Abnormal patterns of the retinal vascular system have been associated with several heart and cerebral diseases. However, these correlations were obtained using 2D imaging of the eye fundus, disregarding information on the third component (depth) of the vascular system. In this paper, we show that the depth component is relevant and should not be disregarded in this analysis. In this way, the relevance of the an...
Optical coherence tomography (OCT) is an imaging modality broadly used in biologial tissue imaging. In this chapte, we review the history of OCT and its development throughout the last years.
In this paper we present a rigorous proof for the stability of a class of finite difference schemes applied to nonlinear complex diffusion equations. Complex diffusion is a common and broadly used denoising procedure in image processing. To illustrate the theoretical results we present some numerical examples based on an explicit scheme applied to a nonlinear equation in the context of image denoising.
Optical coherence tomography (OCT) is becoming one of the most important imaging modalities in ophthalmology due to its non-invasiveness and by allowing the visualisation the human retina structure in detail. It was recently proposed that OCT data embeds functional information from the human retina. Specifically, it was proposed that blood–retinal barrier status information is present within OCT data from the h...
Neste texto pretendemos ilustrar algumas aplicações de matemática no campo da medicina, nomeadamente na imagiologia do fundo ocular. Vamos enumerar algumas técnicas, problemas actuais e em aberto nos quais a Matemática pode ser útil.
The use of synthetic images is needed for testing the performance of image processing methods in order to establish a ground truth to test performance metrics. However, these synthetic images do not represent real applications. The aim of this paper is to build a mathematical model to obtain a synthetic noise-free image mimicking a real Optical Coherence Tomography (OCT) B-scan or volume from the human retina, ...
Imaging the ocular fundus, namely the retina, to detect and/or monitor changes over time from the healthy condition is of fundamental importance to assess onset and disease progression and is a valuable tool to understand the basic mechanisms of ocular diseases. Current trends point to the need for less or non-invasive approaches, to the need for detailed (higher spatial and temporal resolution) imaging systems...
Purpose: To demonstrate the association between changes in the blood-retinal barrier (BRB) identified by fluorescein leakage and those in the optical properties of the human retina determined by optical coherence tomography (OCT) and show how these changes can be quantified and their location identified within the retina. Methods: Two imaging techniques were applied: the retinal leakage analyzer, to map BRB fun...
Ocular fundus imaging plays a key role in monitoring the health status of the human eye. Currently, a large number of imaging modalities allow the assessment and/or quantification of ocular changes from a healthy status. This review focuses on the main digital fundus imaging modality, color fundus photography, with a brief overview of complementary techniques, such as fluorescein angiography. While focusing on ...
Complex diffusion is a common and broadly used denoising procedure in image processing. The method is based on an explicit finite difference scheme applied to a diffusion equation with a proper complex diffusion parameter in order to preserve edges and the main features of the image, while eliminating noise. In this paper we present a rigorous proof for the stability condition of complex diffusion finite differ...
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