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The trapeziometacarpal joint enables the prehensile function of the thumb. Unfortunately, this joint is vulnerable to osteoarthritis (OA) that typically affects the local shape of the trapezium. A novel, local statistical shape model is defined that employs a differentiable locality measure based on the weighted variance of point coordinates per mode. The simplicity of the function and the smooth derivative enable to quickly determine localized components for densely sampled surfaces. The method is employed to assess a set of 60 trapezia (38 healthy, 22 with OA). The localized components predominantly model regions affected by OA, contrary to shape variations found with PCA. Furthermore, identification of pathological trapezia based on the localized modes of variation is improved compared to PCA.

Localized Component Analysis for Arthritis Detection in the Trapeziometacarpal Joint