General Retinal Vessel Segmentation Using Regularization-Based Multiconcavity Modeling

Detecting blood vessels in retinal images with the presence of bright and dark lesions is a challenging unsolved problem. In this paper, a novel multiconcavity modeling approach is proposed to handle both healthy and unhealthy retinas simultaneously. The differentiable concavity measure is proposed to handle bright lesions in a perceptive space. The line-shape concavity measure is proposed to remove dark lesions which have an intensity structure different from the line-shaped vessels in a retina. The locally normalized concavity measure is designed to deal with unevenly distributed noise due to the spherical intensity variation in a retinal image. These concavity measures are combined together according to their statistical distributions to detect vessels in general retinal images. Very encouraging experimental results demonstrate that the proposed method consistently yields the best performance over existing state-of-the-art methods on the abnormal retinas and its accuracy outperforms the human observer, which has not been achieved by any of the state-of-the-art benchmark methods. Most importantly, unlike existing methods, the proposed method shows very attractive performances not only on healthy retinas but also on a mixture of healthy and pathological retinas.

Related papers:

title: USE OF JOSLIN VISION NETWORK DIGITAL-VIDEO NONMYDRIATIC RETINAL IMAGING TO ASSESS DIABETIC RETINOPATHY IN A CLINICAL PROGRAM
abstract: To incorporate a nonmydriatic, digital-video retinal imaging system into a Diabetes Outpatient Intensive Treatment Program and to evaluate the system’s ability to assess diabetic retinopathy (DR), determine follow-up, and appropriately refer to retinal specialist ophthalmologists.  Fundus images were obtained according to Joslin Vision Network (JVN) protocol and evaluated by certified JVN readers. Patients with significant retinal disease underwent evaluation by retinal specialists.  A total of 268 (51.0%) of 525 imaged patients had comprehensive eye examination by a retinal specialist owing to referable JVN-assessed clinical level of DR, nondiabetic ocular disease, ungradeable images, last eye examination ≥12 months prior, or patient request for examination. JVN diagnosis of a clinical level of DR agreed exactly with clinical findings in 388 eyes (72.5%) or within one level in 478 eyes (89.3%). JVN referral based on most severe diagnosis in either eye matched retinal specialist-recommended follow-up in 248/268 of patients (92.5%). A total of 136/525 (25.9%) of JVN patients had nondiabetic ocular abnormalities requiring referral.  Recommended follow-up from JVN imaging compared favorably to clinical examination by a retinal specialist. Nondiabetic ocular pathology was identified. JVN assessment of DR level compares favorably to clinical practice, potentially improving access to eye care and enhancing diabetes management.

title: Clinical evaluation of patients with diabetic retinopathy: accuracy of the Inoveon diabetic retinopathy-3DT system.
abstract: This study analyzed the accuracy of the Inoveon Diabetic Retinopathy (DR-3DT) system (Inoveon Corp., Oklahoma City, OK), a scalable evaluation method for the management of diabetic retinopathy using high-quality digital retinal imaging.



An independent, masked, cross-sectional, clinical validation study.



Two hundred ninety adult patients with diabetes from the Chickasaw Nation's Carl Albert Indian Health Facility in Ada, Oklahoma.



All participants underwent DRS7 imaging using a Zeiss FF450 fundus camera with images recorded on 35-mm film and a Kodak DCS520 digital camera back. Masked double grading with independent third reader adjudication yielded an Early Treatment Diabetic Retinopathy Study (ETDRS) Final Retinopathy Severity Scale Level (ETDRS Level) and macular edema stage for each eye. The presence of greater-than-or-equal ETDRS Level 53, questionable or definite clinically significant macular edema in either eye, or ungradeable images was defined as a threshold event requiring referral.



Accuracy (sensitivity, specificity, predictive values) of the digital system relative to the film "gold standard" on the threshold referral criteria per patient.



All patients with gradeable 35-mm slides from at least one eye were included in this per patient analysis (n = 290). The prevalence of threshold events was 19.3%. The sensitivity of the digital system in detecting threshold events was 98.2% (95% confidence interval [CI], 90.5%-100.0%) and specificity 89.7% (95% CI, 85.1%-93.3%). The positive predictive value was 69.5% and negative predictive value 99.5% for this sample.



When compared with the "gold standard," Inoveon's DR-3DT system provides highly accurate diabetic retinopathy referral decisions. Given their inherent advantages, high-quality digital imaging systems could replace the film "gold standard" as the basis for scalable, accessible, diabetic retinopathy evaluation.

title: Automatic detection of red lesions in digital color fundus photographs
abstract: The robust detection of red lesions in digital color fundus photographs is a critical step in the development of automated screening systems for diabetic retinopathy. In this paper, a novel red lesion detection method is presented based on a hybrid approach, combining prior works by Spencer et al. (1996) and Frame et al. (1998) with two important new contributions. The first contribution is a new red lesion candidate detection system based on pixel classification. Using this technique, vasculature and red lesions are separated from the background of the image. After removal of the connected vasculature the remaining objects are considered possible red lesions. Second, an extensive number of new features are added to those proposed by Spencer-Frame. The detected candidate objects are classified using all features and a k-nearest neighbor classifier. An extensive evaluation was performed on a test set composed of images representative of those normally found in a screening set. When determining whether an image contains red lesions the system achieves a sensitivity of 100% at a specificity of 87%. The method is compared with several different automatic systems and is shown to outperform them all. Performance is close to that of a human expert examining the images for the presence of red lesions.

title: Retinal image analysis: Concepts, applications and potential
abstract: As digital imaging and computing power increasingly develop, so too does the potential to use these technologies in ophthalmology. Image processing, analysis and computer vision techniques are increasing in prominence in all fields of medical science, and are especially pertinent to modern ophthalmology, as it is heavily dependent on visually oriented signs. The retinal microvasculature is unique in that it is the only part of the human circulation that can be directly visualised non-invasively in vivo, readily photographed and subject to digital image analysis. Exciting developments in image processing relevant to ophthalmology over the past 15 years includes the progress being made towards developing automated diagnostic systems for conditions, such as diabetic retinopathy, age-related macular degeneration and retinopathy of prematurity. These diagnostic systems offer the potential to be used in large-scale screening programs, with the potential for significant resource savings, as well as being free from observer bias and fatigue. In addition, quantitative measurements of retinal vascular topography using digital image analysis from retinal photography have been used as research tools to better understand the relationship between the retinal microvasculature and cardiovascular disease. Furthermore, advances in electronic media transmission increase the relevance of using image processing in 'teleophthalmology' as an aid in clinical decision-making, with particular relevance to large rural-based communities. In this review, we outline the principles upon which retinal digital image analysis is based. We discuss current techniques used to automatically detect landmark features of the fundus, such as the optic disc, fovea and blood vessels. We review the use of image analysis in the automated diagnosis of pathology (with particular reference to diabetic retinopathy). We also review its role in defining and performing quantitative measurements of vascular topography, how these entities are based on 'optimisation' principles and how they have helped to describe the relationship between systemic cardiovascular disease and retinal vascular changes. We also review the potential future use of fundal image analysis in telemedicine.

title: Image structure clustering for image quality verification of color retina images in diabetic retinopathy screening
abstract: Reliable verification of image quality of retinal screening images is a prerequisite for the development of automatic screening systems for diabetic retinopathy. A system is presented that can automatically determine whether the quality of a retinal screening image is sufficient for automatic analysis. The system is based on the assumption that an image of sufficient quality should contain particular image structures according to a certain pre-defined distribution. We cluster filterbank response vectors to obtain a compact representation of the image structures found within an image. Using this compact representation together with raw histograms of the R, G, and B color planes, a statistical classifier is trained to distinguish normal from low quality images. The presented system does not require any previous segmentation of the image in contrast with previous work. The system was evaluated on a large, representative set of 1000 images obtained in a screening program. The proposed method, using different feature sets and classifiers, was compared with the ratings of a second human observer. The best system, based on a Support Vector Machine, has performance close to optimal with an area under the ROC curve of 0.9968.

title: Automatic segmentation of microaneurysms in retinal angiograms of diabetic patients
abstract: In this paper a method for automatic detection of microaneurysms in digital angiograms of the eye fundus is described. These lesions of the human retina, a characteristic of the earliest phases of diabetic retinopathy, present themselves in the angiographic images as small, round, hyperfluorescent objects. The proposed method includes initial pre-processing and enhancement steps, followed by object segmentation. In the final phase, microaneurysms are validated using two new criteria based on local intensity, contrast and shape relations. The combination of these local features with global image parameters makes possible a high degree of independence from image intensity characteristics.

title: Automated feature extraction in color retinal images by a model based approach
abstract: Color retinal photography is an important tool to detect the evidence of various eye diseases. Novel methods to extract the main features in color retinal images have been developed in this paper. Principal component analysis is employed to locate optic disk; A modified active shape model is proposed in the shape detection of optic disk; A fundus coordinate system is established to provide a better description of the features in the retinal images; An approach to detect exudates by the combined region growing and edge detection is proposed. The success rates of disk localization, disk boundary detection, and fovea localization are 99%, 94%, and 100%, respectively. The sensitivity and specificity of exudate detection are 100 % and 71 %, correspondingly. The success of the proposed algorithms can be attributed to the utilization of the model-based methods. The detection and analysis could be applied to automatic mass screening and diagnosis of the retinal diseases.

title: Measurement of retinal vessel widths from fundus images based on 2-D modeling
abstract: Changes in retinal vessel diameter are an important sign of diseases such as hypertension, arteriosclerosis and diabetes mellitus. Obtaining precise measurements of vascular widths is a critical and demanding process in automated retinal image analysis as the typical vessel is only a few pixels wide. This paper presents an algorithm to measure the vessel diameter to subpixel accuracy. The diameter measurement is based on a two-dimensional difference of Gaussian model, which is optimized to fit a two-dimensional intensity vessel segment. The performance of the method is evaluated against Brinchmann-Hansen's half height, Gregson's rectangular profile and Zhou's Gaussian model. Results from 100 sample profiles show that the presented algorithm is over 30% more precise than the compared techniques and is accurate to a third of a pixel.

title: Optic Disc Detection From Normalized Digital Fundus Images by Means of a Vessels' Direction Matched Filter
abstract: Optic disc (OD) detection is a main step while developing automated screening systems for diabetic retinopathy. We present in this paper a method to automatically detect the position of the OD in digital retinal fundus images. The method starts by normalizing luminosity and contrast through out the image using illumination equalization and adaptive histogram equalization methods respectively. The OD detection algorithm is based on matching the expected directional pattern of the retinal blood vessels. Hence, a simple matched filter is proposed to roughly match the direction of the vessels at the OD vicinity. The retinal vessels are segmented using a simple and standard 2-D Gaussian matched filter. Consequently, a vessels direction map of the segmented retinal vessels is obtained using the same segmentation algorithm. The segmented vessels are then thinned, and filtered using local intensity, to represent finally the OD-center candidates. The difference between the proposed matched filter resized into four different sizes, and the vessels' directions at the surrounding area of each of the OD-center candidates is measured. The minimum difference provides an estimate of the OD-center coordinates. The proposed method was evaluated using a subset of the STARE project's dataset, containing 81 fundus images of both normal and diseased retinas, and initially used by literature OD detection methods. The OD-center was detected correctly in 80 out of the 81 images (98.77%). In addition, the OD-center was detected correctly in all of the 40 images (100%) using the publicly available DRIVE dataset.

title: Detection of Anatomic Structures in Human Retinal Imagery
abstract: The widespread availability of electronic imaging devices throughout the medical community is leading to a growing body of research on image processing and analysis to diagnose retinal disease such as diabetic retinopathy (DR). Productive computer-based screening of large, at-risk populations at low cost requires robust, automated image analysis. In this paper we present results for the automatic detection of the optic nerve and localization of the macula using digital red-free fundus photography. Our method relies on the accurate segmentation of the vasculature of the retina followed by the determination of spatial features describing the density, average thickness, and average orientation of the vasculature in relation to the position of the optic nerve. Localization of the macula follows using knowledge of the optic nerve location to detect the horizontal raphe of the retina using a geometric model of the vasculature. We report 90.4% detection performance for the optic nerve and 92.5% localization performance for the macula for red-free fundus images representing a population of 345 images corresponding to 269 patients with 18 different pathologies associated with DR and other common retinal diseases such as age-related macular degeneration.

title: Segmentation of candidate dark lesions in fundus images based on local thresholding and pixel density
abstract: Due to its blood microcirculation, the retina is one of the first organs affected by hypertension and diabetes: retinal damages can lead to serious visual loss, that can be avoided by an early diagnosis. The most distinctive sign of diabetic retinopathy or severe hypertensive retinopathy are dark lesions such as haemorrhages and microaneurysms (HM), and bright lesions such as hard exudates (HE) and cotton wool spots (CWS). Automatic detection of their presence in the retina is thus of paramount importance for assessing the presence of retinopathy, and therefore relieve the burden of image examination by retinal experts. The most widespread scheme for automatically detect retinal lesion rely on a initial segmentation and a subsequent refinement stage, usually by means of a supervised classification or based on heuristic rules. The first step is therefore required not to lose any possible lesions, at the same time discarding as much of the normal retina as possible. In this work we propose a simple and effective method to detect and identify haemorrhagic (dark) lesions in retinal images, by using a simple local thresholding followed by an evaluation of a measure of the spatial density of the pixels selected at the first step. We evaluate the algorithm on 6 images presenting dark lesions extracted from a database of 60 annotated images, resulting in a mean detection rate of 94% the lesions present in an image, with good performance in term of false candidate rejection.

title: Automated detection of fundus photographic red lesions in diabetic retinopathy.
abstract: To compare a fundus image-analysis algorithm for automated detection of hemorrhages and microaneurysms with visual detection of retinopathy in patients with diabetes.



Four hundred fundus photographs (35-mm color transparencies) were obtained in 200 eyes of 100 patients with diabetes who were randomly selected from the Welsh Community Diabetic Retinopathy Study. A gold standard reference was defined by classifying each patient as having or not having diabetic retinopathy based on overall visual grading of the digitized transparencies. A single-lesion visual grading was made independently, comprising meticulous outlining of all single lesions in all photographs and used to develop the automated red lesion detection system. A comparison of visual and automated single-lesion detection in replicating the overall visual grading was then performed.



Automated red lesion detection demonstrated a specificity of 71.4% and a resulting sensitivity of 96.7% in detecting diabetic retinopathy when applied at a tentative threshold setting for use in diabetic retinopathy screening. The accuracy of 79% could be raised to 85% by adjustment of a single user-supplied parameter determining the balance between the screening priorities, for which a considerable range of options was demonstrated by the receiver-operating characteristic (area under the curve 90.3%). The agreement of automated lesion detection with overall visual grading (0.659) was comparable to the mean agreement of six ophthalmologists (0.648).



Detection of diabetic retinopathy by automated detection of single fundus lesions can be achieved with a performance comparable to that of experienced ophthalmologists. The results warrant further investigation of automated fundus image analysis as a tool for diabetic retinopathy screening.

title: A novel automatic image processing algorithm for detection of hard exudates based on retinal image analysis.
abstract: We present an automatic image processing algorithm to detect hard exudates. Automatic detection of hard exudates from retinal images is an important problem since hard exudates are associated with diabetic retinopathy and have been found to be one of the most prevalent earliest signs of retinopathy. The algorithm is based on Fisher's linear discriminant analysis and makes use of colour information to perform the classification of retinal exudates. We prospectively assessed the algorithm performance using a database containing 58 retinal images with variable colour, brightness, and quality. Our proposed algorithm obtained a sensitivity of 88% with a mean number of 4.83+/-4.64 false positives per image using the lesion-based performance evaluation criterion, and achieved an image-based classification accuracy of 100% (sensitivity of 100% and specificity of 100%).

title: Optimal Wavelet Transform for the Detection of Microaneurysms in Retina Photographs
abstract: In this paper, we propose an automatic method to detect microaneurysms in retina photographs. Microaneurysms are the most frequent and usually the first lesions to appear as a consequence of diabetic retinopathy. So, their detection is necessary for both screening the pathology and follow up (progression measurement). Automating this task, which is currently performed manually, would bring more objectivity and reproducibility. We propose to detect them by locally matching a lesion template in sub- bands of wavelet transformed images. To improve the method performance, we have searched for the best adapted wavelet within the lifting scheme framework. The optimization process is based on a genetic algorithm followed by Powell's direction set descent. Results are evaluated on 120 retinal images analyzed by an expert and the optimal wavelet is compared to different conventional mother wavelets. These images are of three different modalities: there are color photographs, green filtered photographs, and angiographs. Depending on the imaging modality, microaneurysms were detected with a sensitivity of respectively 89.62%, 90.24%, and 93.74% and a positive predictive value of respectively 89.50%, 89.75%, and 91.67%, which is better than previously published methods.

title: Retinal Vessel Centerline Extraction Using Multiscale Matched Filters, Confidence and Edge Measures
abstract: Motivated by the goals of improving detection of low-contrast and narrow vessels and eliminating false detections at nonvascular structures, a new technique is presented for extracting vessels in retinal images. The core of the technique is a new likelihood ratio test that combines matched-filter responses, confidence measures and vessel boundary measures. Matched filter responses are derived in scale-space to extract vessels of widely varying widths. A vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile. Vessel boundary measures and associated confidences are computed at potential vessel boundaries. Combined, these responses form a six-dimensional measurement vector at each pixel. A training technique is used to develop a mapping of this vector to a likelihood ratio that measures the "vesselness" at each pixel. Results comparing this vesselness measure to matched filters alone and to measures based on the Hessian of intensities show substantial improvements, both qualitatively and quantitatively. The Hessian can be used in place of the matched filter to obtain similar but less-substantial improvements or to steer the matched filter by preselecting kernel orientations. Finally, the new vesselness likelihood ratio is embedded into a vessel tracing framework, resulting in an efficient and effective vessel centerline extraction algorithm

title: Retinal Vessel Centerline Extraction Using Multiscale Matched Filters, Confidence and Edge Measures
abstract: Motivated by the goals of improving detection of low-contrast and narrow vessels and eliminating false detections at nonvascular structures, a new technique is presented for extracting vessels in retinal images. The core of the technique is a new likelihood ratio test that combines matched-filter responses, confidence measures and vessel boundary measures. Matched filter responses are derived in scale-space to extract vessels of widely varying widths. A vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile. Vessel boundary measures and associated confidences are computed at potential vessel boundaries. Combined, these responses form a six-dimensional measurement vector at each pixel. A training technique is used to develop a mapping of this vector to a likelihood ratio that measures the "vesselness" at each pixel. Results comparing this vesselness measure to matched filters alone and to measures based on the Hessian of intensities show substantial improvements, both qualitatively and quantitatively. The Hessian can be used in place of the matched filter to obtain similar but less-substantial improvements or to steer the matched filter by preselecting kernel orientations. Finally, the new vesselness likelihood ratio is embedded into a vessel tracing framework, resulting in an efficient and effective vessel centerline extraction algorithm

title: A multimodal registration algorithm of eye fundus images using vessels detection and Hough transform
abstract: Image registration is a real challenge because physicians handle many images. Temporal registration is necessary in order to follow the various steps of a disease, whereas multimodal registration allows us to improve the identification of some lesions or to compare pieces of information gathered from different sources. This paper presents an algorithm for temporal and/or multimodal registration of retinal images based on point correspondence. As an example, the algorithm has been applied to the registration of fluorescein images (obtained after a fluorescein dye injection) with green images (green filter of a color image). The vascular tree is first detected in each type of images and bifurcation points are labeled with surrounding vessel orientations. An angle-based invariant is then computed in order to give a probability for two points to match. Then a Bayesian Hough transform is used to sort the transformations with their respective likelihoods. A precise affine estimate is finally computed for most likely transformations. The best transformation is chosen for registration.

title: A Novel Method for the Automatic Grading of Retinal Vessel Tortuosity
abstract: Tortuosity is among the first alterations in the retinal vessel network to appear in many retinopathies, such as those due to hypertension. An automatic evaluation of retinal vessel tortuosity would help the early detection of such retinopathies. Quite a few techniques for tortuosity measurement and classification have been proposed, but they do not always match the clinical concept of tortuosity. This justifies the need for a new definition, able to express in mathematical terms the tortuosity as perceived by ophthalmologists. We propose here a new algorithm for the evaluation of tortuosity in vessels recognized in digital fundus images. It is based on partitioning each vessel in segments of constant-sign curvature and then combining together each evaluation of such segments and their number. The algorithm has been compared with other available tortuosity measures on a set of 30 arteries and one of 30 veins from 60 different images. These vessels had been preliminarily ordered by a retina specialist by increasing perceived tortuosity. The proposed algorithm proved to be the best one in matching the clinically perceived vessel tortuosity.

title: Segmentation of the Optic Disc, Macula and Vascular Arch in Fundus Photographs
abstract: An automatic system is presented to find the location of the major anatomical structures in color fundus photographs; the optic disc, the macula, and the vascular arch. These structures are found by fitting a single point-distribution-model to the image, that contains points on each structure. The method can handle optic disc and macula centered images of both the left and the right eye. The system uses a cost function, which is based on a combination of both global and local cues, to find the correct position of the model points. The global terms in the cost function are based on the orientation and width of the vascular pattern in the image. The local term is derived from the image structure around the points of the model. To optimize the fit of the point-distribution-model to an image, a sophisticated combination of optimization processes is proposed which combines optimization in the parameter space of the model and in the image space, where points are moved directly. Experimental results are presented demonstrating that our specific choices for the cost function components and optimization scheme are needed to obtain good results. The system was developed and trained on a set of 500 screening images, and tested on a completely independent set of 500 screening images. In addition to this the system was also tested on a separate set of 100 pathological images. In the screening set it was able to find the vascular arch in 93.2%, the macula in 94.4%, the optic disc location in 98.4% and whether it is dealing with a left or right eye in 100% of all tested cases. For the pathological images test set, this was 77.0%, 92.0%, 94.0%, and 100% respectively

title: Automated microaneurysm detection using local contrast normalization and local vessel detection
abstract: Screening programs using retinal photography for the detection of diabetic eye disease are being introduced in the U.K. and elsewhere. Automatic grading of the images is being considered by health boards so that the human grading task is reduced. Microaneurysms (MAs) are the earliest sign of this disease and so are very important for classifying whether images show signs of retinopathy. This paper describes automatic methods for MA detection and shows how image contrast normalization can improve the ability to distinguish between MAs and other dots that occur on the retina. Various methods for contrast normalization are compared. Best results were obtained with a method that uses the watershed transform to derive a region that contains no vessels or other lesions. Dots within vessels are handled successfully using a local vessel detection technique. Results are presented for detection of individual MAs and for detection of images containing MAs. Images containing MAs are detected with sensitivity 85.4% and specificity 83.1%

title: Retinal image analysis to detect and quantify lesions associated with diabetic retinopathy
abstract: An automatic method to detect hard exudates, a lesion associated with diabetic retinopathy, is proposed. The algorithm found on their color, using a statistical classification, and their sharp edges, applying an edge detector, to localize them. A sensitivity of 79.62% with a mean number of 3 false positives per image is obtained in a database of 20 retinal image with variable color, brightness and quality. In that way, we evaluate the robustness of the method in order to make adequate to a clinical environment. Further efforts will be done to improve its performance.

title: Automated detection and differentiation of drusen, exudates, and cotton-wool spots in digital color fundus photographs for diabetic retinopathy diagnosis.
abstract: To describe and evaluate a machine learning-based, automated system to detect exudates and cotton-wool spots in digital color fundus photographs and differentiate them from drusen, for early diagnosis of diabetic retinopathy.



Three hundred retinal images from one eye of 300 patients with diabetes were selected from a diabetic retinopathy telediagnosis database (nonmydriatic camera, two-field photography): 100 with previously diagnosed bright lesions and 200 without. A machine learning computer program was developed that can identify and differentiate among drusen, (hard) exudates, and cotton-wool spots. A human expert standard for the 300 images was obtained by consensus annotation by two retinal specialists. Sensitivities and specificities of the annotations on the 300 images by the automated system and a third retinal specialist were determined.



The system achieved an area under the receiver operating characteristic (ROC) curve of 0.95 and sensitivity/specificity pairs of 0.95/0.88 for the detection of bright lesions of any type, and 0.95/0.86, 0.70/0.93, and 0.77/0.88 for the detection of exudates, cotton-wool spots, and drusen, respectively. The third retinal specialist achieved pairs of 0.95/0.74 for bright lesions and 0.90/0.98, 0.87/0.98, and 0.92/0.79 per lesion type.



A machine learning-based, automated system capable of detecting exudates and cotton-wool spots and differentiating them from drusen in color images obtained in community based diabetic patients has been developed and approaches the performance level of retinal experts. If the machine learning can be improved with additional training data sets, it may be useful for detecting clinically important bright lesions, enhancing early diagnosis, and reducing visual loss in patients with diabetes.

title: Abnormality detection in automated mass screening system of diabetic retinopathy
abstract: An approach to abnormality detection from colour fundus images for an automated mass screening system is proposed in this paper, which uses the object-based colour difference image. Four colour models, viz. RGB, Luv, Lab and HVC, are evaluated based on hand-labelled feature maps, and Luv and Lab are selected for computing the colour difference because of their good performances in object classification. The object-based colour difference images of bright objects (e.g. exudates) and dark objects (e.g. haemorrhages and blood vessels) are obtained respectively according to the 2D histogram distribution on the L-u plane, and then a watershed transform is performed on the colour difference image to extract object candidates. A pre-thresholding and a post-verification procedure are performed to deal with the over-segmentation problem of the watershed transform.

title: Detection of blood vessels in retinal images using two-dimensional matched filters.
abstract: Blood vessels usually have poor local contrast, and the application of existing edge detection algorithms yield results which are not satisfactory. An operator for feature extraction based on the optical and spatial properties of objects to be recognized is introduced. The gray-level profile of the cross section of a blood vessel is approximated by a Gaussian-shaped curve. The concept of matched filter detection of signals is used to detect piecewise linear segments of blood vessels in these images. Twelve different templates that are used to search for vessel segments along all possible directions are constructed. Various issues related to the implementation of these matched filters are discussed. The results are compared to those obtained with other methods.

title: Locating blood vessels in retinal images by piecewise threshold probing of a matched filter response
abstract: Describes an automated method to locate and outline blood vessels in images of the ocular fundus. Such a tool should prove useful to eye care specialists for purposes of patient screening, treatment evaluation, and clinical study. The authors' method differs from previously known methods in that it uses local and global vessel features cooperatively to segment the vessel network. The authors evaluate their method using hand-labeled ground truth segmentations of 20 images. A plot of the operating characteristic shows that the authors' method reduces false positives by as much as 15 times over basic thresholding of a matched filter response (MFR), at up to a 75% true positive rate. For a baseline, they also compared the ground truth against a second hand-labeling, yielding a 90% true positive and a 4% false positive detection rate, on average. These numbers suggest there is still room for a 15% true positive rate improvement, with the same false positive rate, over the authors' method. They are making all their images and hand labelings publicly available for interested researchers to use in evaluating related methods.

title: Adaptive Local Thresholding by Verification-Based Multithreshold Probing with Application to Vessel Detection in Retinal Images
abstract: In this paper, we propose a general framework of adaptive local thresholding based on a verification-based multithreshold probing scheme. Object hypotheses are generated by binarization using hypothetic thresholds and accepted/rejected by a verification procedure. The application-dependent verification procedure can be designed to fully utilize all relevant informations about the objects of interest. In this sense, our approach is regarded as knowledge-guided adaptive thresholding, in contrast to most algorithms known from the literature. We apply our general framework to detect vessels in retinal images. An experimental evaluation demonstrates superior performance over global thresholding and a vessel detection method recently reported in the literature. Due to its simplicity and general nature, our novel approach is expected to be applicable to a variety of other applications.

title: Retinal Blood Vessel Segmentation Using Line Operators and Support Vector Classification
abstract: In the framework of computer-aided diagnosis of eye diseases, retinal vessel segmentation based on line operators is proposed. A line detector, previously used in mammography, is applied to the green channel of the retinal image. It is based on the evaluation of the average grey level along lines of fixed length passing through the target pixel at different orientations. Two segmentation methods are considered. The first uses the basic line detector whose response is thresholded to obtain unsupervised pixel classification. As a further development, we employ two orthogonal line detectors along with the grey level of the target pixel to construct a feature vector for supervised classification using a support vector machine. The effectiveness of both methods is demonstrated through receiver operating characteristic analysis on two publicly available databases of color fundus images.

title: Cellular Neural Networks With Virtual Template Expansion for Retinal Vessel Segmentation
abstract: A retinal vessel segmentation method based on cellular neural networks (CNNs) is proposed. The CNN design is characterized by a virtual template expansion obtained through a multistep operation. It is based on linear space-invariant 3times3 templates and can be realized using existing chip prototypes like the ACE16K. The proposed design is capable of performing vessel segmentation within a short computation time. It was tested on a publicly available database of color images of the retina, using receiver operating characteristic curves. The simulation results show good performance comparable with that of the best existing methods

title: A fuzzy vessel tracking algorithm for retinal images based on fuzzy clustering
abstract: In this paper the authors present a new unsupervised fuzzy algorithm for vessel tracking that is applied to the detection of the ocular fundus vessels. The proposed method overcomes the problems of initialization and vessel profile modeling that are encountered in the literature and automatically tracks fundus vessels using linguistic descriptions like "vessel" and "nonvessel." The main tool for determining vessel and nonvessel regions along a vessel profile is the fuzzy C-means clustering algorithm that is fed with properly preprocessed data, Additional procedures for checking the validity of the detected vessels and handling junctions and forks are also presented. The application of the proposed algorithm to fundus images and simulated vessels resulted in very good overall performance and consistent estimation of vessel parameters.

title: Ridge-based vessel segmentation in color images of the retina
abstract: A method is presented for automated segmentation of vessels in two-dimensional color images of the retina. This method can be used in computer analyses of retinal images, e.g., in automated screening for diabetic retinopathy. The system is based on extraction of image ridges, which coincide approximately with vessel centerlines. The ridges are used to compose primitives in the form of line elements. With the line elements an image is partitioned into patches by assigning each image pixel to the closest line element. Every line element constitutes a local coordinate frame for its corresponding patch. For every pixel, feature vectors are computed that make use of properties of the patches and the line elements. The feature vectors are classified using a kNN-classifier and sequential forward feature selection. The algorithm was tested on a database consisting of 40 manually labeled images. The method achieves an area under the receiver operating characteristic curve of 0.952. The method is compared with two recently published rule-based methods of Hoover et al. and Jiang et al. . The results show that our method is significantly better than the two rule-based methods (p<0.01). The accuracy of our method is 0.944 versus 0.947 for a second observer.

title: Comparative study of retinal vessel segmentation methods on a new publicly available database
abstract: In this work we compare the performance of a number of vessel segmentation algorithms on a newly constructed retinal vessel image database. Retinal vessel segmentation is important for the detection of numerous eye diseases and plays an important role in automatic retinal disease screening systems. A large number of methods for retinal vessel segmentation have been published, yet an evaluation of these methods on a common database of screening images has not been performed. To compare the performance of retinal vessel segmentation methods we have constructed a large database of retinal images. The database contains forty images in which the vessel trees have been manually segmented. For twenty of those forty images a second independent manual segmentation is available. This allows for a comparison between the performance of automatic methods and the performance of a human observer. The database is available to the research community. Interested researchers are encouraged to upload their segmentation results to our website (http://www.isi.uu.nl/Research/Databases). The performance of five different algorithms has been compared. Four of these methods have been implemented as described in the literature. The fifth pixel classification based method was developed specifically for the segmentation of retinal vessels and is the only supervised method in this test. We define the segmentation accuracy with respect to our gold standard as the performance measure. Results show that the pixel classification method performs best, but the second observer still performs significantly better.

title: Segmentation of retinal blood vessels by combining the detection of centerlines and morphological reconstruction
abstract: This paper presents an automated method for the segmentation of the vascular network in retinal images. The algorithm starts with the extraction of vessel centerlines, which are used as guidelines for the subsequent vessel filling phase. For this purpose, the outputs of four directional differential operators are processed in order to select connected sets of candidate points to be further classified as centerline pixels using vessel derived features. The final segmentation is obtained using an iterative region growing method that integrates the contents of several binary images resulting from vessel width dependent morphological filters. Our approach was tested on two publicly available databases and its results are compared with recently published methods. The results demonstrate that our algorithm outperforms other solutions and approximates the average accuracy of a human observer without a significant degradation of sensitivity and specificity

title: A Novel Vessel Segmentation Algorithm for Pathological Retina Images Based on the Divergence of Vector Fields
abstract: In this paper, a method is proposed for detecting blood vessels in pathological retina images. In the proposed method, blood vessel-like objects are extracted using the Laplacian operator and noisy objects are pruned according to the centerlines, which are detected using the normalized gradient vector field. The method has been tested with all the pathological retina images in the publicly available STARE database. Experiment results show that the method can avoid detecting false vessels in pathological regions and can produce reliable results for healthy regions.

title: Edge Detection and Ridge Detection with Automatic Scale Selection
abstract: When computing descriptors of image data, the type of information that can be extracted may be strongly dependent on the scales at which the image operators are applied. This article presents a systematic methodology for addressing this problem. A mechanism is presented for automatic selection of scale levels when detecting one-dimensional image features, such as edges and ridges.A novel concept of a scale-space edge is introduced, defined as a connected set of points in scale-space at which: (i) the gradient magnitude assumes a local maximum in the gradient direction, and (ii) a normalized measure of the strength of the edge response is locally maximal over scales. An important consequence of this definition is that it allows the scale levels to vary along the edge. Two specific measures of edge strength are analyzed in detail, the gradient magnitude and a differential expression derived from the third-order derivative in the gradient direction. For a certain way of normalizing these differential descriptors, by expressing them in terms of so-called γ-normalized derivatives, an immediate consequence of this definition is that the edge detector will adapt its scale levels to the local image structure. Specifically, sharp edges will be detected at fine scales so as to reduce the shape distortions due to scale-space smoothing, whereas sufficiently coarse scales will be selected at diffuse edges, such that an edge model is a valid abstraction of the intensity profile across the edge.Since the scale-space edge is defined from the intersection of two zero-crossing surfaces in scale-space, the edges will by definition form closed curves. This simplifies selection of salient edges, and a novel significance measure is proposed, by integrating the edge strength along the edge. Moreover, the scale information associated with each edge provides useful clues to the physical nature of the edge.With just slight modifications, similar ideas can be used for formulating ridge detectors with automatic selection, having the characteristic property that the selected scales on a scale-space ridge instead reflect the width of the ridge.It is shown how the methodology can be implemented in terms of straightforward visual front-end operations, and the validity of the approach is supported by theoretical analysis as well as experiments on real-world and synthetic data.

title: Image processing and analysis - variational, PDE, wavelet, and stochastic methods
abstract: Preface 1.  Some modern image analysis tools 3. Image modeling and representation 4. Image denoising 5. Image deblurring 6. Image inpainting 7. Image processing: segmentation Bibliography Index.

title: The digital TV filter and nonlinear denoising
abstract: Motivated by the classical TV (total variation) restoration model, we propose a new nonlinear filter-the digital TV filter for denoising and enhancing digital images, or more generally, data living on graphs. The digital TV filter is a data dependent lowpass filter, capable of denoising data without blurring jumps or edges. In iterations, it solves a global total variational (or L(1)) optimization problem, which differs from most statistical filters. Applications are given in the denoising of one dimensional (1-D) signals, two-dimensional (2-D) data with irregular structures, gray scale and color images, and nonflat image features such as chromaticity.

title: Linear structures in mammographic images: detection and classification
abstract: We describe methods for detecting linear structures in mammograms, and for classifying them into anatomical types (vessels, spicules, ducts, etc). Several different detection methods are compared, using realistic synthetic images and receiver operating characteristic (ROC) analysis. There are significant differences (p<0.001) between the methods, with the best giving an A/sub z/ value for pixel-level detection of 0.943. We also investigate methods for classifying the detected linear structures into anatomical types, using their cross-sectional profiles, with particular emphasis on recognising the "spicules" and "ducts" associated with some of the more subtle abnormalities. Automatic classification results are compared with expert annotations using ROC analysis, demonstrating useful discrimination between anatomical classes (A/sub z/=0.746). Some of this discrimination relies on simple attributes such as profile width and contrast, but important information is also carried by the shape of the profile (A/sub z/=0.653). The methods presented have potentially wide application in improving the specificity of abnormality detection by exploiting additional anatomical information.

title: Handbook of mathematics
abstract: Geometry.- Linear  Algebra and Discrete Mathematics.- Differentiation.- Infinite Series.- Integral Calculus.- Differential Equations.- Calculus of Variations.- Linear Integral Equations.- Functional Analysis.- Vector Analysis and Vector Fields.- Function Theory.- Integral Transformations.- Probability Theory and Mathematical  Dynamical Systems and Chaos.- Optimization.- Numerical Analysis.- Computer Algebra Systems-Example Mathematica.

title: Simultaneous feature selection and clustering using mixture models
abstract: Clustering is a common unsupervised learning technique used to discover group structure in a set of data. While there exist many algorithms for clustering, the important issue of feature selection, that is, what attributes of the data should be used by the clustering algorithms, is rarely touched upon. Feature selection for clustering is difficult because, unlike in supervised learning, there are no class labels for the data and, thus, no obvious criteria to guide the search. Another important problem in clustering is the determination of the number of clusters, which clearly impacts and is influenced by the feature selection issue. In this paper, we propose the concept of feature saliency and introduce an expectation-maximization (EM) algorithm to estimate it, in the context of mixture-based clustering. Due to the introduction of a minimum message length model selection criterion, the saliency of irrelevant features is driven toward zero, which corresponds to performing feature selection. The criterion and algorithm are then extended to simultaneously estimate the feature saliencies and the number of clusters.

title: Introduction to Probability
abstract: The course is attended by a large number of undergraduate and graduate students with diverse backgrounds. Acccordingly, we have tried to strike a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis has been just sketched or intuitively explained in the text, so that complex proofs do not stand in the way of an otherwise simple exposition. At the same time, some of this analysis and the necessary mathematical results are developed (at the level of advanced calculus) in theoretical problems, which are included at the end of the corresponding chapter. The theoretical problems (marked by *) constitute an important component of the text, and ensure that the mathematically oriented reader will find here a smooth development without major gaps.

title: On Combining Classifiers
abstract: We develop a common theoretical framework for combining classifiers which use distinct pattern representations and show that many existing schemes can be considered as special cases of compound classification where all the pattern representations are used jointly to make a decision. An experimental comparison of various classifier combination schemes demonstrates that the combination rule developed under the most restrictive assumptions-the sum rule-outperforms other classifier combinations schemes. A sensitivity analysis of the various schemes to estimation errors is carried out to show that this finding can be justified theoretically.

title: Receiver operating characteristic curves and their use in radiology.
abstract: Sensitivity and specificity are the basic measures of accuracy of a diagnostic test; however, they depend on the cut point used to define "positive" and "negative" test results. As the cut point shifts, sensitivity and specificity shift. The receiver operating characteristic (ROC) curve is a plot of the sensitivity of a test versus its false-positive rate for all possible cut points. The advantages of the ROC curve as a means of defining the accuracy of a test, construction of the ROC, and identification of the optimal cut point on the ROC curve are discussed. Several summary measures of the accuracy of a test, including the commonly used percentage of correct diagnoses and area under the ROC curve, are described and compared. Two examples of ROC curve application in radiologic research are presented.