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The seminal work of Horn and Schunck is the first variational method for optical flow estimation. It introduced a novel framework where the optical flow is computed as the solution of a minimization problem. From the assumption that pixel intensities do not change over time, the optical flow constraint equation is derived. This equation relates the optical flow with the derivatives of the image. There are infinitely many vector fields that satisfy the optical flow constraint, thus the problem is ill-posed. To overcome this problem, Horn and Schunck introduced an additional regularity condition that restricts the possible solutions. Their method minimizes both the optical flow constraint and the magnitude of the variations of the flow field, producing smooth vector fields. One of the limitations of this method is that, typically, it can only estimate small motions. In the presence of large displacements, this method fails when the gradient of the image is not smooth enough. In this work, we describe an implementation of the original Horn and Schunck method and also introduce a multi-scale strategy in order to deal with larger displacements. For this multi-scale strategy, we create a pyramidal structure of downsampled images and change the optical flow constraint equation with a nonlinear formulation. In order to tackle this nonlinear formula, we linearize it and solve the method iteratively in each scale. In this sense, there are two common approaches: one that computes the motion increment in the iterations; or the one we follow, that computes the full flow during the iterations. The solutions are incrementally refined over the scales. This pyramidal structure is a standard tool in many optical flow methods. Source Code A standalone ANSI C implementation is available 1. This file contains two main programs: horn schunck classic.c, which implements the original Horn and Schunck method; and the implementation of the multi-scale approach, in file horn schunck pyramidal.c. This latter implementation is best suited for general image sequences.

The prevalence of diabetes is expected to increase dramatically in coming years; already today it accounts for a major proportion of the health care budget in many countries. Diabetic Retinopathy (DR), a micro vascular complication very often seen in diabetes patients, is the most common cause of visual loss in working age population of developed countries today. Since the possibility of slowing or even stopping the progress of this disease depends on the early detection of DR, an automatic analysis of fundus images would be of great help to the ophthalmologist due to the small size of the symptoms and the large number of patients. An important symptom for DR are abnormally wide veins leading to an unusually low ratio of the average diameter of arteries to veins (AVR). There are also other diseases like high blood pressure or diseases of the pancreas with one symptom being an abnormal AVR value. To determine it, a classification of vessels as arteries or veins is indispensable. As to our knowledge despite the importance there have only been two approaches to vessel classification yet. Therefore we propose an improved method. We compare two feature extraction methods and two classification methods based on support vector machines and neural networks. Given a hand-segmentation of vessels our approach achieves 95.32% correctly classified vessel pixels. This value decreases by 10% on average, if the result of a segmentation algorithm is used as basis for the classification.

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