On the Relation between Edge and Vertex Modelling in Shape Analysis

Hobolth, Asger; Kent, John T.; Dryden, Ian L.

doi:10.1111/1467-9469.00295

Cited by 18 publications

(16 citation statements)

References 15 publications

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“…(2011) for an application of shape analysis to fingerprints. In fact, entire polygons comprising ordered vertices, or being even star shaped as considered here, may be represented in a Euclidean space, rendering their analysis particularly simple (Hobolth et al. , 2002; Hotz et al.…”

Section: Discussion On the Paper By Neumann Evett And Skerrettmentioning

confidence: 99%

Quantifying the Weight of Evidence from a Forensic Fingerprint Comparison: A New Paradigm

Neumann

Evett

Skerrett

2012

Journal of the Royal Statistical Society Series A: Statistics in Society

135

106

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Summary. The fingerprint has, with considerable justification, come to be regarded as the acme of forensic identification. Over the last century, millions of cases have been resolved world wide because of marks left at crime scenes. The comparison methodology has not evolved greatly during its history and it is universal practice to present fingerprint evidence to a court as a categoric opinion of identification or exclusion, or to classify the evidence as inconclusive and not to report it. There has been a growing movement to supplement the fingerprint examination process by one that has a statistical model, supported by appropriate databases for calculating numerical measures of weight of evidence. The movement calls for the establishment of a logical framework for informing conclusions, based on explicit assumptions and data and open to revision and improvement. The aim is to enable the numerical evaluation of evidence that would currently be reported as a categorical identification and also of evidence that would currently be classified as inconclusive. The paper presents the results of a project carried out by the Forensic Science Service that aims to attain this goal. After a historical review, we describe a formal model for assigning numerical values to configurations of minutiae in fingerprints. We describe how the parameters of the model have been optimized to take account of interoperator variability and distortion of the finger pad, and we present the results of a substantial validation experiment that was based on searches that have been carried out on the US national fingerprint database of approximately 600 million fingerprints.

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Section: Discussion On the Paper By Neumann Evett And Skerrettmentioning

confidence: 99%

Quantifying the Weight of Evidence from a Forensic Fingerprint Comparison: A New Paradigm

Neumann

Evett

Skerrett

2012

Journal of the Royal Statistical Society Series A: Statistics in Society

135

106

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“…. We suppose that Y t is star-shaped with respect to a point z ∈ R 2 for all t. Then, the boundary of Y t can be determined by its radius vector function R t = {R t (θ ) : θ ∈ [0, 2π)} with respect to z, where Hobolth et al (2003), a deformable template model is introduced, describing a random planar object as a stochastic deformation of a known star-shaped template, see also the closely related models described in Hobolth and Jensen (2000), Kent et al (2000) and Hobolth et al (2002). We use this approach here and describe the object at time t + 1 as a stochastic transformation of the object at time t, such that…”

Section: The Gaussian Radial Growth Modelmentioning

confidence: 99%

“…The model is called p-order because it can be derived as a limit of discrete p-order Markov models defined on a finite, systematic set of angles θ , cf. Hobolth et al (2002).…”

Section: The Fourier Coefficientsmentioning

confidence: 99%

Gaussian Radial Growth

Jónsdóttir¹,

Jensen²

2011

Image Anal Stereol

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The growth of planar and spatial objects is often modelled using one-dimensional size parameters, e.g., volume, area or average width. We take a more detailed approach and model how the boundary of a growing object expands in time. We mainly consider star-shaped planar objects. The model can be regarded as a dynamic deformable template model. The limiting shape of the object may be circular but this is only one possibility among a range of limiting shapes. An application to tumour growth is presented. A 3D version of the model is presented and an extension of the model, involving time series, is briefly touched upon.

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“…by placing the main vein of the leaf tangentially to the positive vertical axis as described above, we can immediately use the spherical representation X Å −1 X Å in S k m . Alternatively, we might consider the vertex transformation vectors of Hobolth et al (2002). They viewed planar star-shaped objects with k landmarks as deformations of a regular k-sided polygon.…”

Section: Shapes Of Poplar Leavesmentioning

confidence: 99%

Shape spaces for prealigned star-shaped objects-studying the growth of plants by principal components analysis

Hotz

Huckemann

Munk

et al. 2009

Journal of the Royal Statistical Society: Series C (Applied Statistics)

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We analyse the shapes of star-shaped objects which are prealigned. This is motivated from two examples studying the growth of leaves, and the temporal evolution of tree rings. In the latter case measurements were taken at fixed angles whereas in the former case the angles were free. Subsequently, this leads to different shape spaces, related to different concepts of size, for the analysis. Whereas several shape spaces already existed in the literature when the angles are fixed, a new shape space for free angles, called spherical shape space, needed to be introduced. We compare these different shape spaces both regarding their mathematical properties and in their adequacy to the data at hand; we then apply suitably defined principal component analysis on these. In both examples we find that the shapes evolve mainly along the first principal component during growth; this is the 'geodesic hypothesis' that was formulated by Le and Kume. Moreover, we could link change-points of this evolution to significant changes in environmental conditions.

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On the Relation between Edge and Vertex Modelling in Shape Analysis

Cited by 18 publications

References 15 publications

Quantifying the Weight of Evidence from a Forensic Fingerprint Comparison: A New Paradigm

Quantifying the Weight of Evidence from a Forensic Fingerprint Comparison: A New Paradigm

Gaussian Radial Growth

Shape spaces for prealigned star-shaped objects-studying the growth of plants by principal components analysis

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