Statistical shape analysis using non-Euclidean metrics

Larsen, Rasmus; Hilger, Klaus Baggesen

doi:10.1016/s1361-8415(03)00040-9

Cited by 13 publications

(9 citation statements)

References 9 publications

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“…The application of the MNF transform to the internal and external scoliosis datasets, a relatively new method in biomedical engineering. 17 This paper generalizes this transform to a functional context, and allows for the caracterization of trunk and spine coefficients in terms of their noise content through the SN R, an innovation that is particularly critical for working with data emanating from the noisy lateral X-ray reconstructions.…”

Section: Discussionmentioning

confidence: 99%

Robust prediction of three-dimensional spinal curve from back surface for non-invasive follow-up of scoliosis

2005

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Spinal curvature progression in scoliosis patients is monitored from X-rays, and this serial exposure to harmful radiation increases the incidence of developing cancer. With the aim of reducing the invasiveness of follow-up, this study seeks to relate the three-dimensional external surface to the internal geometry, having assumed that that the physiological links between these are sufficiently regular across patients. A database was used of 194 quasi-simultaneous acquisitions of two X-rays and a 3D laser scan of the entire trunk. Data was processed to sets of datapoints representing the trunk surface and spinal curve. Functional data analyses were performed using generalized Fourier series using a Haar basis and functional minimum noise fractions. The resulting coefficients became inputs and outputs, respectively, to an array of support vector regression (SVR) machines. SVR parameters were set based on theoretical results, and cross-validation increased confidence in the system's performance. Predicted lateral and frontal views of the spinal curve from the back surface demonstrated average L 2 -errors of 6.13 and 4.38 millimetres, respectively, across the test set; these compared favourably with measurement error in data. This constitutes a first robust prediction of the 3D spinal curve from external data using learning techniques.

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Section: Discussionmentioning

confidence: 99%

Robust prediction of three-dimensional spinal curve from back surface for non-invasive follow-up of scoliosis

2005

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“…This is particularly useful when classifications are viewed as lossy compressions of images. As close relationships among ICA and maximum autocorrelation factors (MAF) transform is well established [46], research efforts on informational analyses of image and non-image datasets can be joined to improve our understanding about information dynamics with respect to data fusion.…”

Section: Applicabilities Of the Proposed Methods And Some Topics For mentioning

confidence: 99%

Quantifying Information Content in Multispectral Remote-Sensing Images Based on Image Transforms and Geostatistical Modelling

Zhang

Yang

2020

Remote Sensing

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Quantifying information content in remote-sensing images is fundamental for information-theoretic characterization of remote sensing information processes, with the images being usually information sources. Information-theoretic methods, being complementary to conventional statistical methods, enable images and their derivatives to be described and analyzed in terms of information as defined in information theory rather than data per se. However, accurately quantifying images’ information content is nontrivial, as information redundancy due to spectral and spatial dependence needs to be properly handled. There has been little systematic research on this, hampering wide applications of information theory. This paper seeks to fill this important research niche by proposing a strategy for quantifying information content in multispectral images based on information theory, geostatistics, and image transformations, by which interband spectral dependence, intraband spatial dependence, and additive noise inherent to multispectral images are effectively dealt with. Specifically, to handle spectral dependence, independent component analysis (ICA) is performed to transform a multispectral image into one with statistically independent image bands (not spectral bands of the original image). The ICA-transformed image is further normal-transformed to facilitate computation of information content based on entropy formulas for Gaussian distributions. Normal transform facilitates straightforward incorporation of spatial dependence in entropy computation for the aforementioned double-transformed image bands with inter-pixel spatial correlation modeled via variograms. Experiments were undertaken using Landsat ETM+ and TM image subsets featuring different dominant land cover types (i.e., built-up, agricultural, and hilly). The experimental results confirm that the proposed methods provide more objective estimates of information content than otherwise when spectral dependence, spatial dependence, or non-normality is not accommodated properly. The differences in information content between image subsets obtained with ETM+ and TM were found to be about 3.6 bits/pixel, indicating the former’s greater information content. The proposed methods can be adapted for information-theoretic analyses of remote sensing information processes.

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“…CCA maximizes the correlation between linear combinations of two multivariate groups of variables, see [5,14,16]. We jointly analyse pairs of landmark variables (x, y), with dispersions Σ 11 and Σ 22 and cross-covariance Σ 12 = Σ 21 T , and find sets of linear combinations (called canonical variates, CVs) of the zero mean original variables that maximize correlation ρ = Corr{a T x, b T y}, under a T Σ 11 a = b T Σ 22 b = 1.…”

Section: Clinical Validation Of Gcd Obtained Correspondencementioning

confidence: 99%

“…This work is primarily based on the theory of point distribution models, which are widely used in modelling biological shape variability over a set of annotated training data, [6,7], based on generalized Procrustes alignment, [10], and decomposition, [16], in shape tangent space. The data are mandibular surfaces acquired from computed tomography (CT) scans of subjects with Apert syndrome.…”

Section: Introductionmentioning

confidence: 99%

Active Shape Analysis of Mandibular Growth

Hilger

Larsen

Kreiborg

et al. 2003

Lecture Notes in Computer Science

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Abstract. This work contains a clinical validation using biological landmarks of a Geometry Constrained Diffusion registration of mandibular surfaces. Canonical Correlations Analysis is extended to analyse 3D landmarks and the correlations are used as similarity measures for landmark clustering. A novel Active Shape Model is proposed targeting growth modelling by applying Partial Least Squares regression in decomposing the Procrustes tangent space. Shape centroid size is applied as dependent variable but the method generalizes to handle other, both uni-and multivariate, effects probing for high covariation wrt. shape variation.

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Statistical shape analysis using non-Euclidean metrics

Cited by 13 publications

References 9 publications

Robust prediction of three-dimensional spinal curve from back surface for non-invasive follow-up of scoliosis

Robust prediction of three-dimensional spinal curve from back surface for non-invasive follow-up of scoliosis

Quantifying Information Content in Multispectral Remote-Sensing Images Based on Image Transforms and Geostatistical Modelling

Active Shape Analysis of Mandibular Growth

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