Model-based interpretation of complex and variable images

Initial Investigations of the Cranial Size and Shape of Adult Eurasian Otters (Lutra lutra) in Great Britain

Three-dimensional (3D) surface scans were carried out in order to determine the shapes of the upper sections of (skeletal) crania of adult Eurasian otters (Lutra lutra) from Great Britain. Landmark points were placed on these shapes using a graphical user interface (GUI) and distance measurements (i.e., the length, height, and width of the crania) were found by using the landmark points. Male otters had significantly larger skulls than females (P < 0.001). Differences in size also occurred by geographical area in Great Britain (P < 0.05). Multilevel Principal Components Analysis (mPCA) indicated that sex and geographical area explained 31.1% and 9.6% of shape variation in "unscaled" shape data and that they explained 17.2% and 9.7% of variation in "scaled" data. The first mode of variation at level 1 (sex) correctly reflected size changes between males and females for "unscaled" shape data. Modes at level 2 (geographical area) also showed possible changes in size and shape. Clustering by sex and geographical area was observed in standardized component scores. Such clustering in a cranial shape by geographical area might reflect genetic differences in otter populations in Great Britain, although other potentially confounding factors (e.g., population age-structure, diet, etc.) might also drive regional differences. This work provides a successful first test of the effectiveness of 3D surface scans and multivariate methods, such as mPCA, to study the cranial morphology of otters.

What's in a Smile? Initial Analyses of Dynamic Changes in Facial Shape and Appearance

Single-level principal component analysis (PCA) and multi-level PCA (mPCA) methods are applied here to a set of (2D frontal) facial images from a group of 80 Finnish subjects (34 male; 46 female) with two different facial expressions (smiling and neutral) per subject. Inspection of eigenvalues gives insight into the importance of different factors affecting shapes, including: biological sex, facial expression (neutral versus smiling), and all other variations. Biological sex and facial expression are shown to be reflected in those components at appropriate levels of the mPCA model. Dynamic 3D shape data for all phases of a smile made up a second dataset sampled from 60 adult British subjects (31 male; 29 female). Modes of variation reflected the act of smiling at the correct level of the mPCA model. Seven phases of the dynamic smiles are identified: rest pre-smile, onset 1 (acceleration), onset 2 (deceleration), apex, offset 1 (acceleration), offset 2 (deceleration), and rest post-smile. A clear cycle is observed in standardized scores at an appropriate level for mPCA and in single-level PCA. mPCA can be used to study static shapes and images, as well as dynamic changes in shape. It gave us much insight into the question “what’s in a smile?”.

Multilevel principal component analysis (mPCA) in shape analysis: A feasibility study in medical and dental imaging

BACKGROUND AND OBJECTIVE

Methods used in image processing should reflect any multilevel structures inherent in the image dataset or they run the risk of functioning inadequately. We wish to test the feasibility of multilevel principal components analysis (PCA) to build active shape models (ASMs) for cases relevant to medical and dental imaging.

METHODS

Multilevel PCA was used to carry out model fitting to sets of landmark points and it was compared to the results of "standard" (single-level) PCA. Proof of principle was tested by applying mPCA to model basic peri-oral expressions (happy, neutral, sad) approximated to the junction between the mouth/lips. Monte Carlo simulations were used to create this data which allowed exploration of practical implementation issues such as the number of landmark points, number of images, and number of groups (i.e., "expressions" for this example). To further test the robustness of the method, mPCA was subsequently applied to a dental imaging dataset utilising landmark points (placed by different clinicians) along the boundary of mandibular cortical bone in panoramic radiographs of the face.

RESULTS

Changes of expression that varied between groups were modelled correctly at one level of the model and changes in lip width that varied within groups at another for the Monte Carlo dataset. Extreme cases in the test dataset were modelled adequately by mPCA but not by standard PCA. Similarly, variations in the shape of the cortical bone were modelled by one level of mPCA and variations between the experts at another for the panoramic radiographs dataset. Results for mPCA were found to be comparable to those of standard PCA for point-to-point errors via miss-one-out testing for this dataset. These errors reduce with increasing number of eigenvectors/values retained, as expected.

CONCLUSIONS

We have shown that mPCA can be used in shape models for dental and medical image processing. mPCA was found to provide more control and flexibility when compared to standard "single-level" PCA. Specifically, mPCA is preferable to "standard" PCA when multiple levels occur naturally in the dataset.

The contribution of hip geometry to the prediction of hip osteoarthritis

OBJECTIVE

To determine how well measures of hip geometry can predict radiological incident hip osteoarthritis (HOA) compared to well known clinical risk factors.

DESIGN

The study population is part of the Rotterdam Study, a prospective population-based cohort. Baseline pelvic radiographs were used to measure hip geometry by two methods: Statistical Shape Models (SSM) and predefined geometry parameters (PGPs). Incident HOA (Kellgren and Lawrence (KL) ≥ 2) was assessed in 688 participants after 6.5 years without radiographic HOA at baseline. The ability to predict HOA was quantified using the area under the Receiver Operating Characteristics (ROC) curve (AUC).

RESULTS

Comparison of the two methods showed that both contain information that is not captured by the other method. At 6.5 years follow-up 132 hips had incident HOA. Five PGPs (Wiberg angle, Neck Width (NW), Pelvic Width (PW), Hip Axis Length (HAL) and Triangular Index (TI)) and two SSM (modes 5 and 9) were significant predictors of HOA (P = 0.007). Hip geometry added 7% to the prediction obtained by clinical risk factors (AUC = 0.67 (geometry), 0.66 (gender, age, Body Mass Index (BMI)) and combining both: AUC = 0.73, respectively). Mode 12 (associated with position of the femoral head in acetabulum) and Wiberg angle were predictors of HOA in participants without radiological signs at baseline (KL = 0). Although the strength of the prediction decreased for all variables at a longer follow-up, the contribution of hip geometry was still significant (P = 0.01).

CONCLUSIONS

Hip geometry has a moderate ability to predict HOA in participants with and without initial signs of osteoarthritis (OA), similar to and largely independent of the predictive value of clinical risk factors.

Measurement error in statistical models of shape

Active shape models (ASMs) are popular and sophisticated methods of extracting features in (especially medical) images. Here we analyse the error in placing ASM points on the boundary of the feature. By using replications, a corrected covariance matrix is presented that should reduce the effects of placement error. We show analytically and via simulations that the cumulative variability for a given number of eigenvalues retained in principal components analysis (PCA) ought to be reduced by increasing levels of point-placement error. Results for predicted errors are in excellent agreement with the set-up parameters of two simulated shapes and with anecdotal evidence from the trained experts for real data taken from the OSTEODENT project. We derive an equation for the reliability of placing the points and we find values of 0.79 and 0.85 (where 0=bad and 1=good) for the two clinical experts for the OSTEODENT data. These analyses help us to understand the sources and effects of measurement error in shape models.

The knowledge used in vision and where it comes from

Knowledge is often thought to be something brought from outside to act upon the visual messages received from the eye in a 'top-down' fashion, but this is a misleadingly narrow view. First, the visual system is a multilevel heterarchy with connections acting in all directions so it has no 'top'; and second, knowledge is provided through innately determined structure and by analysis of the redundancy in sensory messages themselves, as well as from outside. This paper gives evidence about mechanisms analysing sensory redundancy in biological vision. Automatic gain controls for luminance and contrast depend upon feedback from the input, and there are strong indications that the autocorrelation function, and other associations between input variables, affect the contrast sensitivity function and our subjective experience of the world. The associative structure of sensory message can provide much knowledge about the world we live in, and neural mechanisms that discount established associative structure in the input messages by recoding them can improve survival by making new structure more easily detectable. These mechanisms may be responsible for illusions, such as those produced by a concave face-mask, that are classically attributed to top-down influences.