Statistical Analysis of Complex Shape Graphs.

Machine learning methods using convolution neural networks (CNN) are one technique which has played an important role in many biomedical applications. Here we apply the techniques to the detection of retinal blood vessels in ophthalmological images. Since the eye is one of the most important sensory organs in the human body, it is critical to diagnose diseases in the early stages. Early symptoms of various diseases like glaucoma, diabetic retinopathy, and cardiovascular diseases can be detected via the structure of the blood vessels of the retina. Studying the retinal blood vessel structures and network requires blood vessel segmentation. Deep learning has been used for the last five years and achieved state-of-the-art performance. More specifically, the latest development has been implemented to segment blood vessels more efficiently by using the u-net architecture. In the process, we used forward convolutional long short-term memory (convLSTM) to combine the feature map of the encoding path and the corresponding decoding path in lieu of simple concatenation in the skip connection of the u-net. We also used a connected convolution layer to the last layers of the encoding path to obtain more diverse features. The images used were from the DRIVE database and preprocessing was performed to obtain more accurate results. We achieved 95% accuracy, a precision of 91%, a sensitivity of 52%, and a specificity of 99%. Even with a low sensitivity of 52%, all the major blood vessels are found successfully.

Fréchet PDF based Matched Filter Approach for Retinal Blood Vessels Segmentation

We propose a novel extension of matched filter approach by applying contrast-limited adaptive histogram equalization in pre-processing module and second derivative of Gaussian based matched filter to achieve a better retinal blood vessel structure. Proposed approach also concentrates towards extraction of thin as well as thick retinal blood vessels. The experimental results obtained for both DRIVE and STARE databases confirms that the proposed method has a higher true positive rate (sensitivity) as compared with other available retinal blood vessel segmentation approaches in literature. Further, the performance of the proposed method is also better for the extraction of pathological retinal images.

Scientific study revealed that eyes are the best indicators of many diseases like glaucoma, diabetic retinopathy, hypertension, and stroke. By examining the segmented retinal blood vessel network, ophthalmologist can get the information regarding the abnormality. The objective of this research is to provide reliable segmented retinal blood vessel to assist the ophthalmologists to figure out the abnormality precisely. In this work, enhanced Gabor filter in multiple orientation is employed for the retinal blood vessel extraction. The suggested method combines sharpening operation and median filtering with Gabor transform to get enhanced Gabor transformed images. Finally, to get the segmented output hysteresis thresholding is applied on the enhanced Gabor transformed images. As hysteresis thresholding takes into consideration the connectedness between neighboring pixels, it performs better in segmenting the vessels. The suggested integrated approach has improved the accuracy and specificity. Experiment on 20 retinal images of DRIVE database indicated 95.06% accuracy and 98.83% specificity.

With today's advancing technology, support of developing hardware and software systems, the developments in the field of medicine have increased considerably. In particular, medical image analysis and processing systems have taken a considerable lead. The development of an automatic system could provide great convenience for doctors and practitioners in the field. The image processing techniques proposed in this study can contribute to more effective analysis and more accurate diagnosis, regardless of the individual levels of experience of the users or particular situations and conditions such as fatigue or image quality. This paper presents a robust method for retinal blood vessel segmentation and some automatic algorithms for analyzing the vessel network and pixel classification into vessel and non-vessel .The aim of the work extraction or segmentation of retinal blood vessels used computer vision and image processing for getting high accuracy (comparison with manual) .Also We used the preprocessing techniques for enhancement of the image .And used two types of filter for comparing result to get best scenario. Also for simulation result we used the matlab and implement on DRIVE database.

International Conference on Artificial Intelligence and Data Processing (IDAP) -- SEP 28-30, 2018 -- Inonu Univ, Malatya, TURKEY

Assessment of blood vessels in retinal images is an important factor for many medical disorders. The changes in the retinal vessels due to the pathologies can be easily identified by segmenting the retinal vessels. Segmentation of retinal vessels is done to identify the early diagnosis of the disease like glaucoma, diabetic retinopathy, macular degeneration, hypertensive retinopathy and arteriosclerosis. In this paper, we propose two automatic blood vessel segmentation methods. The first proposed algorithm starts with the extraction of blood vessel centerline pixels. The final segmentation is obtained using an iterative region growing method that merges the contents of several binary images resulting from vessel width dependent modified morphological filters on normalized retinal images. In the second proposed algorithm the blood vessel is segmented using normalized modified morphological operations and neuro fuzzy classifier. Normalized morphological operations are used to enhance the vessels and neuro fuzzy classifier is used to segment retinal blood vessels. These methods are applied on the publicly available DRIVE database and the experimental results obtained by using green channel images have been presented and their results are compared with recently published methods. The results demonstrate that our algorithms are very effective methods to detect retinal blood vessels. DOI: http://dx.doi.org/10.11591/ijece.v4i3.5829

The large deformation matching (LDM) framework is a method for registration of images and other data structures, used in computational anatomy. We show how to reformulate the large deformation matching framework for registration in a geometric way. The general framework also allows to generalize the large deformation matching framework to include multiple scales by using the iterated semidirect product of groups. An important ingredient in the LDM framework is the choice of a suitable Riemannian metric on the space of diffeomorphisms. Since the space in question is infinite-dimensional, not every choice of the metric is suitable. In particular the geodesic distance, which is defined as the infimum over the length of all paths connecting two points, may vanish. For the family of Sobolev-type Hs-metrics on the diffeomorphism groups of R and S1 we establish that the geodesic distance vanishes for metrics of order 0 ≤ s ≤ [half]. The geodesic distance also vanishes for the L2-metric on the Virasoro-Bott group, which is a central extension of the diffeomorphism group of the circle. Vanishing of geodesic distance implies that the length-functional, which assigns to each curve in the manifold its length, has no global minima, when restricted to paths with fixed endpoints. We show that for the L2-metric on the diffeomorphism group of R and the Virasoro-Bott group doesn't have any local minima either. The large deformation matching framework is not the only approach to the registration and shape comparison. For curves and surfaces it is possible to define a Riemannian metric directly on the space of curves or surfaces and use geodesics with respect to this metric to measure differences in shape. We use the family of Sobolev-type metrics on surfaces from [7]. We show how to discretize the geodesic equations and solve the boundary value problem via a shooting method on the initial velocity. The discrete equations are implemented via the finite element method.

In this paper, we have developed a new method of accurate detection of retinal blood vessels based on a deep convolutional neural network (CNN) model. This method plays an important role in the observation of many eye diseases. Retinal Images have many issues that make the process of vessels segmentation very hard. We treat each issue of the retina image with the greatest observation to obtain a well-segmented image. The first step is to apply a pre-processing method based on fuzzy logic and image processing tactics. In a second step, in order to generate the segmented images, we propose a strided encoder-decoder CNN model. This network is trained and optimized using the Dice Loss function that supports the class imbalance problem that is in the database. The proposed model has a U-Net shape, but it is deeper and the pooling layers are replaced with strided convolutional layers in the encoder. This modification allows for a more precise segmentation of vessels and accelerates the training process. The last step is post-processing for removing the noisy pixels as well as the shadow of the optic disc. The performance of the proposed method was evaluated on DRIVE and STARE databases. The proposed method gives a sensitivity of 0.802 and 0.801 respectively on DRIVE and STARE, with an accuracy of 0.959 and 0.961 respectively. We focused on sensitivity and accuracy measurements that represent the accuracy of the model, especially tiny vessels. According to the results, the model outperforms many other proposed methods, especially in the above-mentioned measures.

Automated retinal blood vessel segmentation is a fundamental component in computer aided retinal disease screening system and diagnosis. This paper presents a novel method of Hausdorff symmetry operator for automatic centerline pixel selection towards retinal blood vessel segmentation. Centerline pixels are determined by considering geometrical symmetry (distance and orientation) and Hausdorff distance based point set matching at the centerline pixel. This is performed in subpixel resolution to achieve higher accuracy. Then K-means clustering is applied to remove false centerline pixels. The selected centerline pixels act as seed points to be used in region growing to segment the retinal blood vessels. Our proposed method is evaluated on DRIVE and STARE databases. The experimental results demonstrate that the performance of the proposed method is comparable with state-of-the-art techniques. The advantages of the proposed method include its ability to correctly segment thin blood vessels, vessels containing light reflex, and disc area is not misclassified as vessels.

Accurate segmentation of retinal blood vessels is an important task in computer aided diagnosis of retinopathy. In this paper, we propose an automated retinal blood vessel segmentation approach based on artificial bee colony optimisation in conjunction with fuzzy c-means clustering. Artificial bee colony optimisation is applied as a global search method to find cluster centers of the fuzzy c-means objective function. Vessels with small diameters appear distorted and hence cannot be correctly segmented at the first segmentation level due to confusion with nearby pixels. We employ a pattern search approach to optimisation in order to localise small vessels with a different fitness function. The proposed algorithm is tested on the publicly available DRIVE and STARE retinal image databases and confirmed to deliver performance that is comparable with state-of-the-art techniques in terms of accuracy, sensitivity and specificity.

Statistical shape modeling (SSM) is a valuable and powerful tool to generate a detailed representation of complex anatomy that enables quantitative analysis and the comparison of shapes and their variations. SSM applies mathematics, statistics, and computing to parse the shape into a quantitative representation (such as correspondence points or landmarks) that will help answer various questions about the anatomical variations across the population. Complex anatomical structures have many diverse parts with varying interactions or intricate architecture. For example, the heart is a four-chambered anatomy with several shared boundaries between chambers. Coordinated and efficient contraction of the chambers of the heart is necessary to adequately perfuse end organs throughout the body. Subtle shape changes within these shared boundaries of the heart can indicate potential pathological changes that lead to uncoordinated contraction and poor end-organ perfusion. Early detection and robust quantification could provide insight into ideal treatment techniques and intervention timing. However, existing SSM approaches fall short of explicitly modeling the statistics of shared boundaries. In this paper, we present a general and flexible data-driven approach for building statistical shape models of multi-organ anatomies with shared boundaries that captures morphological and alignment changes of individual anatomies and their shared boundary surfaces throughout the population. We demonstrate the effectiveness of the proposed methods using a biventricular heart dataset by developing shape models that consistently parameterize the cardiac biventricular structure and the interventricular septum (shared boundary surface) across the population data.

Distances on merge trees facilitate visual comparison of collections of scalar fields. Two desirable properties for these distances to exhibit are 1) the ability to discern between scalar fields which other, less complex topological summaries cannot and 2) to still be robust to perturbations in the dataset. The combination of these two properties, known respectively as stability and discriminativity, has led to theoretical distances which are either thought to be or shown to be computationally complex and thus their implementations have been scarce. In order to design similarity measures on merge trees which are computationally feasible for more complex merge trees, many researchers have elected to loosen the restrictions on at least one of these two properties. The question still remains, however, if there are practical situations where trading these desirable properties is necessary. Here we construct a distance between merge trees which is designed to retain both discriminativity and stability. While our approach can be expensive for large merge trees, we illustrate its use in a setting where the number of nodes is small. This setting can be made more practical since we also provide a proof that persistence simplification increases the outputted distance by at most half of the simplified value. We demonstrate our distance measure on applications in shape comparison and on detection of periodicity in the von Kármán vortex street.

Teichmuller shape space is a finite dimensional Riemannian manifold, where each point represents a class of surfaces, which are conformally equivalent, and a path represents a deformation process from one shape to the other. Two surfaces in the real world correspond to the same point in the Teichmuller space, only if they can be conformally mapped to each other. Teichmuller shape space can be used for surface classification purpose in shape modeling. This work focuses on the computation of the coordinates of high genus surfaces in the Teichmuller space. The coordinates are called as Fenchel-Nielsen coordinates. The main idea is to deform the surface conformally using surface Ricci flow, such that the Gaussian curvature is −1 everywhere. The surface is decomposed to several pairs of hyperbolic pants. Each pair of pants is a genus zero surface with three boundaries, equipped with hyperbolic metric. Furthermore, all the boundaries are geodesics. Each pair of hyperbolic pants can be uniquely described by the lengths of its boundaries. The way of gluing different pairs of pants can be represented by the twisting angles between two adjacent pairs of pants which share a common boundary. The algorithms are based on Teichmuller space theory in conformal geometry, and they utilize the discrete surface Ricci flow. Most computations are carried out using hyperbolic geometry. The method is automatic, rigorous and efficient. The Teichmuller shape space coordinates can be used for surface classification and indexing. Experimental results on surfaces acquired from real world showed the practical value of the method for geometric database indexing, shape comparison and classification.

This paper studies the dynamic single-source shortest paths SSSP in Erdos-Renyi random graphs generated by Gn,i¾?p model. In 2014, Ding and Lin AAIM 2014, LNCS 8546, 197---207 first considered the dynamic SSSP in general digraphs with arbitrary positive weights, and devised a nontrivial local search algorithm named DSPI which takes at most $$On\cdot \max \{1, n\log n / m\}$$Oni¾?max{1,nlogn/m} expected update time to handle a single weight increase, where n is the number of nodes and m is the number of edges in the digraph. DSPI also works on undirected graphs. This paper analyzes the expected update time of DSPI dealing with edge weight increases or edge deletions in Erdos-Renyi a.k.a., Gn,i¾?p random graphs. For weighted Gn,i¾?p random graphs with arbitrary positive edge weights, DSPI takes at most $$OhT_s$$OhTs expected update time to deal with a single edge weight increase as well as $$Opn^2 hT_s$$Opn2hTs total update time, where $$hT_s$$hTs is the height of input SSSP tree $$T_s$$Ts. For Gn,i¾?p random graphs, DSPI takes $$O\ln n$$Olnn expected update time to handle a single edge deletion as well as $$Opn^2 \ln n$$Opn2lnn total update time when $$20\ln n / n \le p \sqrt{2\ln n / n}$$p>2lnn/n. Specifically, DSPI takes the least total update time of $$On\ln n hT_s$$OnlnnhTs for weighted Gn,i¾?p random graphs with $$p = c\ln n / n, c > 1$$p=clnn/n,c>1 as well as $$On^{3/2}\ln n^{1/2}$$On3/2lnn1/2 for Gn,i¾?p random graphs with $$p = c\sqrt{\ln n / n}, c > \sqrt{2}$$p=clnn/n,c>2.