Compact Representations for Fast Nonrigid Registration of Medical Images

We develop efficient techniques for the non-rigid registration of medical images by using representations that adapt to the anatomy found in such images. Images of anatomical structures typically have uniform intensity interiors and smooth boundaries. We create methods to represent such regions compactly using tetrahedra. Unlike voxel-based representations, tetrahedra can accurately describe the expected smooth surfaces of medical objects. Furthermore, the interior of such objects can be represented using a small number of tetrahedra. Rather than describing a medical object using tens of thousands of voxels, our representations generally contain only a few thousand elements. Tetrahedra facilitate the creation of efficient non-rigid registration algorithms based on finite element methods (FEM). We create a fast, FEM-based method to non-rigidly register segmented anatomical structures from two subjects. Using our compact tetrahedral representations, this method generally requires less than one minute of processing time on a desktop PC. We also create a novel method for the non-rigid registration of gray scale images. To facilitate a fast method, we create a tetrahedral representation of a displacement field that automatically adapts to both the anatomy in an image and to the displacement field. The resulting algorithm has a computational cost that is dominated by the number of nodes in the mesh (about 10,000), rather than the number of voxels in an image (nearly 10,000,000). For many non-rigid registration problems, we can find a transformation from one image to another in five minutes. This speed is important as it allows use of the algorithm during surgery. We apply our algorithms to find correlations between the shape of anatomical structures and the presence of schizophrenia. We show that a study based on our representations outperforms studies based on other representations. We also use the results of our non-rigid registration algorithm as the basis of a segmentation algorithm. That algorithm also outperforms other methods in our tests, producing smoother segmentations and more accurately reproducing manual segmentations.

Representation and Detection of Shapes in Images

We present a set of techniques that can be used to represent and detect shapes in images. Our methods revolve around a particular shape representation based on the description of objects using triangulated polygons. This representation is similar to the medial axis transform and has important properties from a computational perspective. The first problem we consider is the detection of non-rigid objects in images using deformable models. We present an efficient algorithm to solve this problem in a wide range of situations, and show examples in both natural and medical images. We also consider the problem of learning an accurate non-rigid shape model for a class of objects from examples. We show how to learn good models while constraining them to the form required by the detection algorithm. Finally, we consider the problem of low-level image segmentation and grouping. We describe a stochastic grammar that generates arbitrary triangulated polygons while capturing Gestalt principles of shape regularity. This grammar is used as a prior model over random shapes in a low level algorithm that detects objects in images.

Pre-Attentive Segmentation in the Primary Visual Cortex

Stimuli outside classical receptive fields have been shown to exert significant influence over the activities of neurons in primary visual cortexWe propose that contextual influences are used for pre-attentive visual segmentation, in a new framework called segmentation without classification. This means that segmentation of an image into regions occurs without classification of features within a region or comparison of features between regions. This segmentation framework is simpler than previous computational approaches, making it implementable by V1 mechanisms, though higher leve l visual mechanisms are needed to refine its output. However, it easily handles a class of segmentation problems that are tricky in conventional methods. The cortex computes global region boundaries by detecting the breakdown of homogeneity or translation invariance in the input, using local intra-cortical interactions mediated by the horizontal connections. The difference between contextual influences near and far from region boundaries makes neural activities near region boundaries higher than elsewhere, making boundaries more salient for perceptual pop-out. This proposal is implemented in a biologically based model of V1, and demonstrated using examples of texture segmentation and figure-ground segregation. The model performs segmentation in exactly the same neural circuit that solves the dual problem of the enhancement of contours, as is suggested by experimental observations. Its behavior is compared with psychophysical and physiological data on segmentation, contour enhancement, and contextual influences. We discuss the implications of segmentation without classification and the predictions of our V1 model, and relate it to other phenomena such as asymmetry in visual search.

Image Based Rendering Using Algebraic Techniques

This paper presents an image-based rendering system using algebraic relations between different views of an object. The system uses pictures of an object taken from known positions. Given three such images it can generate "virtual'' ones as the object would look from any position near the ones that the two input images were taken from. The extrapolation from the example images can be up to about 60 degrees of rotation. The system is based on the trilinear constraints that bind any three view so fan object. As a side result, we propose two new methods for camera calibration. We developed and used one of them. We implemented the system and tested it on real images of objects and faces. We also show experimentally that even when only two images taken from unknown positions are given, the system can be used to render the object from other view points as long as we have a good estimate of the internal parameters of the camera used and we are able to find good correspondence between the example images. In addition, we present the relation between these algebraic constraints and a factorization method for shape and motion estimation. As a result we propose a method for motion estimation in the special case of orthographic projection.

Visual Segmentation without Classification in a Model of the Primary Visual Cortex

Stimuli outside classical receptive fields significantly influence the neurons' activities in primary visual cortex. We propose that such contextual influences are used to segment regions by detecting the breakdown of homogeneity or translation invariance in the input, thus computing global region boundaries using local interactions. This is implemented in a biologically based model of V1, and demonstrated in examples of texture segmentation and figure-ground segregation. By contrast with traditional approaches, segmentation occurs without classification or comparison of features within or between regions and is performed by exactly the same neural circuit responsible for the dual problem of the grouping and enhancement of contours.

The agreement between ipsative and normative questionnaires using compositional data analysis techniques

The main instrument used in psychological measurement is the self-report questionnaire. One of its major drawbacks however is its susceptibility to response biases. A known strategy to control these biases has been the use of so-called ipsative items. Ipsative items are items that require the respondent to make between-scale comparisons within each item. The selected option determines to which scale the weight of the answer is attributed. Consequently in questionnaires only consisting of ipsative items every respondent is allotted an equal amount, i.e. the total score, that each can distribute differently over the scales. Therefore this type of response format yields data that can be considered compositional from its inception. Methodological oriented psychologists have heavily criticized this type of item format, since the resulting data is also marked by the associated unfavourable statistical properties. Nevertheless, clinicians have kept using these questionnaires to their satisfaction. This investigation therefore aims to evaluate both positions and addresses the similarities and differences between the two data collection methods. The ultimate objective is to formulate a guideline when to use which type of item format. The comparison is based on data obtained with both an ipsative and normative version of three psychological questionnaires, which were administered to 502 first-year students in psychology according to a balanced within-subjects design. Previous research only compared the direct ipsative scale scores with the derived ipsative scale scores. The use of compositional data analysis techniques also enables one to compare derived normative score ratios with direct normative score ratios. The addition of the second comparison not only offers the advantage of a better-balanced research strategy. In principle it also allows for parametric testing in the evaluation

Discovering similarities in the time use patterns of the Spanish Autonomous Communities by Fuzzy techniques

In 2000 the European Statistical Office published the guidelines for developing the Harmonized European Time Use Surveys system. Under such a unified framework, the first Time Use Survey of national scope was conducted in Spain during 2002– 03. The aim of these surveys is to understand human behavior and the lifestyle of people. Time allocation data are of compositional nature in origin, that is, they are subject to non-negativity and constant-sum constraints. Thus, standard multivariate techniques cannot be directly applied to analyze them. The goal of this work is to identify homogeneous Spanish Autonomous Communities with regard to the typical activity pattern of their respective populations. To this end, fuzzy clustering approach is followed. Rather than the hard partitioning of classical clustering, where objects are allocated to only a single group, fuzzy method identify overlapping groups of objects by allowing them to belong to more than one group. Concretely, the probabilistic fuzzy c-means algorithm is conveniently adapted to deal with the Spanish Time Use Survey microdata. As a result, a map distinguishing Autonomous Communities with similar activity pattern is drawn. Key words: Time use data, Fuzzy clustering; FCM; simplex space; Aitchison distance

Analysis of Pleistocene paleodrainage evolution in the Po Basin (Italy) by multivariate statistical techniques

In order to obtain a high-resolution Pleistocene stratigraphy, eleven continuously cored boreholes, 100 to 220m deep were drilled in the northern part of the Po Plain by Regione Lombardia in the last five years. Quantitative provenance analysis (QPA, Weltje and von Eynatten, 2004) of Pleistocene sands was carried out by using multivariate statistical analysis (principal component analysis, PCA, and similarity analysis) on an integrated data set, including high-resolution bulk petrography and heavy-mineral analyses on Pleistocene sands and of 250 major and minor modern rivers draining the southern flank of the Alps from West to East (Garzanti et al, 2004; 2006). Prior to the onset of major Alpine glaciations, metamorphic and quartzofeldspathic detritus from the Western and Central Alps was carried from the axial belt to the Po basin longitudinally parallel to the SouthAlpine belt by a trunk river (Vezzoli and Garzanti, 2008). This scenario rapidly changed during the marine isotope stage 22 (0.87 Ma), with the onset of the first major Pleistocene glaciation in the Alps (Muttoni et al, 2003). PCA and similarity analysis from core samples show that the longitudinal trunk river at this time was shifted southward by the rapid southward and westward progradation of transverse alluvial river systems fed from the Central and Southern Alps. Sediments were transported southward by braided river systems as well as glacial sediments transported by Alpine valley glaciers invaded the alluvial plain. Kew words: Detrital modes; Modern sands; Provenance; Principal Components Analysis; Similarity, Canberra Distance; palaeodrainage

Clustering compositional data trajectories

Our essay aims at studying suitable statistical methods for the clustering of compositional data in situations where observations are constituted by trajectories of compositional data, that is, by sequences of composition measurements along a domain. Observed trajectories are known as “functional data” and several methods have been proposed for their analysis. In particular, methods for clustering functional data, known as Functional Cluster Analysis (FCA), have been applied by practitioners and scientists in many fields. To our knowledge, FCA techniques have not been extended to cope with the problem of clustering compositional data trajectories. In order to extend FCA techniques to the analysis of compositional data, FCA clustering techniques have to be adapted by using a suitable compositional algebra. The present work centres on the following question: given a sample of compositional data trajectories, how can we formulate a segmentation procedure giving homogeneous classes? To address this problem we follow the steps described below. First of all we adapt the well-known spline smoothing techniques in order to cope with the smoothing of compositional data trajectories. In fact, an observed curve can be thought of as the sum of a smooth part plus some noise due to measurement errors. Spline smoothing techniques are used to isolate the smooth part of the trajectory: clustering algorithms are then applied to these smooth curves. The second step consists in building suitable metrics for measuring the dissimilarity between trajectories: we propose a metric that accounts for difference in both shape and level, and a metric accounting for differences in shape only. A simulation study is performed in order to evaluate the proposed methodologies, using both hierarchical and partitional clustering algorithm. The quality of the obtained results is assessed by means of several indices

Caracterització i diagnosi de masses en imatges de mamografia

Els objectius del projecte es divideixen en tres blocs: Primerament, realitzar una segmentació automàtica del contorn d'una imatge on hi ha una massa central. Tot seguit, a partir del contorn trobat, caracteritzar la massa. I finalment, utilitzant les característiques anteriors classificar la massa en benigne o maligne. En el projecte s'utilitza el Matlab com a eina de programació. Concretament les funcions enfocades al processat de imatges del toolbox de Image processing (propi de Matlab) i els classificadors de la PRTools de la Delft University of Technology

Colour image processing

In the context of the round table the following topics related to image colour processing will be discussed: historical point of view. Studies of Aguilonius, Gerritsen, Newton and Maxwell. CIE standard (Commission International de lpsilaEclaraige). Colour models. RGB, HIS, etc. Colour segmentation based on HSI model. Industrial applications. Summary and discussion. At the end, video images showing the robustness of colour in front of B/W images will be presented

Robust fault detection using consistency techniques for uncertainty handling

Often practical performance of analytical redundancy for fault detection and diagnosis is decreased by uncertainties prevailing not only in the system model, but also in the measurements. In this paper, the problem of fault detection is stated as a constraint satisfaction problem over continuous domains with a big number of variables and constraints. This problem can be solved using modal interval analysis and consistency techniques. Consistency techniques are then shown to be particularly efficient to check the consistency of the analytical redundancy relations (ARRs), dealing with uncertain measurements and parameters. Through the work presented in this paper, it can be observed that consistency techniques can be used to increase the performance of a robust fault detection tool, which is based on interval arithmetic. The proposed method is illustrated using a nonlinear dynamic model of a hydraulic system

Microcalcification evaluation in computer assisted diagnosis for digital mammography

In order to develop applications for z;isual interpretation of medical images, the early detection and evaluation of microcalcifications in digital mammograms is verg important since their presence is often associated with a high incidence of breast cancers. Accurate classification into benign and malignant groups would help improve diagnostic sensitivity as well as reduce the number of unnecessa y biopsies. The challenge here is the selection of the useful features to distinguish benign from malignant micro calcifications. Our purpose in this work is to analyse a microcalcification evaluation method based on a set of shapebased features extracted from the digitised mammography. The segmentation of the microcalcifications is performed using a fixed-tolerance region growing method to extract boundaries of calcifications with manually selected seed pixels. Taking into account that shapes and sizes of clustered microcalcifications have been associated with a high risk of carcinoma based on digerent subjective measures, such as whether or not the calcifications are irregular, linear, vermiform, branched, rounded or ring like, our efforts were addressed to obtain a feature set related to the shape. The identification of the pammeters concerning the malignant character of the microcalcifications was performed on a set of 146 mammograms with their real diagnosis known in advance from biopsies. This allowed identifying the following shape-based parameters as the relevant ones: Number of clusters, Number of holes, Area, Feret elongation, Roughness, and Elongation. Further experiments on a set of 70 new mammogmms showed that the performance of the classification scheme is close to the mean performance of three expert radiologists, which allows to consider the proposed method for assisting the diagnosis and encourages to continue the investigation in the sense of adding new features not only related to the shape

A new approach to segmentation based on fusing circumscribed contours, region growing and clustering

One of the major problems in machine vision is the segmentation of images of natural scenes. This paper presents a new proposal for the image segmentation problem which has been based on the integration of edge and region information. The main contours of the scene are detected and used to guide the posterior region growing process. The algorithm places a number of seeds at both sides of a contour allowing stating a set of concurrent growing processes. A previous analysis of the seeds permits to adjust the homogeneity criterion to the regions's characteristics. A new homogeneity criterion based on clustering analysis and convex hull construction is proposed

Unsupervised active regions for multiresolution image segmentation

An unsupervised approach to image segmentation which fuses region and boundary information is presented. The proposed approach takes advantage of the combined use of 3 different strategies: the guidance of seed placement, the control of decision criterion, and the boundary refinement. The new algorithm uses the boundary information to initialize a set of active regions which compete for the pixels in order to segment the whole image. The method is implemented on a multiresolution representation which ensures noise robustness as well as computation efficiency. The accuracy of the segmentation results has been proven through an objective comparative evaluation of the method