Abstract
Bone shape estimation from partial observations, such as fluoroscopy or ultrasound, has been subject of significant interest over the past decade and can be regarded as the driving force behind several advances in statistical modelling of shape. While statistical models were initially used mostly as regularisers constraining shape matching algorithms, they are now increasingly employed due to their predictive ability, when only limited observations are available. With the current efforts toward minimal invasiveness, radiation exposure reduction, and optimization of the cost-effectiveness of procedures, two major challenges emerge on the field of statistical modelling. The first one is to develop methods that enable the use of as much information as possible that can be relevant for a specific shape prediction task, within the aforementioned limits. The second challenge concerns the accuracy of the resulting predictions, which needs to be quantified in order to evaluate the associated risks, and to optimise the data acquisition procedures.
In terms of shape prediction, most studies so far have concentrated on individualizing statistical atlases based on imaging data. However, relevant information about skeletal morphology can also be obtained from simple anthropometric and morphometric measurements such as gender, age, body-mass index, and bone specific measurements. We develop a multivariate regression framework that enables to take into account such combinations of predictors simultaneously with sparse observations of the bone surface for improved prediction of the complete bone shape. In particular, we describe in a quantitative and localised fashion the individual contributions but also the complementarities of the heterogeneous sources of information with respect to bone morphology assessment. To do so, we compare the prediction errors obtained with different combinations of predictors, relying on cross-validation experiments. In addition to providing valuable and complementary predictive information, non-imaging measurements can be exploited to automatically initialise surface registration algorithms which increase their robustness for the determination of patient specific morphologies.
A statistical model, by essence, is a mathematical model resulting from a learning phase using a set of training data. Statistical model based prediction is affected by three main sources of errors. The pre-processing of the training data, in particular the establishment of anatomical correspondences between the different samples, and the limited number of training elements constitute a first source of uncertainties. Second, the predictors can be affected by measurement noise, which will then propagate through the prediction process. Finally, and this is particularly important in the context of sparse observation data, the limited correlations between the predictors and the shape to predict imply theoretical limits for the achievable accuracy of such approaches. We have developed a framework enabling to account for these various sources of uncertainty, and propagating them through the prediction pipeline to generate confidence regions around the predicted shape. It relies extensively on cross-validation experiments in order to quantify the limitations of the statistical model with respect to the representation of new shapes (generalization ability) and to their prediction from partial data. Furthermore, we demonstrate the reliability of the obtained regions, following the procedure initially proposed in.
We evaluate our approaches on a database of 140 femur bones, age range: 23–83, mean 62.57, stdv 15; 46% males and 54% females, with known age, height and weight. Morphometric measurements such as bone length, inter-condyle distance or anteversion angle are considered, either as predictors, together with sparse point clouds around the femoral head and greater trochanter, or as a pose-independent quality-of-fit metric. Cross-validation experiments indicate that a higher accuracy can be reached when complementing surface-based predictors with relevant anthropometric and morphometric information, and that reliable confidence regions can be estimated.
