentation models, which can be potential in solving the domain shift problems in the medical imaging domain. Codes are available at: https://github.com/LDSeg/LDSeg., Comment: 9 pages, 7 figures

Diffusion models have shown impressive performance for image generation, often times outperforming other generative models. Since their introduction, researchers have extended the powerful noise-to-image denoising pipeline to discriminative tasks, including image segmentation. In this work we propose a conditional score-based generative modeling framework for medical image segmentation which relies on a parametric surface representation for the segmentation masks. The surface re-parameterization allows the direct application of standard diffusion theory, as opposed to when the mask is represented as a binary mask. Moreover, we adapted an extended variant of the diffusion technique known as the "cold-diffusion" where the diffusion model can be constructed with deterministic perturbations instead of Gaussian noise, which facilitates significantly faster convergence in the reverse diffusion. We evaluated our method on the segmentation of the left ventricle from 65 transthoracic echocardiogram videos (2230 echo image frames) and compared its performance to the most popular and widely used image segmentation models. Our proposed model not only outperformed the compared methods in terms of segmentation accuracy, but also showed potential in estimating segmentation uncertainties for further downstream analyses due to its inherent generative nature., Comment: 5 pages, 5 figures, conference

In this paper, we introduce U-Net v2, a new robust and efficient U-Net variant for medical image segmentation. It aims to augment the infusion of semantic information into low-level features while simultaneously refining high-level features with finer details. For an input image, we begin by extracting multi-level features with a deep neural network encoder. Next, we enhance the feature map of each level by infusing semantic information from higher-level features and integrating finer details from lower-level features through Hadamard product. Our novel skip connections empower features of all the levels with enriched semantic characteristics and intricate details. The improved features are subsequently transmitted to the decoder for further processing and segmentation. Our method can be seamlessly integrated into any Encoder-Decoder network. We evaluate our method on several public medical image segmentation datasets for skin lesion segmentation and polyp segmentation, and the experimental results demonstrate the segmentation accuracy of our new method over state-of-the-art methods, while preserving memory and computational efficiency. Code is available at: https://github.com/yaoppeng/U-Net_v2

Quantum image processing is a growing field attracting attention from both the quantum computing and image processing communities. We propose a novel method in combining a graph-theoretic approach for optimal surface segmentation and hybrid quantum-classical optimization of the problem-directed graph. The surface segmentation is modeled classically as a graph partitioning problem in which a smoothness constraint is imposed to control surface variation for realistic segmentation. Specifically, segmentation refers to a source set identified by a minimum s-t cut that divides graph nodes into the source (s) and sink (t) sets. The resulting surface consists of graph nodes located on the boundary between the source and the sink. Characteristics of the problem-specific graph, including its directed edges, connectivity, and edge capacities, are embedded in a quadratic objective function whose minimum value corresponds to the ground state energy of an equivalent Ising Hamiltonian. This work explores the use of quantum processors in image segmentation problems, which has important applications in medical image analysis. Here, we present a theoretical basis for the quantum implementation of LOGISMOS and the results of a simulation study on simple images. Quantum Approximate Optimization Algorithm (QAOA) approach was utilized to conduct two simulation studies whose objective was to determine the ground state energies and identify bitstring solutions that encode the optimal segmentation of objective functions. The objective function encodes tasks associated with surface segmentation in 2-D and 3-D images while incorporating a smoothness constraint. In this work, we demonstrate that the proposed approach can solve the geometric-constrained surface segmentation problem optimally with the capability of locating multiple minimum points corresponding to the globally minimal solution., Comment: 11 pages, 2 figures; typos corrected in Figure 1's caption

We describe a method for verifying the output of a deep neural network for medical image segmentation that is robust to several classes of random as well as worst-case perturbations i.e. adversarial attacks. This method is based on a general approach recently developed by the authors called "Trust, but Verify" wherein an auxiliary verification network produces predictions about certain masked features in the input image using the segmentation as an input. A well-designed auxiliary network will produce high-quality predictions when the input segmentations are accurate, but will produce low-quality predictions when the segmentations are incorrect. Checking the predictions of such a network with the original image allows us to detect bad segmentations. However, to ensure the verification method is truly robust, we need a method for checking the quality of the predictions that does not itself rely on a black-box neural network. Indeed, we show that previous methods for segmentation evaluation that do use deep neural regression networks are vulnerable to false negatives i.e. can inaccurately label bad segmentations as good. We describe the design of a verification network that avoids such vulnerability and present results to demonstrate its robustness compared to previous methods., Comment: 5 Pages, 8 Figures, conference

This paper considers a novel application of deep AUC maximization (DAM) for multi-instance learning (MIL), in which a single class label is assigned to a bag of instances (e.g., multiple 2D slices of a CT scan for a patient). We address a neglected yet non-negligible computational challenge of MIL in the context of DAM, i.e., bag size is too large to be loaded into {GPU} memory for backpropagation, which is required by the standard pooling methods of MIL. To tackle this challenge, we propose variance-reduced stochastic pooling methods in the spirit of stochastic optimization by formulating the loss function over the pooled prediction as a multi-level compositional function. By synthesizing techniques from stochastic compositional optimization and non-convex min-max optimization, we propose a unified and provable muli-instance DAM (MIDAM) algorithm with stochastic smoothed-max pooling or stochastic attention-based pooling, which only samples a few instances for each bag to compute a stochastic gradient estimator and to update the model parameter. We establish a similar convergence rate of the proposed MIDAM algorithm as the state-of-the-art DAM algorithms. Our extensive experiments on conventional MIL datasets and medical datasets demonstrate the superiority of our MIDAM algorithm., Comment: To appear in ICML2023, 23 pages

Background: Changes in choroidal thickness are associated with various ocular diseases and the choroid can be imaged using spectral-domain optical coherence tomography (SDOCT) and enhanced depth imaging OCT (EDIOCT). New Method: Eighty macular SDOCT volumes from 80 patients were obtained using the Zeiss Cirrus machine. Eleven additional control subjects had two Cirrus scans done in one visit along with EDIOCT using the Heidelberg Spectralis machine. To automatically segment choroidal layers from the OCT volumes, our graph-theoretic approach was utilized. The segmentation results were compared with reference standards from two graders, and the accuracy of automated segmentation was calculated using unsigned to signed border positioning thickness errors and Dice similarity coefficient (DSC). The repeatability and reproducibility of our choroidal thicknesses were determined by intraclass correlation coefficient (ICC), coefficient of variation (CV), and repeatability coefficient (RC). Results: The mean unsigned to signed border positioning errors for the choroidal inner and outer surfaces are 3.39plusminus1.26microns (mean plusminus SD) to minus1.52 plusminus 1.63microns and 16.09 plusminus 6.21microns to 4.73 plusminus 9.53microns, respectively. The mean unsigned to signed choroidal thickness errors are 16.54 plusminus 6.47microns to 6.25 plusminus 9.91microns, and the mean DSC is 0.949 plusminus 0.025. The ICC (95% CI), CV, RC values are 0.991 (0.977 to 0.997), 2.48%, 3.15microns for the repeatability and 0.991 (0.977 to 0.997), 2.49%, 0.53microns for the reproducibility studies, respectively. Comparison with Existing Method(s): The proposed method outperformed our previous method using choroidal vessel segmentation and inter-grader variability. Conclusions: This automated segmentation method can reliably measure choroidal thickness using different OCT platforms.

Deep AUC Maximization (DAM) is a new paradigm for learning a deep neural network by maximizing the AUC score of the model on a dataset. Most previous works of AUC maximization focus on the perspective of optimization by designing efficient stochastic algorithms, and studies on generalization performance of large-scale DAM on difficult tasks are missing. In this work, we aim to make DAM more practical for interesting real-world applications (e.g., medical image classification). First, we propose a new margin-based min-max surrogate loss function for the AUC score (named as AUC min-max-margin loss or simply AUC margin loss for short). It is more robust than the commonly used AUC square loss, while enjoying the same advantage in terms of large-scale stochastic optimization. Second, we conduct extensive empirical studies of our DAM method on four difficult medical image classification tasks, namely (i) classification of chest x-ray images for identifying many threatening diseases, (ii) classification of images of skin lesions for identifying melanoma, (iii) classification of mammogram for breast cancer screening, and (iv) classification of microscopic images for identifying tumor tissue. Our studies demonstrate that the proposed DAM method improves the performance of optimizing cross-entropy loss by a large margin, and also achieves better performance than optimizing the existing AUC square loss on these medical image classification tasks. Specifically, our DAM method has achieved the 1st place on Stanford CheXpert competition on Aug. 31, 2020. To the best of our knowledge, this is the first work that makes DAM succeed on large-scale medical image datasets. We also conduct extensive ablation studies to demonstrate the advantages of the new AUC margin loss over the AUC square loss on benchmark datasets. The proposed method is implemented in our open-sourced library LibAUC (www.libauc.org)., Comment: Accepted by ICCV2021

The novel corona-virus disease (COVID-19) pandemic has caused a major outbreak in more than 200 countries around the world, leading to a severe impact on the health and life of many people globally. As of Aug 25th of 2020, more than 20 million people are infected, and more than 800,000 death are reported. Computed Tomography (CT) images can be used as a as an alternative to the time-consuming "reverse transcription polymerase chain reaction (RT-PCR)" test, to detect COVID-19. In this work we developed a deep learning framework to predict COVID-19 from CT images. We propose to use an attentional convolution network, which can focus on the infected areas of chest, enabling it to perform a more accurate prediction. We trained our model on a dataset of more than 2000 CT images, and report its performance in terms of various popular metrics, such as sensitivity, specificity, area under the curve, and also precision-recall curve, and achieve very promising results. We also provide a visualization of the attention maps of the model for several test images, and show that our model is attending to the infected regions as intended. In addition to developing a machine learning modeling framework, we also provide the manual annotation of the potentionally infected regions of chest, with the help of a board-certified radiologist, and make that publicly available for other researchers.

The novel corona-virus disease (COVID-19) pandemic has caused a major outbreak in more than 200 countries around the world, leading to a severe impact on the health and life of many people globally. As of mid-July 2020, more than 12 million people were infected, and more than 570,000 death were reported. Computed Tomography (CT) images can be used as an alternative to the time-consuming RT-PCR test, to detect COVID-19. In this work we propose a segmentation framework to detect chest regions in CT images, which are infected by COVID-19. We use an architecture similar to U-Net model, and train it to detect ground glass regions, on pixel level. As the infected regions tend to form a connected component (rather than randomly distributed pixels), we add a suitable regularization term to the loss function, to promote connectivity of the segmentation map for COVID-19 pixels. 2D-anisotropic total-variation is used for this purpose, and therefore the proposed model is called "TV-UNet". Through experimental results on a relatively large-scale CT segmentation dataset of around 900 images, we show that adding this new regularization term leads to 2\% gain on overall segmentation performance compared to the U-Net model. Our experimental analysis, ranging from visual evaluation of the predicted segmentation results to quantitative assessment of segmentation performance (precision, recall, Dice score, and mIoU) demonstrated great ability to identify COVID-19 associated regions of the lungs, achieving a mIoU rate of over 99\%, and a Dice score of around 86\%.

Automated segmentation of individual calf muscle compartments from 3D magnetic resonance (MR) images is essential for developing quantitative biomarkers for muscular disease progression and its prediction. Achieving clinically acceptable results is a challenging task due to large variations in muscle shape and MR appearance. Although deep convolutional neural networks (DCNNs) achieved improved accuracy in various image segmentation tasks, certain problems such as utilizing long-range information and incorporating high-level constraints remain unsolved. We present a novel fully convolutional network (FCN), called FilterNet, that utilizes contextual information in a large neighborhood and embeds edge-aware constraints for individual calf muscle compartment segmentations. An encoder-decoder architecture with flexible backbone blocks is used to systematically enlarge convolution receptive field and preserve information at all resolutions. Edge positions derived from the FCN output muscle probability maps are explicitly regularized using kernel-based edge detection in an end-to-end optimization framework. Our FilterNet was evaluated on 40 T1-weighted MR images of 10 healthy and 30 diseased subjects by 4-fold cross-validation. Mean DICE coefficients of 88.00%--91.29% and mean absolute surface positioning errors of 1.04--1.66 mm were achieved for the five 3D muscle compartments., Comment: To be appeared in journal Computerized Medical Imaging and Graphics

The COVID-19 pandemic is causing a major outbreak in more than 150 countries around the world, having a severe impact on the health and life of many people globally. One of the crucial step in fighting COVID-19 is the ability to detect the infected patients early enough, and put them under special care. Detecting this disease from radiography and radiology images is perhaps one of the fastest ways to diagnose the patients. Some of the early studies showed specific abnormalities in the chest radiograms of patients infected with COVID-19. Inspired by earlier works, we study the application of deep learning models to detect COVID-19 patients from their chest radiography images. We first prepare a dataset of 5,000 Chest X-rays from the publicly available datasets. Images exhibiting COVID-19 disease presence were identified by board-certified radiologist. Transfer learning on a subset of 2,000 radiograms was used to train four popular convolutional neural networks, including ResNet18, ResNet50, SqueezeNet, and DenseNet-121, to identify COVID-19 disease in the analyzed chest X-ray images. We evaluated these models on the remaining 3,000 images, and most of these networks achieved a sensitivity rate of 98% ($\pm$ 3%), while having a specificity rate of around 90%. Besides sensitivity and specificity rates, we also present the receiver operating characteristic (ROC) curve, precision-recall curve, average prediction, and confusion matrix of each model. We also used a technique to generate heatmaps of lung regions potentially infected by COVID-19 and show that the generated heatmaps contain most of the infected areas annotated by our board certified radiologist. While the achieved performance is very encouraging, further analysis is required on a larger set of COVID-19 images, to have a more reliable estimation of accuracy rates. The dataset, model implementations (in PyTorch), and evaluations, are all made publicly available for research community at https://github.com/shervinmin/DeepCovid.git, Comment: Accepted by Medical Image Analysis

A novel centerline extraction framework is reported which combines an end-to-end trainable multi-task fully convolutional network (FCN) with a minimal path extractor. The FCN simultaneously computes centerline distance maps and detects branch endpoints. The method generates single-pixel-wide centerlines with no spurious branches. It handles arbitrary tree-structured object with no prior assumption regarding depth of the tree or its bifurcation pattern. It is also robust to substantial scale changes across different parts of the target object and minor imperfections of the object's segmentation mask. To the best of our knowledge, this is the first deep-learning based centerline extraction method that guarantees single-pixel-wide centerline for a complex tree-structured object. The proposed method is validated in coronary artery centerline extraction on a dataset of 620 patients (400 of which used as test set). This application is challenging due to the large number of coronary branches, branch tortuosity, and large variations in length, thickness, shape, etc. The proposed method generates well-positioned centerlines, exhibiting lower number of missing branches and is more robust in the presence of minor imperfections of the object segmentation mask. Compared to a state-of-the-art traditional minimal path approach, our method improves patient-level success rate of centerline extraction from 54.3% to 88.8% according to independent human expert review., Comment: Accepted by the international conference on Information Processing in Medical Imaging (IPMI) 2019

State-of-the-art automated segmentation algorithms are not 100\% accurate especially when segmenting difficult to interpret datasets like those with severe osteoarthritis (OA). We present a novel interactive method called just-enough interaction (JEI), which adds a fast correction step to the automated layered optimal graph segmentation of multiple objects and surfaces (LOGISMOS). After LOGISMOS segmentation in knee MRI, the JEI user interaction does not modify boundary surfaces of the bones and cartilages directly. Local costs of underlying graph nodes are modified instead and the graph is re-optimized, providing globally optimal corrected results. Significant performance improvement ($p \ll 0.001$) was observed when comparing JEI-corrected results to the automated. The algorithm was extended from 3D JEI to longitudinal multi-3D (4D) JEI allowing simultaneous visualization and interaction of multiple-time points of the same patient., Comment: Proceedings of the 3rd International Workshop on Interactive Medical Image Computing (IMIC), Held in Conjunction with MICCAI, 2016

We present a fully automated learning-based approach for segmenting knee cartilage in the presence of osteoarthritis (OA). The algorithm employs a hierarchical set of two random forest classifiers. The first is a neighborhood approximation forest, the output probability map of which is utilized as a feature set for the second random forest (RF) classifier. The output probabilities of the hierarchical approach are used as cost functions in a Layered Optimal Graph Segmentation of Multiple Objects and Surfaces (LOGISMOS). In this work, we highlight a novel post-processing interaction called just-enough interaction (JEI) which enables quick and accurate generation of a large set of training examples. Disjoint sets of 15 and 13 subjects were used for training and tested on another disjoint set of 53 knee datasets. All images were acquired using a double echo steady state (DESS) MRI sequence and are from the osteoarthritis initiative (OAI) database. Segmentation performance using the learning-based cost function showed significant reduction in segmentation errors ($p< 0.05$) in comparison with conventional gradient-based cost functions., Comment: KEYWORDS: Graph based segmentation; Just enough interaction; LOGISMOS; Neighborhood approximation forests; Osteoarthritis; Random forest classifier; knee MRI PMID: 28626842 PMCID: PMC5471813

A fully automated knee MRI segmentation method to study osteoarthritis (OA) was developed using a novel hierarchical set of random forests (RF) classifiers to learn the appearance of cartilage regions and their boundaries. A neighborhood approximation forest is used first to provide contextual feature to the second-level RF classifier that also considers local features and produces location-specific costs for the layered optimal graph image segmentation of multiple objects and surfaces (LOGISMOS) framework. Double echo steady state (DESS) MRIs used in this work originated from the Osteoarthritis Initiative (OAI) study. Trained on 34 MRIs with varying degrees of OA, the performance of the learning-based method tested on 108 MRIs showed a significant reduction in segmentation errors (\emph{p}$<$0.05) compared with the conventional gradient-based and single-stage RF-learned costs. The 3D LOGISMOS was extended to longitudinal-3D (4D) to simultaneously segment multiple follow-up visits of the same patient. As such, data from all time-points of the temporal sequence contribute information to a single optimal solution that utilizes both spatial 3D and temporal contexts. 4D LOGISMOS validation on 108 MRIs from baseline and 12 month follow-up scans of 54 patients showed a significant reduction in segmentation errors (\emph{p}$<$0.01) compared to 3D. Finally, the potential of 4D LOGISMOS was further explored on the same 54 patients using 5 annual follow-up scans demonstrating a significant improvement of measuring cartilage thickness (\emph{p}$<$0.01) compared to the sequential 3D approach., Comment: IEEE Transactions in Medical Imaging, 11 pages

This paper reports Deep LOGISMOS approach to 3D tumor segmentation by incorporating boundary information derived from deep contextual learning to LOGISMOS - layered optimal graph image segmentation of multiple objects and surfaces. Accurate and reliable tumor segmentation is essential to tumor growth analysis and treatment selection. A fully convolutional network (FCN), UNet, is first trained using three adjacent 2D patches centered at the tumor, providing contextual UNet segmentation and probability map for each 2D patch. The UNet segmentation is then refined by Gaussian Mixture Model (GMM) and morphological operations. The refined UNet segmentation is used to provide the initial shape boundary to build a segmentation graph. The cost for each node of the graph is determined by the UNet probability maps. Finally, a max-flow algorithm is employed to find the globally optimal solution thus obtaining the final segmentation. For evaluation, we applied the method to pancreatic tumor segmentation on a dataset of 51 CT scans, among which 30 scans were used for training and 21 for testing. With Deep LOGISMOS, DICE Similarity Coefficient (DSC) and Relative Volume Difference (RVD) reached 83.2+-7.8% and 18.6+-17.4% respectively, both are significantly improved (p<0.05) compared with contextual UNet and/or LOGISMOS alone., Comment: 4 pages,3 figures

We propose an effective optimization algorithm for a general hierarchical segmentation model with geometric interactions between segments. Any given tree can specify a partial order over object labels defining a hierarchy. It is well-established that segment interactions, such as inclusion/exclusion and margin constraints, make the model significantly more discriminant. However, existing optimization methods do not allow full use of such models. Generic -expansion results in weak local minima, while common binary multi-layered formulations lead to non-submodularity, complex high-order potentials, or polar domain unwrapping and shape biases. In practice, applying these methods to arbitrary trees does not work except for simple cases. Our main contribution is an optimization method for the Hierarchically-structured Interacting Segments (HINTS) model with arbitrary trees. Our Path-Moves algorithm is based on multi-label MRF formulation and can be seen as a combination of well-known a-expansion and Ishikawa techniques. We show state-of-the-art biomedical segmentation for many diverse examples of complex trees.

PURPOSE: Establishing and obtaining consistent quantitative indices of retinal thickness from a variety of clinically used Spectral-Domain Optical Coherence Tomography scanners. DESIGN: Retinal images from five Spectral-Domain Optical Coherence Tomography scanners were used to determine total retinal thickness with scanner-specific correction factors establishing consistency of thickness measurement across devices. PARTICIPANTS: 55 Fovea-centered Spectral-Domain Optical Coherence Tomography volumes from eleven subjects were analyzed, obtained from Cirrus HD-OCT, RS-3000, Heidelberg Spectralis, RTVue and Topcon2000, seven subjects with retinal diseases and four normal controls. METHOD: The Iowa Reference Algorithm measured total retinal thickness. Nonlinear model of total retinal thickness measurement comparisons was derived and used for device-specific comparisons. Bland-Altman plots and pairwise predictive equations yielded pairwise scanner-specific differences. Mendel test determined whether measurement biases were constant for each scanner pair. RESULTS: Mendel test revealed that all pairwise scanner differences of total retinal thickness were constant across the cohort (p=0.992). Individual measurements can thus be bias-corrected and the Iowa Reference Algorithm serve as a scanner-agnostic independent standard of total retinal thickness across the five tested SD-OCT scanners. CONCLUSIONS: Combination of the Iowa Reference Algorithm with scanner-specific bias correction yields cross-scanner consistency of total retinal thickness measurements, facilitating scanning-device independent quantitative assessment of total retinal thickness, longitudinal follow-up quantification without requiring patients to be imaged on the same scanner model, and allowing for multi-center studies with heterogeneous device utilization when using the Iowa Reference Algorithm., Comment: 14 pages, 5 tables, 5 figures

Purpose. This study was conducted to determine the thickness map of eleven retinal layers in normal subjects by spectral domain optical coherence tomography (SD-OCT) and evaluate their association with sex and age. Methods. Mean regional retinal thickness of 11 retinal layers were obtained by automatic three-dimensional diffusion-map-based method in 112 normal eyes of 76 Iranian subjects. Results. The thickness map of central foveal area in layer 1, 3, and 4 displayed the minimum thickness (P<0.005 for all). Maximum thickness was observed in nasal to the fovea of layer 1 (P<0.001) and in a circular pattern in the parafoveal retinal area of layers 2, 3 and 4 and in central foveal area of layer 6 (P<0.001). Temporal and inferior quadrants of the total retinal thickness and most of other quadrants of layer 1 were significantly greater in the men than in the women. Surrounding eight sectors of total retinal thickness and a limited number of sectors in layer 1 and 4 significantly correlated with age. Conclusion. SD-OCT demonstrated the three-dimensional thickness distribution of retinal layers in normal eyes. Thickness of layers varied with sex and age and in different sectors. These variables should be considered while evaluating macular thickness., Comment: 32 pages, 10 figures

Optical coherence tomography (OCT) is a powerful and noninvasive method for retinal imaging. In this paper, we introduce a fast segmentation method based on a new variant of spectral graph theory named diffusion maps. The research is performed on spectral domain (SD) OCT images depicting macular and optic nerve head appearance. The presented approach does not require edge-based image information and relies on regional image texture. Consequently, the proposed method demonstrates robustness in situations of low image contrast or poor layer-to-layer image gradients. Diffusion mapping is applied to 2D and 3D OCT datasets composed of two steps, one for partitioning the data into important and less important sections, and another one for localization of internal layers.In the first step, the pixels/voxels are grouped in rectangular/cubic sets to form a graph node.The weights of a graph are calculated based on geometric distances between pixels/voxels and differences of their mean intensity.The first diffusion map clusters the data into three parts, the second of which is the area of interest. The other two sections are eliminated from the remaining calculations. In the second step, the remaining area is subjected to another diffusion map assessment and the internal layers are localized based on their textural similarities.The proposed method was tested on 23 datasets from two patient groups (glaucoma and normals). The mean unsigned border positioning errors(mean - SD) was 8.52 - 3.13 and 7.56 - 2.95 micrometer for the 2D and 3D methods, respectively., Comment: 30 pages,32 figures