Resuming Shapes with Applications

Simó, Amelia; Ves, Esther de; Ayala, Guillermo

doi:10.1023/b:jmiv.0000024039.27561.b9

Cited by 12 publications

(4 citation statements)

References 20 publications

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“…PCA is a purely second-order statistical method, whereas ICA requires the use of higher-order statistics; therefore, ICA can be seen as an extension to PCA.). Secondly, from the image analysis point of view, is the application of FDA in other problems of shape analysis such as the definition of confidence and quantile sets (Simó et al, 2004), or its use when the closed contour of a figure is not always available, such as in Domingo et al (2005), maybe using a discontinuous function. Thirdly, FDA can be exploited in other fields of image analysis besides shape analysis, such as texture analysis (Epifanio et al, 2009).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Functional data analysis in shape analysis

Epifanio

Ventura‐Campos

2011

Computational Statistics & Data Analysis

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Mid-level processes on images often return outputs in functional form. In this context the use of functional data analysis (FDA) in image analysis is considered. In particular, attention is focussed on shape analysis, where the use of FDA in the functional approach (contour functions) shows its superiority over other approaches, such as the landmark based approach or the set theory approach, on two different problems (principal component analysis and discriminant analysis) in a well-known database of bone outlines. Furthermore, a problem that has hardly ever been considered in the literature is dealt with: multivariate functional discrimination. A discriminant function based on independent component analysis for indicating where the differences between groups are and what their level of discrimination is, is proposed. The classification results obtained with the methodology are very promising. Finally, an analysis of hippocampal differences in Alzheimer's disease is carried out.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Functional data analysis in shape analysis

Epifanio

Ventura‐Campos

2011

Computational Statistics & Data Analysis

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“…The Aumann mean is based on the support function of the set, the Vorob'ev mean on the coverage function and the BaddeleyMolchanov on some distance function. Other recent definitions of mean set can we found in [16] and [17].…”

Section: B Mean Setsmentioning

confidence: 99%

Mean sets for building 3D probabilistic liver atlas from perfusion MR images

Durá

Domingo

Rojas-Arboleda

et al. 2012

2012 3rd International Conference on Image Processing Theory, Tools and Applications (IPTA)

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This paper is concerned with liver atlas construction. One of the most important issues in the framework of computational abdominal anatomy is to define an atlas that provides a priori information for common medical task such as registration and segmentation. Unlike other approaches already proposed so far (to our knowledge), in this paper we propose to use the concept of random compact mean set to build probabilistic liver atlases. To accomplish this task a two-tier process was carried out. First a set of 3D images was manually segmented by a physician. We see the different 3D segmented shapes as a realization of a random compact set. Secondly, elements of two known definitions of mean set were applied to build a probabilistic atlas that captures the variability of the cases, keeping nevertheless the essential shape of the liver.

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“…In many scientific fields, such as Biology, Medicine and Anthropometry, we can find a great number of applications where it is necessary to predict a categorical variable as a function of a geometrical object predictor. These geometrical objects can be mathematically characterized in different ways, the most popular being a set of landmarks (Bookstein, 1978; Kendall, 1984; Dryden and Mardia, 2016), compact sets (Serra, 1982; Baddeley and Molchanov, 1998; Simó et al, 2004; Molchanov, 2006) or functions (Loncaric, 1998; Kindratenko, 2003; Gual-Arnau et al, 2013). In this article, the contour of each geometrical object (surface in R3) is represented by a mathematical structure named current.…”

Section: Introductionmentioning

confidence: 99%

Generalized linear models for geometrical current predictors: An application to predict garment fit

Centella

Gual‐Arnau

Ibáñez

et al. 2019

Statistical Modelling

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The aim of this paper is to model an ordinal response variable in terms of vector-valued functional data included on a vector-valued RKHS. In particular, we focus on the vector-valued RKHS obtained when a geometrical object (body) is characterized by a current and on the ordinal regression model. A common way to solve this problem in functional data analysis is to express the data in the orthonormal basis given by decomposition of the covariance operator. But our data present very important differences with respect to the usual functional data setting. On the one hand, they are vector-valued functions, and on the other, they are functions in an RKHS with a previously defined norm. We propose to use three different bases: the orthonormal basis given by the kernel that defines the RKHS, a basis obtained from decomposition of the integral operator defined using the covariance function, and a third basis that combines the previous two. The three approaches are compared and applied to an interesting problem: building a model to predict the fit of children's garment sizes, based on a 3D database of the Spanish child population.

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Resuming Shapes with Applications

Cited by 12 publications

References 20 publications

Functional data analysis in shape analysis

Functional data analysis in shape analysis

Mean sets for building 3D probabilistic liver atlas from perfusion MR images

Generalized linear models for geometrical current predictors: An application to predict garment fit

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