# 3D Anthropometry

3D anthropometric modeling is a basic component of the CADANS plugin. Here, a brief introduction is given to 3D anthropometry and the underlying 3D statistical shape models.

The human body comes in a broad variety of sizes and shapes. Traditional anthropometry is, to some extent, capable of capturing this variability through statistical modeling of 1D measurements, like lengths and circumferences. See Figure 1 for an example. With 3D scanning, however, there is the opportunity to capture dense and more detailed information, useful for optimizing product comfort and function, but, unfortunately, this cannot be conveniently described by traditional anthropometry. Here, 3D statistical shape models (SSM) come into play. Figure 1: The normal distribution is widely used in anthropometrics to describe the variation in 1D body measurements, such as stature, within a population.

Where in traditional anthropometry, 3D shape is described by a set of 1D measurements using univariate statistical distributions (usually Gaussian), 3D SSMs directly describe the whole 3D shape using a single multivariate (Gaussian) distribution. There are a few steps involved in obtaining such a multivariate distribution from a population of 3D scans and the procedure is much more complicated compared to 1D data as in traditional anthropometry. In a first step, each shape of the population is represented with a set of corresponding landmarks (usually thousands), meaning that each landmark is at the same anatomical location on each of the shapes, e.g. at the tip of the nose, the earlobes, etc.. See Figure 2 for an example. Figure 2: the 3D scan of each of these heads is represented with 10.000 landmarks which are placed at corresponding anatomical locations (not limited to the tip of the nose and the eyes).

In a next step, each of these 3D scans is represented as a point in the shape space, which is the space spanned by the coordinates of each of the landmarks. For a population of N shapes, this results in a cloud of N points. Finally, the shape of this cloud is described by a multidimensional Gaussian distribution by the application of principal components analysis (PCA). This results in an average shape and a set of ‘principal’ shape variations. See Figure 3 for an example. Figure 3: Left: mean shape of a population of 100 3D head scans color coded with the amount of variations (little variation in blue and highly variable parts in red). Right: visualisation of the first three principal shape modes of the population after PCA analysis, shown from three viewpoints (anterior, cranial, and lateral). The shape mode is visualised as an offset to the mean surface: the red surface is a negative offset and the white surface is a positive offset, each at three standard deviations.

Although a 3D SSM provides a complete and mathematically elegant description of the population, it is cumbersome to work with for product designers. This is because the principal shape modes do not describe variation in a way that is intuitive for a product developer or anthropometrist, as often a single shape mode describes a combination of shape variations.

Anthropometric 3D SSMs combine the best of both worlds: they provide a dense description of 3D shape variation but then related to 1D anthropometric measurements. This is achieved by finding a relation (with linear regression) between the set of 1D measurements of a shape and the principal shape modes that constitute that shape. As a consequence, the product developer can now explore the influence of, for example, head length on the complete 3D shape of the head, e.g. through visualization of percentiles (P5, P50, P95, see Figure 4). Furthermore, it is even possible to predict the 3D shape of a person from only a few 1D measurements which has applications in product mass-customization. Figure 4: The 3D head shapes corresponding to the P5, P50, and P95 percentiles of head length. It can be seen that not only head length varies, but also head width which is to be expected as there is a correlation between these dimensions.

It should be noted that the above is based on 3D triangle surface models. In general, such models are less suited for CAD. However, the CADANS plugin provides complete CAD compatibility through a free-form representation for these models (B-splines).