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

Farnell, Damian J. J.; Popat, Hashmat; Richmond, Stephen

doi:10.1016/j.cmpb.2016.01.005

Cited by 19 publications

(34 citation statements)

References 27 publications

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“…Indeed, these clinicians had reported anecdotally [8] that placement of the point along the boundaries was difficult and it was observed the first mode of variation for the between-group level correctly reflected this type of variation. The authors concluded [10] that mPCA was found to provide more control and flexibility than standard "single-level" PCA when multiple levels occurred naturally in the dataset.…”

Section: Fig 1 Flowchart Illustrating the "Nested" Nature Of Multilmentioning

confidence: 99%

“…[10]. However, we remark here that we form two covariance matrices for a two-level model, namely: a within-group covariance matrix which is the covariance matrix evaluated over all subjects with a group and with respect to their local group means or centroids, and this matrix is then averaged all groups; and, a between-group covariance matrix that is covariance matrix of the centroids of the groups with respect to an "grand" mean shape z of the average of these centroids.…”

Section: Mathematical Formalismmentioning

confidence: 99%

“…The results of this study showed that mPCA offers more flexibility and allows deformations that classical statistical models cannot generate. Another recent application of using mPCA to form ASMs related to the field of dental imaging [10]. Proof-of-principle was tested by applying mPCA to model basic peri-oral expressions that were approximated to the junction between the mouth/lips.…”

Section: Fig 1 Flowchart Illustrating the "Nested" Nature Of Multilmentioning

confidence: 99%

“…[10] for details) may be implemented straightforwardly to solve this problem iteratively. Importantly, note that the within and between components of variation are fitted to the set of candidate points simultaneously.…”

Section: Mathematical Formalismmentioning

confidence: 99%

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Initial Results of Multilevel Principal Components Analysis of Facial Shape

Farnell

Galloway

Zhurov

et al. 2017

Communications in Computer and Information Science

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Abstract. Traditionally, active shape models (ASMs) do not make a distinction between groups in the subject population and they rely on methods such as (single-level) principal components analysis (PCA). Multilevel principal components analysis (PCA) allows one to model betweengroup effects and within-group effects explicitly. Three dimensional (3D) laser scans were taken from 240 subjects (38 Croatian female, 35 Croatian male, 40 English female, 40 English male, 23 Welsh female, 27 Welsh male, 23 Finnish female, and 24 Finnish male) and 21 landmark points were created subsequently for each scan. After Procrustes transformation, eigenvalues from mPCA and from single-level PCA based on these points were examined. mPCA indicated that the first two eigenvalues of largest magnitude related to within-groups components, but that the next largest eigenvalue related to between-groups components. Eigenvalues from single-level PCA always had a larger magnitude than either within-group or between-group eigenvectors at equivalent eigenvalue number. An examination of the first mode of variation indicated possible mixing of between-group and within-group effects in single-level PCA. Component scores for mPCA indicated clustering with country and gender for the between-groups components (as expected), but not for the within-group terms (also as expected). Clustering of component scores for single-level PCA was harder to resolve. In conclusion, mPCA is viable method of forming shape models that offers distinct advantages over single-level PCA when groups occur naturally in the subject population.Keywords: multilevel principal components analysis; active shape models; facial shape IntroductionActive shape models (ASMs) and active appearance models (AAMs) [1][2][3][4][5][6][7][8] are common techniques in image processing that are used to search for specific features or shapes in images. However, if clustering or multilevel data structures exist naturally in the data set, e.g., as illustrated by the flowchart in Fig. 1, the eigenvectors and eigenvalues from principal components analysis (PCA) will only be partially reflective of the true variation in the set of images / shapes. Multilevel principal components analysis (mPCA) provides a convenient method of modelling both the underlying structures within the images and also any groupings between images. mPCA carries out PCA at both withingroup and between-group levels independently. Note that the within-group level might be thought of as being "nested" within the broader between-group level, e.g., as shown in Fig. 1 for human facial expression. This approach also retains the desirable feature that any segmentation can still be constrained so that a fit of the model never "strays too far" from the training set used in forming the model (described in the methods section below). A previous application of mPCA to form ASMs related to the segmentation of the human spine [9]. The results of this study showed that mPCA offers more flexibility and allows deformations that classical statist...

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Section: Fig 1 Flowchart Illustrating the "Nested" Nature Of Multilmentioning

confidence: 99%

Section: Mathematical Formalismmentioning

confidence: 99%

Section: Fig 1 Flowchart Illustrating the "Nested" Nature Of Multilmentioning

confidence: 99%

Section: Mathematical Formalismmentioning

confidence: 99%

See 2 more Smart Citations

Initial Results of Multilevel Principal Components Analysis of Facial Shape

Farnell

Galloway

Zhurov

et al. 2017

Communications in Computer and Information Science

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“…Indeed, the mPCA approach has previously been shown [21][22][23][24][25] to provide a simple and straightforward method of modeling shape. The mPCA approach is potentially also of much use in active shape models (ASMs) [26][27][28][29][30] and active appearance models (AAMs) [31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

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

Farnell¹,

Galloway²,

Zurov³

et al. 2018

Preprint

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Single-level Principal Components 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?" Keywords: multilevel principal components analysis; shape and image texture; facial expression Preprints (www.preprints.org) | NOT PEER-REVIEWED |

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Enhancement and Segmentation of Dental Radiographs Using Morphological Operations

Jain

Chauhan²

2019

Dental Image Analysis for Disease Diagnosis

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

Cited by 19 publications

References 27 publications

Initial Results of Multilevel Principal Components Analysis of Facial Shape

Initial Results of Multilevel Principal Components Analysis of Facial Shape

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

Enhancement and Segmentation of Dental Radiographs Using Morphological Operations

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

Cited by 19 publications

References 27 publications

Initial Results of Multilevel Principal Components Analysis of Facial Shape

Initial Results of Multilevel Principal Components Analysis of Facial Shape

What&rsquo;s in a Smile? Initial Analyses of Dynamic Changes in Facial Shape and Appearance

Enhancement and Segmentation of Dental Radiographs Using Morphological Operations

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Product

Resources

About

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