Lack-of-fit tests in semiparametric mixed models.

In this paper we obtain the asymptotic distribution of restricted likelihood ratio tests in mixed linear models with a fixed and finite number of random effects. We explain why for such models the often quoted 50:50 mixture of a chi-s quared random variable with one degree of freedom and a point mass at zero does not hold. Our motivation is a study of the use of wavelets for lack-of-fit testing within a mixed model framework. Even though wavelet shave received a lot of attention in the last say 15 years for the estimation of piecewise smooth functions, much less is known about their ability to check the adequacy of a parametric model when fitting the observed data. In particular we study the testing power of wavelets for testing a hypothesized parametric model within a mixed model framework. Experimental results show that in several situations the wavelet-based test significantly outperforms the com-petitor based on penalized regression splines. The obtained results are also applicable for testing in mixed models in general, and shed some new insight into previous results.Lack-off-fittest; Likelihood ratio test; Mixed models; One-sided test; Penalization; Restricted maximum likelihood; Variance components; Wavel; Asymptotic distribution; Distribution; Likelihood; Tests; Models; Model; Random effects; Effects; Studies; Lack-of-fit; Mixed model; Framework; Functions; Data; Power; Regression;

Simulation of Gegenbauer Processes using Wavelet Packets

In this paper, we study the synthesis of Gegenbauer processes using the wavelet packets transform. In order to simulate a 1-factor Gegenbauer process, we introduce an original algorithm, inspired by the one proposed by Coifman and Wickerhauser [1], to adaptively search for the best-ortho-basis in the wavelet packet library where the covariance matrix of the transformed process is nearly diagonal. Our method clearly outperforms the one recently proposed by [2], is very fast, does not depend on the wavelet choice, and is not very sensitive to the length of the time series. From these first results we propose an algorithm to build bases to simulate k-factor Gegenbauer processes. Given its practical simplicity, we feel the general practitioner will be attracted to our simulator. Finally we evaluate the approximation due to the fact that we consider the wavelet packet coefficients as uncorrelated. An empirical study is carried out which supports our results

An Exact Method for Computing the Area Moments of Wavelet and Spline Curves

We present a method for the exact computation of the moments of a region bounded by a curve represented by a scaling function or wavelet basis. Using Green's Theorem, we show that the computation of the area moments is equivalent to applying a suitable multidimensional filter on the coefficients of the curve and thereafter computing a scalar product. The multidimensional filter coefficients are precomputed exactly as the solution of a two-scale relation. To demonstrate the performance improvement of the new method, we compare it with existing methods such as pixel-based approaches and approximation of the region by a polygon. We also propose an alternate scheme when the scaling function is sinc(x)

Parametric shape processing in biomedical imaging

In this thesis, we present a coherent and consistent approach for the estimation of shape and shape attributes from noisy images. As compared to the traditional sequential approach, our scheme is centered on a shape model which drives the feature extraction, shape optimization, and the attribute evaluation modules. In the first section, we deal with the detection of image features that guide the shape-extraction process. We propose a general approach for the design of 2-D feature detectors from a class of steerable functions, based on the optimization of a Canny-like criterion. As compared to previous computational designs, our approach is truly 2-D and yields more orientation selective detectors. We then address the estimation of the global shape from an image. Specifically, we propose to use cubic-spline-based parametric active contour models to solve two shape-extraction problems: (i) the segmentation of closed objects and (ii) the 3-D reconstruction of DNA filaments from their stereo cryo-electron micrographs. We present several enhancements of existing snake algorithms for segmentation. For the detection of 3-D DNA filaments from their orthogonal projections, we introduce the concept of projection-steerable matched filtering. We then use a 3-D snake algorithm to reconstruct the shape. Next, we analyze the efficiency of curve representations using refinable basis functions for the description of shape boundaries. We derive an exact expression for the error when we approximate a periodic signal in a scaling-function basis. Finally, we present a method for the exact computation of the area moments of such shapes

Transform-based surface analysis and representation for CAD models

In most Computer-Aided Design (CAD) systems, the topological and geometrical information in a CAD model is usually represented by the edge-based data structure. With the emergence of concurrent engineering, such issues as product design, manufacturing, and process planning are considered simultaneously at the design stage. The need for the development of high-level models for completely documenting the geometry of a product and supporting manufacturing applications, such as automating the verification of a design for manufacturing (DIM) rules and generating process plans, becomes apparent;This dissertation has addressed the development of a generalized framework for high-level geometric representations of CAD models and form features to automate algorithmic search and retrieval of manufacturing information;A new wavelet-based ranking algorithm is developed to generate surface-based representations as input for the extraction of form features with non-planar surfaces in CAD models. The objective of using a wavelet-based shape analysis approach is to overcome the main limitation of the alternative feature extraction approaches, namely their restriction to planar surfaces or simple curved surfaces;A transform-invariant coding system for CAD models by multi-scale wavelet representations is also presented. The coding procedure is based on both the internal regions and external contours of topology entities---faces

Fast Isogeometric Boundary Element Method based on Independent Field Approximation

An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies, permits an efficient evaluation of geometry related information, a mixed collocation scheme which deals with discontinuous tractions along non-smooth boundaries and a significant reduction of the right hand side of the system of equations for common boundary conditions. All these benefits are achieved without any loss of accuracy compared to conventional isogeometric formulations. The system matrices are approximated by means of hierarchical matrices to reduce the computational complexity for large scale analysis. For the required geometrical bisection of the domain, a strategy for the evaluation of bounding boxes containing the supports of NURBS basis functions is presented. The versatility and accuracy of the proposed methodology is demonstrated by convergence studies showing optimal rates and real world examples in two and three dimensions.Comment: 32 pages, 27 figure

Similarity Measurement of Breast Cancer Mammographic Images Using Combination of Mesh Distance Fourier Transform and Global Features

Similarity measurement in breast cancer is an important aspect of determining the vulnerability of detected masses based on the previous cases. It is used to retrieve the most similar image for a given mammographic query image from a collection of previously archived images. By analyzing these results, doctors and radiologists can more accurately diagnose early-stage breast cancer and determine the best treatment. The direct result is better prognoses for breast cancer patients. Similarity measurement in images has always been a challenging task in the field of pattern recognition. A widely-adopted strategy in Content-Based Image Retrieval (CBIR) is comparison of local shape-based features of images. Contours summarize the orientations and sizes images, allowing for heuristic approach in measuring similarity between images. Similarly, global features of an image have the ability to generalize the entire object with a single vector which is also an important aspect of CBIR. The main objective of this paper is to enhance the similarity measurement between query images and database images so that the best match is chosen from the database for a particular query image, thus decreasing the chance of false positives. In this paper, a method has been proposed which compares both local and global features of images to determine their similarity. Three image filters are applied to make this comparison. First, we filter using the mesh distance Fourier descriptor (MDFD), which is based on the calculation of local features of the mammographic image. After this filter is applied, we retrieve the five most similar images from the database. Two additional filters are applied to the resulting image set to determine the best match. Experiments show that this proposed method overcomes shortcomings of existing methods, increasing accuracy of matches from 68% to 88%