Importance of elliptic Fourier methods for morphometry of complex outlines: application to the distal human femur

The purpose of this technical note is to present an automatic procedure of shape characterisation using new developments in elliptical Fourier methods combined with image analysis techniques. It was applied, as an example, to the outline of the distal extremity of the distal human femur in inferior axial view. This outline was automatically extracted and characterised by an ordered series of harmonics, each harmonic being described by four new parameters called elliptical descriptors. Step by step reconstructions of outlines using an increasing number of harmonics were than performed. The simultaneous study of the elliptic descriptors and of the step by step reconstructions allowed a considerably easier geometric and morphologic interpretation of the harmonic contributions than classically. The main morphologic features of the distal femur (lateral and medial condyles, intercondylar fossa, lateral and medial borders of the articular surface, and patellar groove) were mainly described by the first seven harmonics. These new developments in elliptic Fourier methods open interesting perspectives for the study of complex outlines, providing an accurate individual morphologic characterisation, and thus the possibility of polymorphic analysis.