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This study investigates a variational method to determine the most representative shape of a set of knee kinematic curves with application to knee pathology classification. Although they provide essential information for pathology classification, knee kinematic curves are characterized by high intra-class variability and outliers are often present. As a result, a set of several measurement curves are acquired of any single individual which are then averaged before their use for pathology classification. Rather than using the average of an individual’s recorded measurement curves, this method determines a better representative curve by first correcting the data to account for outliers occurrence and class variability using a variational method. The correction is performed by simultaneous minimization of a set of objective functions, one for each curve in the measurement set, and consisting of a weighed sum of two terms: a data term of conformity of the corrected curve to the given curve, and a regularization term of proximity of the corrected curve to the mean of all the corrected curves to inhibit the influence of outliers in the set. Validation tests were performed to discriminate between knee osteoarthritis data (OA) and non-OA data. Using a support vector machine, the classification accuracy with the proposed representation was 86%, with 81% sensitivity and 90% specificity, compared to 83% accuracy for the standard representation by average, with 76% sensitivity and 90% specificity. The representation has also been tested within the OA category to distinguish the femero-tibial patholgy from the femero-patellar, giving 76% accuracy, with 76% sensitivity and 76% specificity, compared to 69% accuracy, with 62% sensitivity and 76% specificity. These significant improvements by the proposed method warrant its further investigation by application to other biomedical engineering pattern classification problems and datasets.

Knee kinematic curve representation and application to knee pathology classification