Subvoxel Accurate Graph Search Using Non-Euclidean Graph Space

Abstract

Graph search is attractive for the quantitative analysis of volumetric medical images, and especially for layered tissues, because it allows globally optimal solutions in low-order polynomial time. However, because nodes of graphs typically encode evenly distributed voxels of the volume with arcs connecting orthogonally sampled voxels in Euclidean space, segmentation cannot achieve greater precision than a single unit, i.e. the distance between two adjoining nodes, and partial volume effects are ignored. We generalize the graph to non-Euclidean space by allowing non-equidistant spacing between nodes, so that subvoxel accurate segmentation is achievable. Because the number of nodes and edges in the graph remains the same, running time and memory use are similar, while all the advantages of graph search, including global optimality and computational efficiency, are retained. A deformation field calculated from the volume data adaptively changes regional node density so that node density varies with the inverse of the expected cost. We validated our approach using optical coherence tomography (OCT) images of the retina and 3-D MR of the arterial wall, and achieved statistically significant increased accuracy. Our approach allows improved accuracy in volume data acquired with the same hardware, and also, preserved accuracy with lower resolution, more cost-effective, image acquisition equipment. The method is not limited to any specific imaging modality and readily extensible to higher dimensions.

Diabetic retinopathy is a neurodegenerative disorder

“…The recent development of Optical Coherence Tomography (OCT) and 3D quantification using image analysis of the neuroretina (NFL, GCL, and IPL) allow us to observe structural changes of diabetes in humans and in vivo, prior to the development of DR. At Iowa, we have developed image analysis algorithms that allow us to measure changes in retinal layer thickness of less than 0.25μm, substantially below the axial resolution of 5-8μm of clinical OCT devices. 36, 3743 Our algorithms work on all commercially available OCT devices, and are publicly available for any researcher (available at www.iibi.uiowa.edu/content/shared-software-download). In a series of cross-sectional studies, these algorithms have allowed us to determine that the neuroretina (NFL, GCL, and IPL) are thinner in people with both type 1 and type 2 diabetes who have no or minimal, DR. 44-48 …”

Optimal surface segmentation with convex priors in irregularly sampled space

“…between two adjacent surfaces is enforced by adding edges in a similar manner as described in Ref. (Abra`moff et al, 2014) from column a in subgraph Gi to corresponding column a in subgraph Gi+1. Along every column a in Gi, each node ni(a,z) has a directed edge with +∞ weight to the node ni+1(a,z 0 ), (z 0 ∈ z,La(z 0 )−La(z) ≥ di,i+1,La(z 0 − 1) − La(z) < di,i+1).…”

“…To address this problem, the subvoxel accurate graph search method (Abra`moff et al, 2014) was developed to simultaneously segment multiple surfaces in a volumetric image by exploiting the additional partial volume information in the voxels. A displacement field is computed from the original volumetric data.…”

“…The use of convex priors allows for incorporation of many different prior information in the graph framework as discussed previously while attaining subvoxel accuracy. Unlike the subvoxel accurate graph search method (Abra`moff et al, 2014),…”

Fast and memory-efficient LOGISMOS graph search for intraretinal layer segmentation of 3D macular OCT scans

“…Our research group has developed a LOGISMOS family of graph search methods and employed it to several application areas. [1][2][3][4][5][6] Although the graph search approach showed excellent segmentation accuracy, it requires a considerable processing resources to simultaneously segment multiple surfaces from large volumetric images. To overcome this drawback, we introduce a new graph search method that is significantly faster and more memory-efficient with small decrease in segmentation accuracy than the original graph search approach and test it for intraretinal layer segmentation of 3D macular optical coherence tomography (OCT) scans.…”