Statistical Shape Analysis, with Applications in R

Dryden, Ian L.; Mardia, Kantilal V.

doi:10.1002/9781119072492

Cited by 674 publications

(841 citation statements)

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“…Using the SAS IML procedure and its NLPQN subroutine, we calculated the positions of the sliding semilandmarks that minimized the sum of the squared Procrustes distances obtained in a full ordinary Procrustes analysis (OPA; Dryden & Mardia, 2016) of the landmarks and semilandmarks.…”

Section: Methodsmentioning

confidence: 99%

Allometry and integration do not strongly constrain beak shape evolution in large‐billed (Corvus macrorhynchos) and carrion crows (Corvus corone)

Yamasaki

Aoki

Tokita

2018

Ecology and Evolution

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A recent geometric morphometric study on certain landbird lineages revealed that a major part of the variation in beak shape is accounted for by skull size and cranial shape. The study interpreted this result as evidence for the presence of strong evolutionary constraints that severely prevented beak shape from evolving substantially away from predictions of allometry and morphological integration. However, there is another overlooked but similarly plausible explanation for this result: The reason why beak shape does not depart much from predictions might simply be that selection pressures favoring such changes in shape are themselves rare. Here, to evaluate the intensity of evolutionary constraints on avian beak shape more appropriately, we selected large‐billed (Corvus macrorhynchos) and carrion crows (Corvus corone) as study objects. These landbird species seem to experience selection pressures favoring a departure from an allometric trajectory. A landmark‐based geometric morphometric approach using three‐dimensional reconstructions of CT scan images revealed that only 45.4% of the total shape variation was explained by allometry and beak–braincase integration. This suggests that when a selection pressure acts in a different direction to allometry and integration, avian beak shape can react to it and evolve flexibly. As traditionally considered, evolutionary constraints on avian beak shape might not be all that strong.

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Section: Methodsmentioning

confidence: 99%

Allometry and integration do not strongly constrain beak shape evolution in large‐billed (Corvus macrorhynchos) and carrion crows (Corvus corone)

Yamasaki

Aoki

Tokita

2018

Ecology and Evolution

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“…. , m, PA [6,9,8,10,2] computes the d-dimensional reference shape M ∈ R d× and the m transformations T i ∈ R d×d (e.g., affine, Euclidean) that minimize the reference-space model [10,8,2] (see Fig. 2 (a)):…”

Section: Procrustes Analysis Revisitedmentioning

confidence: 99%

Subspace Procrustes Analysis

Perez-Sala

Torre

Igual

et al. 2015

Computer Vision - ECCV 2014 Workshops

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Abstract. Procrustes Analysis (PA) has been a popular technique to align and build 2-D statistical models of shapes. Given a set of 2-D shapes PA is applied to remove rigid transformations. Then, a non-rigid 2-D model is computed by modeling (e.g., PCA) the residual. Although PA has been widely used, it has several limitations for modeling 2-D shapes: occluded landmarks and missing data can result in local minima solutions, and there is no guarantee that the 2-D shapes provide a uniform sampling of the 3-D space of rotations for the object. To address previous issues, this paper proposes Subspace PA (SPA). Given several instances of a 3-D object, SPA computes the mean and a 2-D subspace that can simultaneously model all rigid and non-rigid deformations of the 3-D object. We propose a discrete (DSPA) and continuous (CSPA) formulation for SPA, assuming that 3-D samples of an object are provided. DSPA extends the traditional PA, and produces unbiased 2-D models by uniformly sampling different views of the 3-D object. CSPA provides a continuous approach to uniformly sample the space of 3-D rotations, being more efficient in space and time. Experiments using SPA to learn 2-D models of bodies from motion capture data illustrate the benefits of our approach.

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“…A steepest descent algorithm implemented as the inverse compositional algorithm by Baker and Matthews [14] reduces the registration time to 4-8 minutes per shape registered on a 1.7 GHz laptop PC. From the Procrustes [15], registered shapes a shape model and a deformation model are created. Generally, the impressions do not depict the exact same part of the ear, only an overlapping region; hence, the models are cropped to their common subset.…”

Section: Model Generationmentioning

confidence: 99%

Analysis of Deformation of the Human Ear and Canal Caused by Mandibular Movement

Darkner

Larsen

Paulsen

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2007

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Abstract. Many hearing aid users experience physical discomfort when wearing their device. The main contributor to this problem is believed to be deformation of the ear and ear canal caused by movement of the mandible. Physical discomfort results from added pressure on soft tissue areas in the ear. Identifying features that can predict potential deformation is therefore important for identifying problematic cases in advance. A study on the physical deformation of the human ear and canal due to movement of the mandible is presented. The study is based on laser scannings of 30 pairs of ear impressions from 9 female and 21 male subjects. Two impressions have been taken from each subject, one with open mouth, and one with the mouth closed. All impressions are registered using non-rigid surface registration and a shape model is built. From each pair of impressions a deformation field is generated and propagated to the shape model, enabling the building of a deformation model in the reference frame of the shape model. A relationship between the two models is established, showing that the shape variation can explain approximately 50% of the variation in the deformation model. An hypothesis test for significance of the deformations for each deformation field reveals that all subjects have significant deformation at Tragus and in the canal. Furthermore, a relation between the magnitude of the deformation and the gender of the subject is demonstrated. The results are successfully validated by comparing the outcome to the anatomy by using a single set of high resolution histological sectionings of the region of interest.

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Statistical Shape Analysis, with Applications in R

Cited by 674 publications

References 0 publications

Allometry and integration do not strongly constrain beak shape evolution in large‐billed (Corvus macrorhynchos) and carrion crows (Corvus corone)

Allometry and integration do not strongly constrain beak shape evolution in large‐billed (Corvus macrorhynchos) and carrion crows (Corvus corone)

Subspace Procrustes Analysis

Analysis of Deformation of the Human Ear and Canal Caused by Mandibular Movement

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