An Invariant Geometric Feature for Inter-Subject Lumbar Curve Alignment to Detect Spondylolisthesis

Spondylolisthesis classification commonly relies on the shift distance (SD) feature. This feature measures the displacement between vertebrae but is sensitive to variations in size and rotational alignment of the vertebrae. This study introduces a new diagonal ratio (DR) feature to overcome these limitations. The DR feature, defined as the ratio of the difference in diagonal lengths to the width of the lower vertebra, is robust against variations in vertebral size and effectively detects displacement in curved lumbar spines. The Bhattacharyya coefficients for the DR feature are significantly lower than those for the SD feature, highlighting its superior ability to distinguish between spondylolisthesis classes. Additionally, single-feature classification using Naive Bayes, based on corner points detected by ResNet, achieved its highest accuracy of 83.56% for the anterior-posterior (AP) view and 67.09% for the lateral (LA) view with the proposed DR feature. Factor analysis revealed that the DR feature contributed most significantly, with an average factor loading of 32.1% for the AP view, where the second highest factor loading was 22.4% by ASD, and 42.3% for the LA view, where the second highest factor loading was 24.0% by SDR, across three classifiers—Support Vector Classifier (SVC), Random Forest Classifier (RF), and Gradient Boosting Classifier (GB). These findings underscore our DR feature’s potential to overcome size variation and rotational alignment challenges.