Characterisation of three-dimensional anatomic shapes using principal components: Application to the proximal tibia

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Abstract
The objective of the research is to determine if principal component analysis (PCA) provides an efficient method to characterise the normative shape of the proximal tibia. Bone surface data, converted to analytical surface descriptions, are aligned, and an auto-associative memory matrix is generated. A limited subset of the matrix principal components is used to reconstruct the bone surfaces, and the reconstruction error is assessed. Surface reconstructions based on just six (of 1452) principal components have a mean root-mean-square (RMS) reconstruction error of 1.05% of the mean maximum radial distance at the tibial plateau. Surface reconstruction of bones not included in the auto-associative memory matrix have a mean RMS error of 2.90%. The first principal component represents the average shape of the sample population. Addition of subsequent principal components represents the shape variations most prevalent in the sample and can be visualised in a geometrically meaningful manner. PCA offers an efficient method to characterise the normative shape of the proximal tibia with a high degree of dimensionality reduction.

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