Statistical shape analysis via principal factor analysis

Statistical shape analysis techniques commonly employed in the medical imaging community, such as active shape models or active appearance models, rely on principal component analysis (PCA) to decompose shape variability into a reduced set of interpretable components. In this paper we propose principal factor analysis (PFA) as an alternative and complementary tool to PCA providing a decomposition into modes of variation that can be more easily interpretable, while still being a linear efficient technique that performs dimensionality reduction (as opposed to independent component analysis, ICA). The key difference between PFA and PCA is that PFA models covariance between variables, rather than the total variance in the data. The added value of PFA is illustrated on 2D landmark data of corpora callosa outlines. Then, a study of the 3D shape variability of the human left femur is performed. Finally, we report results on vector-valued 3D deformation fields resulting from non-rigid registration of ventricles in MRI of the brain.

Statistical shape modeling of pathological scoliotic vertebrae: A comparative analysis

Statistical shape models (SSMs) have been used widely as a basis for segmenting and interpreting complex anatomical structures. The robustness of these models are sensitive to the registration procedures, i.e., establishment of a dense correspondence across a training data set. In this work, two SSMs based on the same training data set of scoliotic vertebrae, and registration procedures were compared. The first model was constructed based on the original binary masks without applying any image pre- and post-processing, and the second was obtained by means of a feature preserving smoothing method applied to the original training data set, followed by a standard rasterization algorithm. The accuracies of the correspondences were assessed quantitatively by means of the maximum of the mean minimum distance (MMMD) and Hausdorf distance (H(D)). Anatomical validity of the models were quantified by means of three different criteria, i.e., compactness, specificity, and model generalization ability. The objective of this study was to compare quasi-identical models based on standard metrics. Preliminary results suggest that the MMMD distance and eigenvalues are not sensitive metrics for evaluating the performance and robustness of SSMs.

Quantitative analysis of imprint shape and its relation to mechanical properties measured by microindentation in bone

Microindentation in bone is a micromechanical testing technique routinely used to extract material properties related to bone quality. As the analysis of microindentation data is based on assumptions about the contact between sample and surface, the aim of this study was to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topology was measured by atomic force microscopy. Statistical shape modeling of the residual imprint allowed to define a mean shape and to describe the variability in terms of 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was found to be highly consistent and free of any pile up while differing mostly by depth between species and direction. A few of the topological parameters, in particular depth, showed significant but rather weak and inconsistent correlations to variations in mechanical properties. The mechanical response of bone as well as the residual imprint shape was highly consistent within each category. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small deviations from an ideally flat surface.

Shape model, reference system definition, and cartographic mapping standards for comet 67P/Churyumov-Gerasimenko Stereo-photogrammetric analysis of Rosetta/OSIRIS image data

We analyzed more than 200 OSIRIS NAC images with a pixel scale of 0.9-2.4 m/pixel of comet 67P/Churyumov-Gerasimenko (67P) that have been acquired from onboard the Rosetta spacecraft in August and September 2014 using stereo-photogrammetric methods (SPG). We derived improved spacecraft position and pointing data for the OSIRIS images and a high-resolution shape model that consists of about 16 million facets (2 m horizontal sampling) and a typical vertical accuracy at the decimeter scale. From this model, we derive a volume for the northern hemisphere of 9.35 km(3) +/- 0.1 km(3). With the assumption of a homogeneous density distribution and taking into account the current uncertainty of the position of the comet's center-of-mass, we extrapolated this value to an overall volume of 18.7 km(3) +/- 1.2 km(3), and, with a current best estimate of 1.0 X 10(13) kg for the mass, we derive a bulk density of 535 kg/m(3) +/- 35 kg/m(3). Furthermore, we used SPG methods to analyze the rotational elements of 67P. The rotational period for August and September 2014 was determined to be 12.4041 +/- 0.0004 h. For the orientation of the rotational axis (z-axis of the body-fixed reference frame) we derived a precession model with a half-cone angle of 0.14 degrees, a cone center position at 69.54 degrees/64.11 degrees (RA/Dec J2000 equatorial coordinates), and a precession period of 10.7 days. For the definition of zero longitude (x-axis orientation), we finally selected the boulder-like Cheops feature on the big lobe of 67P and fixed its spherical coordinates to 142.35 degrees right-hand-rule eastern longitude and -0.28 degrees latitude. This completes the definition of the new Cheops reference frame for 67P. Finally, we defined cartographic mapping standards for common use and combined analyses of scientific results that have been obtained not only within the OSIRIS team, but also within other groups of the Rosetta mission.

Investigating interocclusal perception in tactile teeth sensibility using symmetric and asymmetric analysis

The purpose of this clinical trial was to determine the active tactile sensibility of natural teeth and to obtain a statistical analysis method fitting a psychometric function through the observed data points. On 68 complete dentulous test persons (34 males, 34 females, mean age 45.9 ± 16.1 years), one pair of healthy natural teeth each was tested: n = 24 anterior teeth and n = 44 posterior teeth. The computer-assisted, randomized measurement was done by having the subjects bite on thin copper foils of different thickness (5-200 µm) inserted between the teeth. The threshold of active tactile sensibility was defined by the 50% value of correct answers. Additionally, the gradient of the sensibility curve and the support area (90-10% value) as a description of the shape of the sensibility curve were calculated. For modeling the sensibility curve, symmetric and asymmetric functions were used. The mean sensibility threshold was 14.2 ± 12.1 µm. The older the subject, the higher the tactile threshold (r = 0.42, p = 0.0006). The support area was 41.8 ± 43.3 µm. The higher the 50% threshold, the smaller the gradient of the curve and the larger the support area. The curves showing the active tactile sensibility of natural teeth demonstrate a tendency towards asymmetry, so that the active tactile sensibility of natural teeth can mathematically best be described by using the asymmetric Weibull function.

Validation of statistical shape model based reconstruction of the proximal femur - A morphology study

Seventeen bones (sixteen cadaveric bones and one plastic bone) were used to validate a method for reconstructing a surface model of the proximal femur from 2D X-ray radiographs and a statistical shape model that was constructed from thirty training surface models. Unlike previously introduced validation studies, where surface-based distance errors were used to evaluate the reconstruction accuracy, here we propose to use errors measured based on clinically relevant morphometric parameters. For this purpose, a program was developed to robustly extract those morphometric parameters from the thirty training surface models (training population), from the seventeen surface models reconstructed from X-ray radiographs, and from the seventeen ground truth surface models obtained either by a CT-scan reconstruction method or by a laser-scan reconstruction method. A statistical analysis was then performed to classify the seventeen test bones into two categories: normal cases and outliers. This classification step depends on the measured parameters of the particular test bone. In case all parameters of a test bone were covered by the training population's parameter ranges, this bone is classified as normal bone, otherwise as outlier bone. Our experimental results showed that statistically there was no significant difference between the morphometric parameters extracted from the reconstructed surface models of the normal cases and those extracted from the reconstructed surface models of the outliers. Therefore, our statistical shape model based reconstruction technique can be used to reconstruct not only the surface model of a normal bone but also that of an outlier bone.

Early bursts of body size and shape evolution are rare in comparative data

George Gaylord Simpson famously postulated that much of life's diversity originated as adaptive radiations-more or less simultaneous divergences of numerous lines from a single ancestral adaptive type. However, identifying adaptive radiations has proven difficult due to a lack of broad-scale comparative datasets. Here, we use phylogenetic comparative data on body size and shape in a diversity of animal clades to test a key model of adaptive radiation, in which initially rapid morphological evolution is followed by relative stasis. We compared the fit of this model to both single selective peak and random walk models. We found little support for the early-burst model of adaptive radiation, whereas both other models, particularly that of selective peaks, were commonly supported. In addition, we found that the net rate of morphological evolution varied inversely with clade age. The youngest clades appear to evolve most rapidly because long-term change typically does not attain the amount of divergence predicted from rates measured over short time scales. Across our entire analysis, the dominant pattern was one of constraints shaping evolution continually through time rather than rapid evolution followed by stasis. We suggest that the classical model of adaptive radiation, where morphological evolution is initially rapid and slows through time, may be rare in comparative data.