Statistical Shape Analysis

By Anuj Srivastava, Sebastian N. Kurtek, Eric Klassen. Computer Vision, A Reference Guide, 2014

1,081 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/108b4080e00151bd6c17e47698681317a263ae4a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Vision and Pattern Recognition

In Geometry and Topology

Citations in the corpus

Statistical analysis of trajectories on Riemannian manifolds: Bird migration, hurricane tracking and video surveillance (2014, methodology): “In the landmark-based shape analysis of objects, including Dryden and Mardia (1998), Jupp and Kent (1987) and Kume, Dryden and Le (2007), where 2D objects are represented by configurations of salient points or landmarks, the set of all such configurations after removing translation and scale is a re”
Action Recognition Using Rate-Invariant Analysis of Skeletal Shape Trajectories (2016, methodology): “They use a Gaussian mixture model (GMM) to capture the statistical distribution of the postures and demonstrate the superiority of their approach over the 2D silhouette-based approach.”
Complex Elliptically Symmetric Distributions: Survey, New Results and Applications (2012, methodology): “The central case (i.e., ) for the complex AG distributions have been widely used in statistical shape analysis [24] , [45], and will play also an important role in this overview.”
A brief review of shape, form, and allometry in geometric morphometrics, with applications to human facial morphology (2013, methodology): “The mathematical properties of the shape space for landmark configurations, usually referred to as Kendall’s shape space, have been studied intensively (e.g., Kendall 1984; Bookstein 1991, 1996; Goodall 1991; Small 1996; Dryden and Mardia 1998; Rohlf 1999; Slice 2001).”
Log-Shape Ratios, Procrustes Superimposition, Elliptic Fourier Analysis: Three Worked Examples in R (2013, methodology): “All configurations (including replicates) were scaled to unit centroid size, translated, rotated, and optimally superimposed through the Generalized partial Procrustes Analysis (Dryden and Mardia, 1998; Claude, 2008).”
A smeary central limit theorem for manifolds with application to high-dimensional spheres (2018, background): “Dryden and Mardia (1998); Kendall et al. (1999), for spaces of three- and higher-dimensional shapes), (c) a general stratified space where all strata are manifolds with compatible Riemannian structures, e.g. phylogenetic tree spaces (cf. Billera et al. (2001); Moulton and Steel (2004), for varying…”
Statistical shape modeling of the left ventricle: myocardial infarct classification challenge (2017, methodology): “Different combinations of GPA, PCA, parallel transport, scale removal, shape centering, endocardium, epicardium, and the full shape (endocardium + epicardium) were explored during training.”
Sticky central limit theorems on open books (2012, background): “hape spaces, representing equivalence classes of point conﬁgurations under operations such as rotation, translation, scaling, projective transformations, or other nonlinear transformations (e.g., see [9, 18, 19] for direct similarities, aﬃne transformations, and projective transformations, resp.); •”
Semilandmarks: a method for quantifying curves and surfaces (2013, methodology): “Shape analysis using geometric morphometrics (GM) is based on the statistical analysis of landmark coordinates (Bookstein, 1991; Dryden and Mardia, 1998; Adams et al., 2004; Slice, 2007; Mitteroecker and Gunz, 2009).”
Visualizations in geometric morphometrics: How to read and how to make graphs showing shape changes (2013, methodology): “This type of presentation of data is rather popular, both in textbooks (Dryden and Mardia, 1998; Monteiro and dos Reis, 1999; Claude, 2008; Weber and Bookstein, 2011; Zelditch et al., 2012) and in research papers (e.g. Bookstein et al. 1999; Robinson et al. 2001; Dworkin and Gibson 2006; Bruner et…”
geomorph: an r package for the collection and analysis of geometric morphometric shape data (2013, methodology): “From the Procrustes-aligned coordinates, a set of shape variables is obtained (Bookstein 1991; Dryden & Mardia 1998; Rohlf 1999), which can be used in multivariate statistical analyses to address a wide range of biological questions.”
Fréchet means and Procrustes analysis in Wasserstein space (2017, methodology): “Specifically, the gradient descent algorithm proceeds by iterating the two steps of a Procrustes analysis (Gower [38]; Dryden & Mardia [30, p. 90]): (1) Registration: Each of the measures {µ1, . . . , µN} is registered to the current template γj , via the optimal transportation (registration) maps t”
Coding Kendall's Shape Trajectories for 3D Action Recognition (2018, methodology): “In view of the spherical structure of C, analytic expressions of the exponential and logarithm maps are well defined [8, 25] and can be easily adapted to S.”
Statistical Aspects of Wasserstein Distances (2018, methodology): “It has the advantage of reducing the multitransport problem of ﬁnding the Fr´echet mean to a succession of pairwise problems that are simpler in nature, in the same spirit as generalised Procrustes analysis (Dryden & Mardia, 1998).”
Dense Object Reconstruction with Semantic Priors (2013, background): “The aforementioned drawbacks of MVS have been widely recognized and several prior works share our philosophy of augmenting reconstruction with prior knowledge.”
Geometric morphometrics in entomology: Basics and applications (2018, methodology): “The same space has been called equivalently as “form space” (Rohlf 1996) or “size-and-shape space” (Dryden & Mardia 1998, 2016) or “allometric space” (Langlade et al. 2005), but Klingenberg (2016) proposed the term 167Entomological Science (2018) 21, 164–184 © 2017 The Entomological Society of…”
Ieee Transactions on Pattern Analysis and Machine Intelligence 1 Matching Shape Sequences in Video with Applications in Human Movement Analysis. Ieee Transactions on Pattern Analysis and Machine Intelligence 2 (positive): “Bookstein [17] and later Dryden and Mardia [18] have furthered the understanding of such landmark based shape descriptions.”