Retinal fundus photographs have been used in the diagnosis of many ocular diseases such as glaucoma, pathological myopia, age-related macular degeneration and diabetic retinopathy. With the development of computer science, computer aided diagnosis has been developed to process and analyse the retinal images automatically. One of the challenges in the analysis is that the quality of the retinal image is often degraded. For example, a cataract in human lens will attenuate the retinal image, just as a cloudy camera lens which reduces the quality of a photograph. It often obscures the details in the retinal images and posts challenges in retinal image processing and analysing tasks. In this paper, we approximate the degradation of the retinal images as a combination of human-lens attenuation and scattering. A novel structure-preserving guided retinal image filtering (SGRIF) is then proposed to restore images based on the attenuation and scattering model. The proposed SGRIF consists of a step of global structure transferring and a step of global edge-preserving smoothing. Our results show that the proposed SGRIF method is able to improve the contrast of retinal images, measured by histogram flatness measure, histogram spread and variability of local luminosity. In addition, we further explored the benefits of SGRIF for subsequent retinal image processing and analysing tasks. In the two applications of deep learning based optic cup segmentation and sparse learning based cup-to-disc ratio (CDR) computation, our results show that we are able to achieve more accurate optic cup segmentation and CDR measurements from images processed by SGRIF.
Submodular functions are discrete analogs of convex functions, which have applications in various fields, including machine learning and computer vision. However, in large-scale applications, solving Submodular Function Minimization (SFM) problems remains challenging. In this paper, we make the first attempt to extend the emerging technique named screening in large-scale sparse learning to SFM for accelerating its optimization process. We first conduct a careful studying of the relationships between SFM and the corresponding convex proximal problems, as well as the accurate primal optimum estimation of the proximal problems. Relying on this study, we subsequently propose a novel safe screening method to quickly identify the elements guaranteed to be included (we refer to them as active) or excluded (inactive) in the final optimal solution of SFM during the optimization process. By removing the inactive elements and fixing the active ones, the problem size can be dramatically reduced, leading to great savings in the computational cost without sacrificing any accuracy. To the best of our knowledge, the proposed method is the first screening method in the fields of SFM and even combinatorial optimization, thus pointing out a new direction for accelerating SFM algorithms. Experiment results on both synthetic and real datasets demonstrate the significant speedups gained by our approach.
We present safe active incremental feature selection~(SAIF) to scale up the computation of LASSO solutions. SAIF does not require a solution from a heavier penalty parameter as in sequential screening or updating the full model for each iteration as in dynamic screening. Different from these existing screening methods, SAIF starts from a small number of features and incrementally recruits active features and updates the significantly reduced model. Hence, it is much more computationally efficient and scalable with the number of features. More critically, SAIF has the safe guarantee as it has the convergence guarantee to the optimal solution to the original full LASSO problem. Such an incremental procedure and theoretical convergence guarantee can be extended to fused LASSO problems. Compared with state-of-the-art screening methods as well as working set and homotopy methods, which may not always guarantee the optimal solution, SAIF can achieve superior or comparable efficiency and high scalability with the safe guarantee when facing extremely high dimensional data sets. Experiments with both synthetic and real-world data sets show that SAIF can be up to 50 times faster than dynamic screening, and hundreds of times faster than computing LASSO or fused LASSO solutions without screening.