Archetypoids: A new approach to define representative archetypal data

[EN] The new concept archetypoids is introduced. Archetypoid analysis represents each observation in a dataset as a mixture of actual observations in the dataset, which are pure type or archetypoids. Unlike archetype analysis, archetypoids are real observations, not a mixture of observations. This is relevant when existing archetypal observations are needed, rather than fictitious ones. An algorithm is proposed to find them and some of their theoretical properties are introduced. It is also shown how they can be obtained when only dissimilarities between observations are known (features are unavailable). Archetypoid analysis is illustrated in two design problems and several examples, compar…

Clustering of spatial point patterns

Spatial point patterns arise as the natural sampling information in many problems. An ophthalmologic problem gave rise to the problem of detecting clusters of point patterns. A set of human corneal endothelium images is given. Each image is described by using a point pattern, the cell centroids. The main problem is to find groups of images corresponding with groups of spatial point patterns. This is interesting from a descriptive point of view and for clinical purposes. A new image can be compared with prototypes of each group and finally evaluated by the physician. Usual descriptors of spatial point patterns such as the empty-space function, the nearest distribution function or Ripley's K-…

Archetypal analysis: contributions for estimating boundary cases in multivariate accommodation problem

[EN] The use of archetypal analysis is proposed in order to determine a set of representative cases that entail a certain percentage of the population, in the accommodation problem. A well-known anthropometric database has been used in order to compare our methodology with the common used PCA-approach, showing the advantages of our methodology: the level of accommodation is reached unlike the PCA approach, no more adjustments are necessary, the user can decide the number of archetypes to consider or leave the selection by a criterion. Unlike PCA, the objective of the archetypal analysis is obtaining extreme individuals, so it is the appropriate statistical technique for solving this type of…

Perceptually weighted optical flow for motion-based segmentation in MPEG-4 paradigm

In the MPEG-4 paradigm, the sequence must be described in terms of meaningful objects. This meaningful, high-level representation should emerge from low-level primitives such as optical flow and prediction error which are the basic elements of previous-generation video coders. The accuracy of the high-level models strongly depends on the robustness of the primitives used. It is shown how perceptual weighting in optical flow computation gives rise to better motion estimates which consistently improve motion-based segmentation compared to equivalent unweighted motion estimates.

Linear transform for simultaneous diagonalization of covariance and perceptual metric matrix in image coding

Two types ofredundancies are contained in images: statistical redundancy and psychovisual redundancy. Image representation techniques for image coding should remove both redundancies in order to obtain good results. In order to establish an appropriate representation, the standard approach to transform coding only considers the statistical redundancy, whereas the psychovisual factors are introduced after the selection ofthe representation as a simple scalar weighting in the transform domain. In this work, we take into account the psychovisual factors in the de8nition of the representation together with the statistical factors, by means of the perceptual metric and the covariance matrix, res…

Archetypal analysis: an alternative to clustering for unsupervised texture segmentation

Texture segmentation is one of the main tasks in image applications, specifically in remote sensing, where the objective is to segment high-resolution images of natural landscapes into different cover types. Often the focus is on the selection of discriminant textural features, and although these are really fundamental, there is another part of the process that is also influential, partitioning different homogeneous textures into groups. A methodology based on archetype analysis (AA) of the local textural measurements is proposed. AA seeks the purest textures in the image and it can find the borders between pure textures, as those regions composed of mixtures of several archetypes. The prop…

Apparel sizing using trimmed PAM and OWA operators

This paper is concerned with apparel sizing system design. One of the most important issues in the apparel development process is to define a sizing system that provides a good fit to the majority of the population. A sizing system classifies a specific population into homogeneous subgroups based on some key body dimensions. Standard sizing systems range linearly from very small to very large. However, anthropometric measures do not grow linearly with size, so they can not accommodate all body types. It is important to determine each class in the sizing system based on a real prototype that is as representative as possible of each class. In this paper we propose a methodology to develop an …

What motion information is perceptually relevant?

Importance of quantiser design compared to optimal multigrid motion estimation in video coding

Adaptive flow computation and DCT quantisation play complementary roles in motion compensated video coding schemes. Since the introduction of the intuitive entropy-constrained motion estimation of Dufaux et al. (1995), several optimal variable-size block matching algorithms have been proposed. Many of these approaches put forward their intrinsic optimality, but the corresponding visual effect has not been explored. The relative importance of optimal multigrid motion estimation with regard to quantisation is addressed in the context of MPEG-like coding. It is shown that while simpler (suboptimal) motion estimates give subjective results as good as the optimal motion estimates, small enhancem…

Forecasting basketball players' performance using sparse functional data*

Statistics and analytic methods are becoming increasingly important in basketball. In particular, predicting players’ performance using past observations is a considerable challenge. The purpose of this study is to forecast the future behavior of basketball players. The available data are sparse functional data, which are very common in sports. So far, however, no forecasting method designed for sparse functional data has been used in sports. A methodology based on two methods to handle sparse and irregular data, together with the analogous method and functional archetypoid analysis is proposed. Results in comparison with traditional methods show that our approach is competitive and additio…

Non-linear Invertible Representation for Joint Statistical and Perceptual Feature Decorrelation

The aim of many image mappings is representing the signal in a basis of decorrelated features. Two fundamental aspects must be taken into account in the basis selection problem: data distribution and the qualitative meaning of the underlying space. The classical PCA techniques reduce the statistical correlation using the data distribution. However, in applications where human vision has to be taken into account, there are perceptual factors that make the feature space uneven, and additional interaction among the dimensions may arise. In this work a common framework is presented to analyse the perceptual and statistical interactions among the coefficients of any representation. Using a recen…