Analysis of Rotational Deformations From Directional Data

Schulz, Jörn; Jung, Sungkyu; Huckemann, Stephan; Pierrynowski, M.R.; Marron, J. S.; Pizer, Stephen M.

doi:10.1080/10618600.2014.914947

Cited by 20 publications

(29 citation statements)

References 46 publications

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“…In these models, describing the variation of rotational deformations can be transformed into a problem of exploring the motion of directional vectors on the unit two‐sphere. As argued in Schulz et al (), directional vectors representing rotational deformations tend to be concentrated on small circles on the unit sphere; a toy data example in Figure shows a typical pattern of such observations.…”

Section: Introductionsupporting

confidence: 59%

“…The performance of our estimators in fitting the underlying small spheres

scriptC false(μ_{0}, ν false)

is numerically compared with those of competing estimators obtained from assuming the BM distribution and the LS methods of Schulz et al (). The BM distribution has originally been defined only for data on

{double-struckS}^{2}

, but we use a natural extension given by a special case of iMS1.…”

Section: Numerical Studiesmentioning

confidence: 99%

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Small‐sphere distributions for directional data with application to medical imaging

Kim

Huckemann

Schulz

et al. 2019

Scandinavian J Statistics

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We propose novel parametric concentric multi‐unimodal small‐subsphere families of densities for p − 1 ≥ 2‐dimensional spherical data. Their parameters describe a common axis for K small hypersubspheres, an array of K directional modes, one mode for each subsphere, and K pairs of concentrations parameters, each pair governing horizontal (within the subsphere) and vertical (orthogonal to the subsphere) concentrations. We introduce two kinds of distributions. In its one‐subsphere version, the first kind coincides with a special case of the Fisher–Bingham distribution, and the second kind is a novel adaption that models independent horizontal and vertical variations. In its multisubsphere version, the second kind allows for a correlation of horizontal variation over different subspheres. In medical imaging, the situation of p − 1 = 2 occurs precisely in modeling the variation of a skeletally represented organ shape due to rotation, twisting, and bending. For both kinds, we provide new computationally feasible algorithms for simulation and estimation and propose several tests. To the best knowledge of the authors, our proposed models are the first to treat the variation of directional data along several concentric small hypersubspheres, concentrated near modes on each subsphere, let alone horizontal dependence. Using several simulations, we show that our methods are more powerful than a recent nonparametric method and ad hoc methods. Using data from medical imaging, we demonstrate the advantage of our method and infer on the dominating axis of rotation of the human knee joint at different walking phases.

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Section: Introductionsupporting

confidence: 59%

“…The performance of our estimators in fitting the underlying small spheres

scriptC false(μ_{0}, ν false)

{double-struckS}^{2}

, but we use a natural extension given by a special case of iMS1.…”

Section: Numerical Studiesmentioning

confidence: 99%

Small‐sphere distributions for directional data with application to medical imaging

Kim

Huckemann

Schulz

et al. 2019

Scandinavian J Statistics

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“…This representation does not rely on any inherent parameterization. Statistical analysis is applied to these sparse spokes [19, 24, 33]. …”

Section: Introductionmentioning

confidence: 99%

Skeletal Shape Correspondence Through Entropy

Styner

Vicory

et al. 2018

IEEE Trans. Med. Imaging

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We present a novel approach for improving the shape statistics of medical image objects by generating correspondence of skeletal points. Each object’s interior is modeled by an s-rep, i.e., by a sampled, folded, 2-sided skeletal sheet with spoke vectors proceeding from the skeletal sheet to the boundary. The skeleton is divided into three parts: the up side, the down side and the fold curve. The spokes on each part are treated separately and, using spoke interpolation, are shifted along that skeleton in each training sample so as to tighten the probability distribution on those spokes’ geometric properties while sampling the object interior regularly. As with the surface/boundary-based correspondence method of Cates et al., entropy is used to measure both the probability distribution tightness and sampling regularity, here of the spokes’ geometric properties. Evaluation on synthetic and real world lateral ventricle and hippocampus datasets demonstrate improvement in the performance of statistics using the resulting probability distributions. This improvement is greater than that achieved by an entropy-based correspondence method on the boundary points.

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“…Hartley et al [49] analyse the problem of rotation averaging from the theoretical side, again emphasizing the importance of the geodesic distance. Schulz et al introduced a framework which employs the geodesic distance to find deformations within 3D models of real objects [50]. In addition, the geodesic distance has been proven to be effective in practical applications, e.g.…”

Section: Related Workmentioning

confidence: 99%

Learning Kinematic Structure Correspondences Using Multi-Order Similarities

Chang

Fischer

Petit

et al. 2018

IEEE Trans. Pattern Anal. Mach. Intell.

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Abstract-In this paper, we present a novel framework for finding the kinematic structure correspondences between two articulated objects in videos via hypergraph matching. In contrast to appearance and graph alignment based matching methods, which have been applied among two similar static images, the proposed method finds correspondences between two dynamic kinematic structures of heterogeneous objects in videos. Thus our method allows matching the structure of objects which have similar topologies or motions, or a combination of the two. Our main contributions can be summarised as follows: (i) casting the kinematic structure correspondence problem into a hypergraph matching problem by incorporating multi-order similarities with normalising weights, (ii) introducing a structural topology similarity measure by aggregating topology constrained subgraph isomorphisms, (iii) measuring kinematic correlations between pairwise nodes, and (iv) proposing a combinatorial local motion similarity measure using geodesic distance on the Riemannian manifold. We demonstrate the robustness and accuracy of our method through a number of experiments on synthetic and real data, outperforming various other state of the art methods. Our method is not limited to a specific application nor sensor, and can be used as building block in applications such as action recognition, human motion retargeting to robots, and articulated object manipulation amongst others.

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Analysis of Rotational Deformations From Directional Data

Cited by 20 publications

References 46 publications

Small‐sphere distributions for directional data with application to medical imaging

Small‐sphere distributions for directional data with application to medical imaging

Skeletal Shape Correspondence Through Entropy

Learning Kinematic Structure Correspondences Using Multi-Order Similarities

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