Technical note: A new method for measuring long bone curvature using 3D landmarks and semi‐landmarks

Here we describe and evaluate a new method for quantifying long bone curvature using geometric morphometric and semi‐landmark analysis of the human femur. The technique is compared with traditional ways of measuring subtense and point of maximum curvature using either coordinate calipers or projection onto graph paper. Of the traditional methods the graph paper method is more reliable than using coordinate calipers. Measurement error is consistently lower for measuring point of maximum curvature than for measuring subtense. The results warrant caution when comparing data collected by the different traditional methods. Landmark data collection proves reliable and has a low measurement error. However, measurement error increases with the number of semi‐landmarks included in the analysis of curvature. Measurements of subtense can be estimated more reliably using 3D landmarks along the curve than using traditional techniques. We use equidistant semi‐landmarks to quantify the curve because sliding the semi‐landmarks masks the curvature signal. Principal components analysis of these equidistant semi‐landmarks provides the added benefit of describing the shape of the curve. These results are promising for functional and forensic analysis of long bone curvature in modern human populations and in the fossil record. Am J Phys Anthropol, 2010. © 2010 Wiley‐Liss, Inc.     

Multisegmental image fusion of the spine]

Fusion of medical images is a technique that permits the correlation of homologous anatomical structures in different imaging modalities on the basis of a spatial transformation of the data sets. CT and MRI of the spine provide complementary information of possible relevance for diagnostic and therapeutic decisions. Methods enabling a multisegmental CT-MRI fusion of the spine were developed. These solve the problem of altered spatial relationships of the individual anatomical structures due to differing patient positioning in successive data acquisitions. Routine clinical CT and MRI data of a thoracic section of the spine were obtained and transferred to a PC-workstation. Following segmentation of the CT-data, landmarks for each individual vertebra were defined in the CT and MRI data. For each individual vertebra the algorithm we developed then carried out a rigid registration of the CT information to the MR data. The fused data sets were presented as colour-coded images or on the basis of dynamic variation of transparency. To assess registration precision, fiducial registration errors (FRE) and target registration errors (TRE) were calculated. The algorithm permitted multi-segmental image fusion of the spine. The average time required for defining the landmarks was 22 seconds per landmark for CT, and 34 seconds per landmark for MR. The average FRE was 1.53 mm. The TRE for the vertebrae was less than 2 mm. The colour-coded images were particularly suitable for assessing the contours of the anatomical structures, whereas dynamic variation of the transparency of overlapping CT images enabled a better overall assessment of the spatial relationship of the anatomical structures. The algorithm permits precise multi-segmental fusion of CT and MR of the spine, which was not possible using current fusion-algorithms due to variations in the spatial orientation of the anatomical structures caused by different positioning of the axial skeleton in successive examinations.     

Sharing is caring? Measurement error and the issues arising from combining 3D morphometric datasets

Geometric morphometrics is routinely used in ecology and evolution and morphometric datasets are increasingly shared among researchers, allowing for more comprehensive studies and higher statistical power (as a consequence of increased sample size). However, sharing of morphometric data opens up the question of how much nonbiologically relevant variation (i.e., measurement error) is introduced in the resulting datasets and how this variation affects analyses. We perform a set of analyses based on an empirical 3D geometric morphometric dataset. In particular, we quantify the amount of error associated with combining data from multiple devices and digitized by multiple operators and test for the presence of bias. We also extend these analyses to a dataset obtained with a recently developed automated method, which does not require human‐digitized landmarks. Further, we analyze how measurement error affects estimates of phylogenetic signal and how its effect compares with the effect of phylogenetic uncertainty. We show that measurement error can be substantial when combining surface models produced by different devices and even more among landmarks digitized by different operators. We also document the presence of small, but significant, amounts of nonrandom error (i.e., bias). Measurement error is heavily reduced by excluding landmarks that are difficult to digitize. The automated method we tested had low levels of error, if used in combination with a procedure for dimensionality reduction. Estimates of phylogenetic signal can be more affected by measurement error than by phylogenetic uncertainty. Our results generally highlight the importance of landmark choice and the usefulness of estimating measurement error. Further, measurement error may limit comparisons of estimates of phylogenetic signal across studies if these have been performed using different devices or by different operators. Finally, we also show how widely held assumptions do not always hold true, particularly that measurement error affects inference more at a shallower phylogenetic scale and that automated methods perform worse than human digitization.     

Landmarking the Brain for Geometric Morphometric Analysis: An Error Study

Neuroanatomic phenotypes are often assessed using volumetric analysis. Although powerful and versatile, this approach is limited in that it is unable to quantify changes in shape, to describe how regions are interrelated, or to determine whether changes in size are global or local. Statistical shape analysis using coordinate data from biologically relevant landmarks is the preferred method for testing these aspects of phenotype. To date, approximately fifty landmarks have been used to study brain shape. Of the studies that have used landmark-based statistical shape analysis of the brain, most have not published protocols for landmark identification or the results of reliability studies on these landmarks. The primary aims of this study were two-fold: (1) to collaboratively develop detailed data collection protocols for a set of brain landmarks, and (2) to complete an intra- and inter-observer validation study of the set of landmarks. Detailed protocols were developed for 29 cortical and subcortical landmarks using a sample of 10 boys aged 12 years old. Average intra-observer error for the final set of landmarks was 1.9 mm with a range of 0.72 mm–5.6 mm. Average inter-observer error was 1.1 mm with a range of 0.40 mm–3.4 mm. This study successfully establishes landmark protocols with a minimal level of error that can be used by other researchers in the assessment of neuroanatomic phenotypes.     

Capturing data from three-dimensional surfaces using fuzzy landmarks

Anatomical landmarks are defined as biologically meaningful loci that can be unambiguously defined and repeatedly located with a high degree of accuracy and precision. The neurocranial surface is characteristically void of such loci. We define a new class of landmarks, termed fuzzy landmarks, that will allow us to represent the form of the neurocranium. A fuzzy landmark represents the position of a biological structure that is precisely delineated, but occupies an area that is larger than a single point in the observer's reference system. In this study, we present a test case in which the cranial bosses are evaluated as fuzzy landmarks. Five fuzzy landmarks (the cranial bosses) and three traditional landmarks were placed repeatedly by a single observer on three-dimensional (3D) computed tomography (CT) surface reconstructions of pediatric dry skulls and skulls of pediatric patients, and directly on four of the same dry skulls using a 3Space digitizer. Thirty landmark digitizing trials from CT scans show an average error of 1.15 mm local to each fuzzy landmark, while the average error for the last ten trials was 0.75 mm, suggesting a learning curve. Data collected with the 3Space digitizer was comparable. Measurement error of fuzzy landmarks is larger than that of traditional landmarks, but is acceptable, especially since fuzzy landmarks allow inclusion of areas that would otherwise go unsampled. The information obtained is valuable in growth studies, clinical evaluation, and volume measurements. Our method of fuzzy landmarking is not limited to cranial bosses, and can be applied to any other anatomical features with fuzzy boundaries. Am J Phys Anthropol 107:113–124, 1998. © 1998 Wiley-Liss, Inc.     

Factors Influencing Superimposition Error of 3D Cephalometric Landmarks by Plane Orientation Method Using 4 Reference Points: 4 Point Superimposition Error Regression Model

Superimposition has been used as a method to evaluate the changes of orthodontic or orthopedic treatment in the dental field. With the introduction of cone beam CT (CBCT), evaluating 3 dimensional changes after treatment became possible by superimposition. 4 point plane orientation is one of the simplest ways to achieve superimposition of 3 dimensional images. To find factors influencing superimposition error of cephalometric landmarks by 4 point plane orientation method and to evaluate the reproducibility of cephalometric landmarks for analyzing superimposition error, 20 patients were analyzed who had normal skeletal and occlusal relationship and took CBCT for diagnosis of temporomandibular disorder. The nasion, sella turcica, basion and midpoint between the left and the right most posterior point of the lesser wing of sphenoidal bone were used to define a three-dimensional (3D) anatomical reference co-ordinate system. Another 15 reference cephalometric points were also determined three times in the same image. Reorientation error of each landmark could be explained substantially (23%) by linear regression model, which consists of 3 factors describing position of each landmark towards reference axes and locating error. 4 point plane orientation system may produce an amount of reorientation error that may vary according to the perpendicular distance between the landmark and the x-axis; the reorientation error also increases as the locating error and shift of reference axes viewed from each landmark increases. Therefore, in order to reduce the reorientation error, accuracy of all landmarks including the reference points is important. Construction of the regression model using reference points of greater precision is required for the clinical application of this model.     

Bias and error in estimates of mean shape in geometric morphometrics

Sampling experiments were performed to investigate mean square error and bias in estimates of mean shape produced by different geometric morphometric methods. The experiments use the isotropic error model, which assumes equal and independent variation at each landmark. The case of three landmarks in the plane (i.e., triangles) was emphasized because it could be investigated systematically and the results displayed on the printed page. The amount of error in the estimates was displayed as RMSE surfaces over the space of all possible configurations of three landmarks. Patterns of bias were shown as vector fields over this same space. Experiments were also performed using particular combinations of four or more landmarks in both two and three dimensions.It was found that the generalized Procrustes analysis method produced estimates with the least error and no pattern of bias. Averages of Bookstein shape coordinates performed well if the longest edge was used as the baseline. The method of moments (Stoyan, 1990, Model. Biomet. J. 32, 843) used in EDMA (Lele, 1993, Math. Geol. 25, 573) exhibits larger errors. When variation is not small, it also shows a pattern of bias for isosceles triangles with one side much shorter than the other two and for triangles whose vertices are approximately collinear causing them to resemble their own reflections. Similar problems were found for the log-distance method of Rao and Suryawanshi (1996, Proc. Nat. Acad. Sci. 95, 4121). These results and their implications for the application of different geometric morphometric methods are discussed.     

View-based navigation in Hymenoptera: multiple strategies of landmark guidance in the approach to a feeder

In order to analyse how landmarks guide the last stages of an insect's approach to a goal, we recorded many flights of individual wasps and honeybees as they flew to an inconspicuous feeder on the ground that was marked by one or by two nearby landmarks. An individual tends to approach the feeder from a constant direction, flying close to the ground. Its body is oriented in roughly the same horizontal direction during the approach so that the feeder and landmarks are viewed over a narrow range of directions. Consequently, when the insect arrives at the feeder, the landmarks take up a standard position on the retina. Three navigational strategies govern the final approach. The insect first aims at a landmark, treating it as a beacon. Secondly, bees learn the appearance of a landmark with frontal retina and they associate with this stored view a motor trajectory which brings them from the landmark sufficiently close to the goal that it can be reached by image matching. Insects then move so as to put the landmark in its standard retinal position. Image matching is shown to be accomplished by a control system which has as set points the standard retinal position of the landmark and some parameter related to its retinal size. Accepted: 1 March 1997     

Are geometric morphometric analyses replicable? Evaluating landmark measurement error and its impact on extant and fossil Microtus classification

Geometric morphometric analyses are frequently employed to quantify biological shape and shape variation. Despite the popularity of this technique, quantification of measurement error in geometric morphometric datasets and its impact on statistical results is seldom assessed in the literature. Here, we evaluate error on 2D landmark coordinate configurations of the lower first molar of five North American Microtus (vole) species. We acquired data from the same specimens several times to quantify error from four data acquisition sources: specimen presentation, imaging devices, interobserver variation, and intraobserver variation. We then evaluated the impact of those errors on linear discriminant analysis‐based classifications of the five species using recent specimens of known species affinity and fossil specimens of unknown species affinity. Results indicate that data acquisition error can be substantial, sometimes explaining >30% of the total variation among datasets. Comparisons of datasets digitized by different individuals exhibit the greatest discrepancies in landmark precision, and comparison of datasets photographed from different presentation angles yields the greatest discrepancies in species classification results. All error sources impact statistical classification to some extent. For example, no two landmark dataset replicates exhibit the same predicted group memberships of recent or fossil specimens. Our findings emphasize the need to mitigate error as much as possible during geometric morphometric data collection. Though the impact of measurement error on statistical fidelity is likely analysis‐specific, we recommend that all geometric morphometric studies standardize specimen imaging equipment, specimen presentations (if analyses are 2D), and landmark digitizers to reduce error and subsequent analytical misinterpretations.     

Measurement precision and reliability in craniofacial anthropometry: implications and suggestions for clinical applications.

Craniofacial anthropometry has become an important tool used by both clinical geneticists and reconstructive surgeons. Yet little attention has been paid to the potentially serious problem of measurement error. This paper examines intra-observer measurement error and precision (also called repeatability or reliability) for 52 commonly used anthropometric variables of the head and face. Two factors proved critical to reliability: magnitude of the measurement in question and the degree to which its constituant landmarks could be readily identified. Thus, all of the measurement variables with means above 10 cm proved to have good or excellent reliability. In contrast measurement variables with means below 10 cm were more likely to have poor reliability. This trend was especially evident in variables with means of 6 cm or less where 18 of the 20 variables in this range had poor reliability. The least reliable variables were those like philtrum breadth, columella breadth, and nasal root breadth that combine small magnitude with difficult to define landmarks. While these results suggest that it may be prudent to avoid using craniofacial variables with small dimensions this may be neither practical nor desirable. In such cases repeat measurements may be the best means for optimizing reliability.     

Allowing for never and episodic consumers when correcting for error in food record measurements of dietary intake

Food records, including 24-hour recalls and diet diaries, are considered to provide generally superior measures of long-term dietary intake relative to questionnaire-based methods. Despite the expense of processing food records, they are increasingly used as the main dietary measurement in nutritional epidemiology, in particular in sub-studies nested within prospective cohorts. Food records are, however, subject to excess reports of zero intake. Measurement error is a serious problem in nutritional epidemiology because of the lack of gold standard measurements and results in biased estimated diet-disease associations. In this paper, a 3-part measurement error model, which we call the never and episodic consumers (NEC) model, is outlined for food records. It allows for both real zeros, due to never consumers, and excess zeros, due to episodic consumers (EC). Repeated measurements are required for some study participants to fit the model. Simulation studies are used to compare the results from using the proposed model to correct for measurement error with the results from 3 alternative approaches: a crude approach using the mean of repeated food record measurements as the exposure, a linear regression calibration (RC) approach, and an EC model which does not allow real zeros. The crude approach results in badly attenuated odds ratio estimates, except in the unlikely situation in which a large number of repeat measurements is available for all participants. Where repeat measurements are available for all participants, the 3 correction methods perform equally well. However, when only a subset of the study population has repeat measurements, the NEC model appears to provide the best method for correcting for measurement error, with the 2 alternative correction methods, in particular the linear RC approach, resulting in greater bias and loss of coverage. The NEC model is extended to include adjustment for measurements from food frequency questionnaires, enabling better estimation of the proportion of never consumers when the number of repeat measurements is small. The methods are applied to 7-day diary measurements of alcohol intake in the EPIC-Norfolk study.     

GEOMETRIC MORPHOMETRICS OF DEVELOPMENTAL INSTABILITY: ANALYZING PATTERNS OF FLUCTUATING ASYMMETRY WITH PROCRUSTES METHODS

Although fluctuating asymmetry has become popular as a measure of developmental instability, few studies have examined its developmental basis. We propose an approach to investigate the role of development for morphological asymmetry by means of morphometric methods. Our approach combines geometric morphometrics with the two-way ANOVA customary for conventional analyses of fluctuating asymmetry and can discover localized features of shape variation by examining the patterns of covariance among landmarks. This approach extends the notion of form used in studies of fluctuating asymmetry from collections of distances between morphological landmarks to an explicitly geometric concept of shape characterized by the configuration of landmarks. We demonstrate this approach with a study of asymmetry in the wings of tsetse flies (Glossina palpalis gambiensis). The analysis revealed significant fluctuating and directional asymmetry for shape as well as ample shape variation among individuals and between the offspring of young and old females. The morphological landmarks differed markedly in their degree of variability but multivariate patterns of landmark covariation identified by principal component analysis were generally similar between fluctuating asymmetry (within-individual variability) and variation among individuals. Therefore there is no evidence that special developmental processes control fluctuating asymmetry. We relate some of the morphometric patterns to processes known to be involved in the development of fly wings.     

An Integrated Approach for Landmark-Based Resistant Shape Analysis in 3D

The study of shape changes in morphology has seen a significant renovation in the last 20 years, particularly as a consequence of the development of geometric morphometric methods based on Cartesian coordinates of points. In order to extract information about shape differences when Cartesian coordinates are used, it is necessary to establish a common reference frame or system for all specimens to be compared. Therefore, a central issue in coordinate-based methods is which criterion should be used to align these configurations of points, since shape differences highly depend on those alignments. This is usually accomplished by aligning the configurations in a way that the sum of squared distances between coordinates of homologous points (landmarks) is minimized: the least-squares superimposition method. However, it is widely recognized that this method has some limitations when shape differences are not homogeneous across landmarks. Here we present an integrated approach for the resistant shape comparison of 3D landmark sets. It includes a new ordinary resistant Procrustes superimposition and its corresponding generalized resistant Procrustes version. In addition, they are combined with existing resistant multivariate statistical techniques for depicting the results. We demonstrate, by using both simulated and real datasets, that resistant Procrustes better detects and measures localized shape variation whenever present in up to half but one of the landmarks. The resistant Procrustes results are highly concordant with a priori biological information, and might dramatically improve the quality of inferences on patterns of shape variation.     

Automatic localization of anatomical landmarks on the back surface and construction of a body-fixed coordinate system

A method for automatic measurement of anatomical landmarks on the back surface is presented. The landmarks correspond to the verteba prominens, the dimples of the posterior superior iliac spines and the sacrum point (beginning of rima ani), which are characterized by distinct surface curvature. The surface curvatures are calculated from rasterstereographic surface measurements. The procedure of isolating a region of interest for each landmark (surface segmentation) and the calculation of the landmark coordinates are described in detail. The accuracy of landmark localization was tested with serial rasterstereographs of 28 patients (with moderate idiopathic scoliosis). From the results the intrinsic accuracy of the method is estimated to be little more than 1 mm (depending on the sampling density of the surface measurement). Therefore, the landmarks may well be used for the objective definition of a body-fixed reference coordinate system. The accuracy is, however, dependent on the specific landmark and a minor influence of posture variations is observed.     

Anatomy of emotion: a 3D study of facial mimicry

Alterations in facial motion severely impair the quality of life and social interaction of patients, and an objective grading of facial function is necessary. A method for the non-invasive detection of 3D facial movements was developed. Sequences of six standardized facial movements (maximum smile; free smile; surprise with closed mouth; surprise with open mouth; right side eye closure; left side eye closure) were recorded in 20 healthy young adults (10 men, 10 women) using an optoelectronic motion analyzer. For each subject, 21 cutaneous landmarks were identified by 2-mm reflective markers, and their 3D movements during each facial animation were computed. Three repetitions of each expression were recorded (within-session error), and four separate sessions were used (between-session error). To assess the within-session error, the technical error of the measurement (random error, TEM) was computed separately for each sex, movement and landmark. To assess the between-session repeatability, the standard deviation among the mean displacements of each landmark (four independent sessions) was computed for each movement. TEM for the single landmarks ranged between 0.3 and 9.42 mm (intrasession error). The sex- and movement-related differences were statistically significant (two-way analysis of variance, p=0.003 for sex comparison, p=0.009 for the six movements, p<0.001 for the sex x movement interaction). Among four different (independent) sessions, the left eye closure had the worst repeatability, the right eye closure had the best one; the differences among various movements were statistically significant (one-way analysis of variance, p=0.041). In conclusion, the current protocol demonstrated a sufficient repeatability for a future clinical application. Great care should be taken to assure a consistent marker positioning in all the subjects.     

Simultaneously mapping and superimposing landmark configurations with parsimony as optimality criterion

All methods proposed to date for mapping landmark configurations on a phylogenetic tree start from an alignment generated by methods that make no use of phylogenetic information, usually by superimposing all configurations against a consensus configuration. In order to properly interpret differences between landmark configurations along the tree as changes in shape, the metric chosen to define the ancestral assignments should also form the basis to superimpose the configurations. Thus, we present here a method that merges both steps, map and align, into a single procedure that (for the given tree) produces a multiple alignment and ancestral assignments such that the sum of the Euclidean distances between the corresponding landmarks along tree nodes is minimized. This approach is an extension of the method proposed by Catalano et al. (2010. Phylogenetic morphometrics (I): the use of landmark data in a phylogenetic framework. Cladistics. 26:539-549) for mapping landmark data with parsimony as optimality criterion. In the context of phylogenetics, this method allows maximizing the degree to which similarity in landmark positions can be accounted for by common ancestry. In the context of morphometrics, this approach guarantees (heuristics aside) that all the transformations inferred on the tree represent changes in shape. The performance of the method was evaluated on different data sets, indicating that the method produces marked improvements in tree score (up to 5% compared with generalized superimpositions, up to 11% compared with ordinary superimpositions). These empirical results stress the importance of incorporating the phylogenetic information into the alignment step.