scholarly journals Stochastic PCA-Based Bone Models from Inverse Transform Sampling: Proof of Concept for Mandibles and Proximal Femurs

2021 ◽  
Vol 11 (11) ◽  
pp. 5204
Author(s):  
Giulia Pascoletti ◽  
Alessandra Aldieri ◽  
Mara Terzini ◽  
Pinaki Bhattacharya ◽  
Michele Calì ◽  
...  
Keyword(s):  
Principal Components ◽  
Proximal Femur ◽  
Three Dimensional ◽  
Shape Models ◽  
Average Shape ◽  
Statistical Shape ◽  
Components Analysis ◽  
Both Bones ◽  
Set Up ◽  
3D Shapes

Principal components analysis is a powerful technique which can be used to reduce data dimensionality. With reference to three-dimensional bone shape models, it can be used to generate an unlimited number of models, defined by thousands of nodes, from a limited (less than twenty) number of scalars. The full procedure has been here described in detail and tested. Two databases were used as input data: the first database comprised 40 mandibles, while the second one comprised 98 proximal femurs. The “average shape” and principal components that were required to cover at least 90% of the whole variance were identified for both bones, as well as the statistical distributions of the respective principal components weights. Fifteen principal components sufficed to describe the mandibular shape, while nine components sufficed to describe the proximal femur morphology. A routine has been set up to generate any number of mandible or proximal femur geometries, according to the actual statistical shape distributions. The set-up procedure can be generalized to any bone shape given a sufficiently large database of the respective 3D shapes.

scholarly journals Particle System Based Adaptive Sampling on Spherical Parameter Space to Improve the MDL Method for Construction of Statistical Shape Models

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Rui Xu ◽  
Xiangrong Zhou ◽  
Yasushi Hirano ◽  
Rie Tachibana ◽  
Takeshi Hara ◽  
...  
Keyword(s):  
Unit Sphere ◽  
Adaptive Sampling ◽  
State Of The Art ◽  
Particle System ◽  
Minimum Description Length ◽  
Statistical Shape Models ◽  
Shape Models ◽  
Statistical Shape ◽  
Left And Right ◽  
3D Shapes

Minimum description length (MDL) based group-wise registration was a state-of-the-art method to determine the corresponding points of 3D shapes for the construction of statistical shape models (SSMs). However, it suffered from the problem that determined corresponding points did not uniformly spread on original shapes, since corresponding points were obtained by uniformly sampling the aligned shape on the parameterized space of unit sphere. We proposed a particle-system based method to obtain adaptive sampling positions on the unit sphere to resolve this problem. Here, a set of particles was placed on the unit sphere to construct a particle system whose energy was related to the distortions of parameterized meshes. By minimizing this energy, each particle was moved on the unit sphere. When the system became steady, particles were treated as vertices to build a spherical mesh, which was then relaxed to slightly adjust vertices to obtain optimal sampling-positions. We used 47 cases of (left and right) lungs and 50 cases of livers, (left and right) kidneys, and spleens for evaluations. Experiments showed that the proposed method was able to resolve the problem of the original MDL method, and the proposed method performed better in the generalization and specificity tests.

Anatomically oriented Principal Components Analysis of three-dimensional tongue surfaces

2017 ◽  
Vol 141 (5) ◽  
pp. 3584-3584
Author(s):  
Steven M. Lulich ◽  
Max Nelson ◽  
Kenneth de Jong ◽  
Kelly Berkson
Keyword(s):  
Principal Components Analysis ◽  
Principal Components ◽  
Three Dimensional ◽  
Components Analysis

scholarly journals Computational Shape Models Characterize Shape Change of the Left Atrium in Atrial Fibrillation

2014 ◽  
Vol 8s1 ◽  
pp. CMC.S15710 ◽  
Author(s):  
Joshua Cates ◽  
Erik Bieging ◽  
Alan Morris ◽  
Gregory Gardner ◽  
Nazem Akoum ◽  
...  
Keyword(s):  
Atrial Fibrillation ◽  
Left Atrium ◽  
Shape Change ◽  
Three Dimensional ◽  
Shape Variation ◽  
Mr Images ◽  
Significant Group ◽  
Empirical Observation ◽  
Shape Models ◽  
Statistical Shape

Shape change of the left atrium (LA) and LA appendage in atrial fibrillation (AF) patients is hypothesized to be linked to AF pathology and to play a role in thrombogenesis; however, many aspects of shape variation in the heart are poorly understood. To date, studies of the LA shape in AF have been limited to empirical observation and summary metrics, such as volume and its likeness to a sphere. This paper describes a more comprehensive approach to the study of the LA shape through the use of computationally derived statistical shape models. We describe practical approaches that we have developed to extract shape parameters automatically from the three-dimensional MR images of the patient. From these images and our techniques, we can produce a more comprehensive description of LA geometric variability than that has been previously possible. We present the methodology and results from two examples of specific analyses using shape models: (1) we describe statistically significant group differences between the normal control and AF patient populations ( n = 137) and (2) we describe characteristic shapes of the LA appendage that are associated with the risk of thrombogenesis determined by transesophageal echocardiography ( n = 203).

scholarly journals Creatingnoisy 3D shapes - an implementation using free and open source tools

2017 ◽  
Author(s):  
Zoltan Derzsi ◽  
Robert Volcic
Keyword(s):  
Open Source ◽  
Operating Systems ◽  
Three Dimensional ◽  
Set Up ◽  
Dimensional Object ◽  
3D Shapes

Distorting the shape of a three-dimensional object in a randomised manner is a very difficult task. We present a script in this paper that programmatically generates spheres with added radius noise, utilising Meshlab’s software back-end. We successfully tested the script on Mac OS, Windows, and Linux operating systems. We also have given instructions on how to set up the environment for each platform, and how to replicate what the script does manually.

scholarly journals Implementing the Automatic Generation of 3D Statistical Shape Models with ITK

2006 ◽  
Author(s):  
Tobias Heimann ◽  
Ipek Oguz ◽  
Ivo Wolf ◽  
Martin Styner ◽  
Hans-Peter Meinzer
Keyword(s):  
Cost Function ◽  
Model Building ◽  
Three Dimensional ◽  
Automatic Generation ◽  
Statistical Shape Models ◽  
Shape Models ◽  
Statistical Shape ◽  
Real World Datasets ◽  
Value Decomposition ◽  
Spatial Locations

Statistical Shape Models are a popular method for segmenting three-dimensional medical images. To obtain the required landmark correspondences, various automatic approaches have been proposed. In this work, we present an improved version of minimizing the description length (MDL) of the model. To initialize the algorithm, we describe a method to distribute landmarks on the training shapes using a conformal parameterization function. Then, we introduce a novel procedure to modify landmark positions locally without disturbing established correspondences. We employ a gradient descent optimization to minimize the MDL cost function, speeding up automatic model building by several orders of magnitude when compared to the original MDL approach. The necessary gradient information is estimated from a singular value decomposition, a more accurate technique to calculate the PCA than the commonly used eigendecomposition of the covariance matrix. In this work, we first present a basic version where spatial locations are used in the MDL cost function; next, we introduce an extended version where any combination of features can be used as a metric. As an example application, we present results based on local curvature measurements. Finally, we present results for synthetic and real-world datasets demonstrating the efficiency of our procedures and give details about the implementation using the Insight Toolkit (ITK).

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