Semivariogram and Semimadogram functions as descriptors for AMD diagnosis on SD-OCT topographic maps using Support Vector Machine

Abstract

Background: Age-related macular degeneration (AMD) is a degenerative ocular disease that develops by the formation of drusen in the macula region leading to blindness. This condition can be detected automatically by automated image processing techniques applied in spectral domain optical coherence tomography (SD-OCT) volumes. The most common approach is the individualized analysis of each slice (B-Scan) of the SD-OCT volumes. However, it ends up losing the correlation between pixels of neighboring slices. The retina representation by topographic maps reveals the similarity of these structures with geographic relief maps, which can be represented by geostatistical descriptors. In this paper, we present a methodology based on geostatistical functions for the automatic diagnosis of AMD in SD-OCT.

Methods: The proposed methodology is based on the construction of a topographic map of the macular region. Over the topographic map, we compute geostatistical features using semivariogram and semimadogram functions as texture descriptors. The extracted descriptors are then used as input for a Support Vector Machine classifier.

Results: For training of the classifier and tests, a database composed of 384 OCT exams (269 volumes of eyes exhibiting AMD and 115 control volumes) with layers segmented and validated by specialists were used. The best classification model, validated with cross-validation k-fold, achieved an accuracy of 95.2% and an AUROC of 0.989.

Conclusion: The presented methodology exclusively uses geostatistical descriptors for the diagnosis of AMD in SD-OCT images of the macular region. The results are promising and the methodology is competitive considering previous results published in literature.

Keywords: CAD-x; Medical images; Optical coherence tomography; Semimadogram; Semivariogram.

Fig. 1

Flow chart of the proposed methodology. This picture shows a view of the necessary stages to perform AMD diagnosis over SD-OCT images

Fig. 2

Representation of SD-OCT layer’s boundaries marks. The image on the left represents the surfaces that determine the marking of the borders of the retina divisions. The right image, in turn, is a B-Scan of the same volume extracted from the image base provided by [5] with emphasis on the demarcation of the borders. In both images the borders that delimit the neurosensorial retina (NSR) and the retinal pigmented epithelium and drusen complex (RPEDC) are represented. The NSR is delineared by internal layer membrane (IML, colored red) and the pigmented epithelium border (PEB, colored blue). In turn, the retinal pigmented epithelium and drusen complex (RPEDC) is delineared by PEB and Bruch’s membrane (BM, colored green) including the drusenoids alterations. The total retina (TR) comprehend the whole region between IML and BM

Fig. 3

Total retinal topographic map generation from a SD-OCT volume. Complete volume is represented in A. B and C presents successive elimination of unnecessary regions. B also demonstrates the delimitation of a ROI with radius $r=5$ mm centered in the marking of fovea marked by specialists. Finally, D presents the topographic map that represents the thickness of the retina for each point

Fig. 4

Reconstruction en face of the border of the RPE. The figure shows the surface of the pigmented epithelium for a retina of the control group (a) and a retina with a diagnosis of AMD (b). The clearer values represent points of greater reflectance

Fig. 5

Semivariogram parameters (left) and the characteristic curve (right)

Fig. 6

Semivariogram and semimadogram response for RPEDC Maps. Rows A and B correspond to exams afflicted by AMD, while C and D present control volumes. The first image of each row corresponds to the volume’s representation through RPEDC’s topographic map and the last two columns respectively show the semivariogram and semimadogram functions in the ${45}^{\circ }$ direction

Fig. 7

Semivariogram and semimadogram functions plots for ${45}^{\circ }$ of the retinal layers. The vertical scale is different for each layer

Fig. 8

ROC plots of each generated SVM model. The best obtained value was 0.989

Fig. 9

ROC plot for comparison of semivariogram peformance with another methods. The best obtained value was 0.989