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Abstract:Accurate extraction of retinal blood vessels is an important task in computer aided diagnosis of retinopathy. The Matched Filter (MF) is a simple yet effective method for vessel extraction. However, a MF will respond not only to vessels but also to non-vessel edges. This will lead to frequent false vessel detection. In this paper we propose a novel extension of the MF approach, namely the MF-FDOG, to detect retinal blood vessels. The proposed MF-FDOG is composed of the original MF, which is a zero-mean Gaussian function, and the first-order derivative of Gaussian (FDOG). The vessels are detected by thresholding the retinal image's response to the MF, while the threshold is adjusted by the image's response to the FDOG. The proposed MF-FDOG method is very simple; however, it reduces significantly the false detections produced by the original MF and detects many fine vessels that are missed by the MF. It achieves competitive vessel detection results as compared with those state-of-the-art schemes but with much lower complexity. In addition, it performs well at extracting vessels from pathological retinal images.

Abstract-The detection of microaneurysms in digital color fundus photographs is a critical first step in automated screening for diabetic retinopathy (DR), a common complication of diabetes. To accomplish this detection numerous methods have been published in the past but none of these was compared with each other on the same data. In this work we present the results of the first international microaneurysm detection competition, organized in The overall results show that microaneurysm detection is a challenging task for both the automatic methods as well as the human expert. There is room for improvement as the best performing system does not reach the performance of the human expert. The data associated with the ROC microaneurysm detection competition will remain publicly available and the website will continue accepting submissions.

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This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also provide examples from machine learning, including principal component analysis, kernel supervised principal component analysis, and Fisher discriminant analysis, which result in eigenvalue and generalized eigenvalue problems. Finally, we introduce the solutions to both eigenvalue and generalized eigenvalue problems.

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