Objective analysis of orbital rim fracture CT images using curve and area measurement

Abstract

The orbital bone presents a closed curve, and fracture results in disfigurement. An image analysis procedure was developed to examine before and after corrective surgery. An ellipse and circumscribed contour embodied the closed curve. Three-dimensional (3D) computed tomography (CT) images were collected from 25 patients. Orbital rim data were generated, and binary images were created to facilitate closed curve analysis. Various indices, including the solidity value (closed curve area/convex hull area) and ellipse distance (discrepancy between the closed curve and the ellipse traversing the curve), were utilized. The ratios of various indices-including the number of vertices, solidity value, and ellipse distance-between the affected and unaffected sides showed postoperative values that were closer to 1, which would indicate perfect symmetry, than the preoperative measurements (P < 0.05). The solidity value increased, while both the ellipse distance and curvature values decreased, reflecting the transformation of bends into smooth contours following reduction surgery (P < 0.05). Significant correlations were observed between 1-solidity, ellipse distance, and curvature using the Pearson correlation test (P < 0.05). This study validated postoperative changes in various indices and established correlations among multiple values, specifically solidity, ellipse distance, and curvature. Employing multiple indices with mutual complements has provided objective information confidently.

Keywords: Area; Computed tomography; Curve; Fracture; Orbital bone.

Fig. 1

Pre- and post-operative comparison of the ratios of affected and unaffected sides. The ratios of vertices (number of vertices in the contour), all points (number of points [pixels] in the contour), solidity value (contour area divided by convex hull area), ellipse distance (average distance between contour and ellipse), and average curvature demonstrated postoperative changes converging towards 1 (P < 0.05). A ratio of 1 indicates symmetry between the bilateral sides. The error bar represents the standard error of the mean.

Fig. 2

Analysis of the right orbital rim. (a) The fractured right orbit showed a prominent groove on the inferior rim preoperatively. The solidity value (green contour area divided by yellow convex hull area) was 0.9709, the ellipse distance (discrepancy between green contour and red ellipse) was 1.482, and the average curvature was 0.2819 preoperatively. (b) The displacement was reduced postoperatively. The three values changed to 0.9796, 0.786, and 0.2641, respectively. The alteration represents convergence to the circumscribing smooth contour and traversing ellipse.

Fig. 3

Analysis of the left orbital rim. (a) The fractured left orbit showed a disfigurement on the inferior medial rim preoperatively. The solidity value (green contour area divided by yellow convex hull area) was 0.9399, the ellipse distance (discrepancy between green contour and red ellipse) was 1.393, and the average curvature was 0.2869 preoperatively. (b) The displacement was reduced postoperatively. The three values changed to 0.9738, 1.077, and 0.2674, respectively. The alteration represents convergence to the circumscribing smooth contour and traversing ellipse.

Fig. 4

Pre- and postoperative correlation measurements: 1-solidity, ellipse distance, and curvature were utilized for the analysis. The values presented significant correlations (P < 0.05).

Fig. 5

Generation of orbital rim contour data. Facial bone CT image processing: The region of interest around the orbits is retained, while the rest of the unit is deleted (a, b). Cube generation and intersection calculation: A cube is generated to overlap with the CT image, and the intersecting surfaces are calculated (c). To ensure data consistency, the CT image is gradually advanced from the cube’s center, and the first surface where the orbital rim contour is closed is used as the reference (d, e). Binary image creation: Noise is removed, and the inside of the contour is filled with 1 (white) and the outside with 0 (black) to create a binary image (f).

Fig. 6

Objective indices for analysis are created at the preoperative (a) and postoperative (b) stages. Vertices (number of vertices in contour) and all points (number of points (pixels) in contour) are figured out on the green contour. The solidity is measured by the green contour area among the yellow convex hull area. A value of 1 corresponds to a solid object, while a value below 1 implies an object with irregular boundaries. The ellipse distance is measured by the average distance between the green contour and the red ellipse. The ellipses are drawn with the fit-ellipse function in the open computer vision library. The function calculates the ellipse that best fits a set of 2D points.