Atlas-based shape analysis and classification of retinal optical coherence tomography images using the functional shape (fshape) framework

Abstract

We propose a novel approach for quantitative shape variability analysis in retinal optical coherence tomography images using the functional shape (fshape) framework. The fshape framework uses surface geometry together with functional measures, such as retinal layer thickness defined on the layer surface, for registration across anatomical shapes. This is used to generate a population mean template of the geometry-function measures from each individual. Shape variability across multiple retinas can be measured by the geometrical deformation and functional residual between the template and each of the observations. To demonstrate the clinical relevance and application of the framework, we generated atlases of the inner layer surface and layer thickness of the Retinal Nerve Fiber Layer (RNFL) of glaucomatous and normal subjects, visualizing detailed spatial pattern of RNFL loss in glaucoma. Additionally, a regularized linear discriminant analysis classifier was used to automatically classify glaucoma, glaucoma-suspect, and control cases based on RNFL fshape metrics.

Metamorphoses of Functional Shapes in Sobolev Spaces

“…The deformation is mostly concentrated along the optical nerve opening while the functional momentum shows the overall decrease in thickness, particularly in a typical crescent region around the opening. Although illustrated here on two particular subjects, such anatomical effects have been analyzed and confirmed statistically in [29].…”

“…These functional shapes or fshapes are essentially scalar signals but, unlike images, supported on deformable shapes as curves, surfaces or more generally submanifolds of given dimension. In other words, they encompass mathematical objects like textured surfaces ( Figure 1); these are increasingly found in datasets issued from medical imaging, one common example being thickness maps estimated on anatomical membranes [29] or functional maps measured on cortical surfaces by fMRI.…”

Age and Glaucoma-Related Characteristics in Retinal Nerve Fiber Layer and Choroid: Localized Morphometrics and Visualization Using Functional Shapes Registration

“…In this section, we briefly summarize the algorithm which is detailed in Lee et al (2017). Let the i th subject's RNFL or choroid thickness be represented by ( X i , f i ), where X is the layer surface (geometry) and f is the surface-indexed function (thickness here) mapped on X .…”

“…Two surfaces were brought into close proximity by minimizing a functional of reproducing kernel Hilbert space norm-based energy and a dissimilarity term, then registered by spherical demons to establish homology. More recently, we introduced the functional shape (fshape), framework (Charlier et al, 2015; Lee et al, 2017). In this framework, the retinal surface (shape or geometry) and any value mapped on the surface, for example, retinal layer thickness (function or signal), are considered together as a single mathematical object called fshape .…”

A Comparison of Handcrafted and Deep Neural Network Feature Extraction for Classifying Optical Coherence Tomography (OCT) Images

“…With reliance on initial template to compute the final mean template, the method requires a good initial template to start with. The study was also limited in terms of the number of evaluated data [9]. Other reported study in OCT is Histogram of Oriented Gradient (HOG) feature extractor and Support Vector Machine for classifying normal, diabetic macular edema (DME), and dry age-related macular degeneration (AMD).…”