scholarly journals Statistical Shape Modeling of Femurs Using Morphing and Principal Component Analysis

2010 ◽  
Vol 4 (2) ◽  
Author(s):  
Najah Hraiech ◽  
Christelle Boichon ◽  
Michel Rochette ◽  
Thierry Marchal ◽  
Marc Horner
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Statistical Shape Model ◽  
Training Data ◽  
Large Database ◽  
Data Set ◽  
Shape Model ◽  
Statistical Shape ◽  
Low Dimensional

In this paper, we describe a method for automatically building a statistical shape model by applying a morphing method and a principal component analysis (PCA) to a large database of femurs. One of the major challenges in building a shape model from a training data set of 3D objects is the determination of the correspondence between different shapes. In our work, we solve this problem by using a morphing method. The morphing method consists of deforming the same template mesh over a large database of femur geometries, which results in isotopological meshes and one to one correspondences; i.e., the resulting meshes have the same number of nodes, the same number of elements, and the same connectivity in all morphed meshes. By applying the morphing-based registration followed by PCA to a large database of femurs, we demonstrate that the method can be used to derive a low dimensional representation of the main variabilities of the femur geometry.

scholarly journals A three-dimensional statistical shape model of the growing mandible

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
C. Klop ◽  
A. G. Becking ◽  
C. Klop ◽  
J. H. Koolstra ◽  
N. H. J. Lobé ◽  
...  
Keyword(s):  
Maxillofacial Surgery ◽  
Three Dimensional ◽  
Principal Component ◽  
Statistical Shape Model ◽  
Total Variance ◽  
Oral And Maxillofacial Surgery ◽  
Data Set ◽  
Shape Model ◽  
Computed Tomography Scanning ◽  
Statistical Shape

AbstractMandibular growth and morphology are important topics in the field of oral and maxillofacial surgery. For diagnostic and planning purposes, a normative database or statistical shape model of the growing mandible can be of great benefit. A collection of 874 cadaveric children’s mandibles with dental age between 1 and 12 years old were digitized using computed tomography scanning and reconstructed to three-dimensional models. Point correspondence was achieved using iterative closest point and coherent point drift algorithms. Principal component analysis (PCA) was applied to find the main modes of variation in the data set. The average mandible was presented, along with the first ten PCA modes. The first mode explained 78% of the total variance; combining the first ten modes accumulated to 95% of the total variance. The first mode was strongly correlated with age and hence, with natural growth. This is the largest study on three-dimensional mandibular shape and development conducted thus far. The main limitation is that the samples lack information such as gender and cause of death. Clinical application of the model first requires validation with contemporary samples.

Computation of a Probabilistic Statistical Shape Model in a Maximum-a-posteriori Framework

2009 ◽  
Vol 48 (04) ◽  
pp. 314-319 ◽  
Author(s):  
X. Pennec ◽  
J. Ehrhardt ◽  
N. Ayache ◽  
H. Handels ◽  
H. Hufnagel
Keyword(s):  
Fundamental Problem ◽  
Statistical Shape Model ◽  
Training Data ◽  
Maximum A Posteriori ◽  
Model Parameters ◽  
A Posteriori ◽  
Data Set ◽  
Shape Model ◽  
Generalization Ability ◽  
Statistical Shape

Summary Objectives: When analyzing shapes and shape variabilities, the first step is bringing those shapes into correspondence. This is a fundamental problem even when solved by manually determining exact correspondences such as landmarks. We developed a method to represent a mean shape and a variability model for a training data set based on probabilistic correspondence computed between the observations. Methods: First, the observations are matched on each other with an affine transformation found by the Expectation-Maximization Iterative-Closest-Points (EM-ICP) registration. We then propose a maximum-a-posteriori (MAP) framework in order to compute the statistical shape model (SSM) parameters which result in an optimal adaptation of the model to the observations. The optimization of the MAP explanation is realized with respect to the observation parameters and the generative model parameters in a global criterion and leads to very efficient and closed-form solutions for (almost) all parameters. Results: We compared our probabilistic SSM to a SSM based on one-to-one correspondences and the PCA (classical SSM). Experiments on synthetic data served to test the performances on non-convex shapes (15 training shapes) which have proved difficult in terms of proper correspondence determination. We then computed the SSMs for real putamen data (21 training shapes). The evaluation was done by measuring the generalization ability as well as the specificity of both SSMs and showed that especially shape detail differences are better modeled by the probabilistic SSM (Hausdorff distance in generalization ability ≈ 25% smaller). Conclusions: The experimental outcome shows the efficiency and advantages of the new approach as the probabilistic SSM performs better in modeling shape details and differences.

Evaluation of the Aging Behavior of High Density Polyethylene in Thermal Oxidative Environment by Principal Component Analysis

2017 ◽  
Vol 727 ◽  
pp. 447-449 ◽  
Author(s):  
Jun Dai ◽  
Hua Yan ◽  
Jian Jian Yang ◽  
Jun Jun Guo
Keyword(s):  
Principal Component Analysis ◽  
Impact Strength ◽  
High Density Polyethylene ◽  
Tensile Modulus ◽  
Principal Component ◽  
Component Analysis ◽  
High Density ◽  
Aging Behavior ◽  
Data Set ◽  
The Impact

To evaluate the aging behavior of high density polyethylene (HDPE) under an artificial accelerated environment, principal component analysis (PCA) was used to establish a non-dimensional expression Z from a data set of multiple degradation parameters of HDPE. In this study, HDPE samples were exposed to the accelerated thermal oxidative environment for different time intervals up to 64 days. The results showed that the combined evaluating parameter Z was characterized by three-stage changes. The combined evaluating parameter Z increased quickly in the first 16 days of exposure and then leveled off. After 40 days, it began to increase again. Among the 10 degradation parameters, branching degree, carbonyl index and hydroxyl index are strongly associated. The tensile modulus is highly correlated with the impact strength. The tensile strength, tensile modulus and impact strength are negatively correlated with the crystallinity.

Comparisons of Environmental Ordinations with Principal Component Vegetational Ordinations for Sets of Data Having Different Degrees of Complexity

1971 ◽  
Vol 1 (2) ◽  
pp. 99-112 ◽  
Author(s):  
J. K. Jeglum ◽  
C. F. Wehrhahn ◽  
J. M. A. Swan
Keyword(s):  
Principal Component Analysis ◽  
Water Level ◽  
Principal Component ◽  
Low Complexity ◽  
Component Analysis ◽  
Two Dimensional ◽  
High Complexity ◽  
Water Conductivity ◽  
Data Set ◽  
Total Data

Data from a survey of lowland, mainly peatland, vegetation were subjected to environmental ordination based on measurements of water level and water conductivity, and to vegetational ordination derived from principal component analysis (P.C.A.). Analyzed were the total set of the data ("all types"), half sets ("nonwoody" and "woody types") and quarter sets (stands of "marshes", "meadows", "shrub fens", and "other woody types"); the number of distinct physiognomic groups in a set of data, and presumably the amount of contained heterogeneity, decreased at each segmentation.The effectiveness of the ordination models was tested by correlating measured distances in two-dimensional ordination models with 2W/(A + B) indices of vegetational similarity for randomly selected pairs of types or stands. As the physiognomic complexity decreased, the effectiveness of the P.C.A. vegetational ordination increased whereas that of the environmental ordination decreased. The environmental ordination seemed most appropriate to the data encompassing high complexity (total data set), while the P.C.A. vegetational ordination seemed most appropriate to data with low complexity (quarter sets of the data).

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