A discrete graph Laplacian for signal processing

In this thesis we exploit diffusion processes on graphs to effect two fundamental problems of image processing: denoising and segmentation. We treat these two low-level vision problems on the pixel-wise level under a unified framework: a graph embedding. Using this framework opens us up to the possibilities of exploiting recently introduced algorithms from the semi-supervised machine learning literature. We contribute two novel edge-preserving smoothing algorithms to the literature. Furthermore we apply these edge-preserving smoothing algorithms to some computational photography tasks. Many recent computational photography tasks require the decomposition of an image into a smooth base layer containing large scale intensity variations and a residual layer capturing fine details. Edge-preserving smoothing is the main computational mechanism in producing these multi-scale image representations. We, in effect, introduce a new approach to edge-preserving multi-scale image decompositions. Where as prior approaches such as the Bilateral filter and weighted-least squares methods require multiple parameters to tune the response of the filters our method only requires one. This parameter can be interpreted as a scale parameter. We demonstrate the utility of our approach by applying the method to computational photography tasks that utilise multi-scale image decompositions. With minimal modification to these edge-preserving smoothing algorithms we show that we can extend them to produce interactive image segmentation. As a result the operations of segmentation and denoising are conducted under a unified framework. Moreover we discuss how our method is related to region based active contours. We benchmark our proposed interactive segmentation algorithms against those based upon energy-minimisation, specifically graph-cut methods. We demonstrate that we achieve competitive performance

Probabilistic Models for Joint Segmentation, Detection and Tracking

Migrace buněk a buněčných částic hraje důležitou roli ve fungování živých organismů. Systematický výzkum buněčné migrace byl umožněn v posledních dvaceti letech rychlým rozvojem neinvazivních zobrazovacích technik a digitálních snímačů. Moderní zobrazovací systémy dovolují studovat chování buněčných populací složených z mnoha ticíců buněk. Manuální analýza takového množství dat by byla velice zdlouhavá, protože některé experimenty vyžadují analyzovat tvar, rychlost a další charakteristiky jednotlivých buněk. Z tohoto důvodu je ve vědecké komunitě velká poptávka po automatických metodách.Migration of cells and subcellular particles plays a crucial role in many processes in living organisms. Despite its importance a systematic research of cell motility has only been possible in last two decades due to rapid development of non-invasive imaging techniques and digital cameras. Modern imaging systems allow to study large populations with thousands of cells. Manual analysis of the acquired data is infeasible, because in order to gain insight into underlying biochemical processes it is sometimes necessary to determine shape, velocity and other characteristics of individual cells. Thus there is a high demand for automatic methods

Analysis of Dynamic Magnetic Resonance Breast Images

Dynamic Magnetic Resonance Imaging is a non-invasive technique that provides an image sequence based on dynamic information for locating lesions and investigating their structures. In this thesis we develop new methodology for analysing dynamic Magnetic Resonance image sequences of the breast. This methodology comprises an image restoration step that reduces random distortions affecting the data and an image classification step that identifies normal, benign or malignant tumoral tissues. In the first part of this thesis we present a non-parametric and a parametric approach for image restoration and classification. Both methods are developed within the Bayesian framework. A prior distribution modelling both spatial homogeneity and temporal continuity between neighbouring image pixels is employed. Statistical inference is performed by means of a Metropolis-Hastings algorithm with a specially chosen proposal distribution that out-performs other algorithms of the same family. We also provide novel procedures for estimating the hyper-parameters of the prior models and the normalizing constant so making the Bayesian methodology automatic. In the second part of this thesis we present new methodology for image classification based on deformable templates of a prototype shape. Our approach uses higher level knowledge about the tumour structure than the spatio-temporal prior distribution of our Bayesian methodology. The prototype shape is deformed to identify the structure of the malignant tumoral tissue by minimizing a novel objective function over the parameters of a set of non-affine transformations. Since these transformations can destroy the connectivity of the shape, we develop a new filter that restores connectivity without smoothing the shape. The restoration and classification results obtained from a small sample of image sequences are very encouraging. In order to validate these results on a larger sample, in the last part of the thesis we present a user friendly software package that implements our methodology

Fast and robust hybrid framework for infant brain classification from structural MRI : a case study for early diagnosis of autism.

The ultimate goal of this work is to develop a computer-aided diagnosis (CAD) system for early autism diagnosis from infant structural magnetic resonance imaging (MRI). The vital step to achieve this goal is to get accurate segmentation of the different brain structures: whitematter, graymatter, and cerebrospinal fluid, which will be the main focus of this thesis. The proposed brain classification approach consists of two major steps. First, the brain is extracted based on the integration of a stochastic model that serves to learn the visual appearance of the brain texture, and a geometric model that preserves the brain geometry during the extraction process. Secondly, the brain tissues are segmented based on shape priors, built using a subset of co-aligned training images, that is adapted during the segmentation process using first- and second-order visual appearance features of infant MRIs. The accuracy of the presented segmentation approach has been tested on 300 infant subjects and evaluated blindly on 15 adult subjects. The experimental results have been evaluated by the MICCAI MR Brain Image Segmentation (MRBrainS13) challenge organizers using three metrics: Dice coefficient, 95-percentile Hausdorff distance, and absolute volume difference. The proposed method has been ranked the first in terms of performance and speed

Predictive modeling using sparse logistic regression with applications

In this thesis, sparse logistic regression models are applied in a set of real world machine learning applications. The studied cases include supervised image segmentation, cancer diagnosis, and MEG data classification. Image segmentation is applied both in component detection in inkjet printed electronics manufacturing and in cell detection from microscope images. The results indicate that a simple linear classification method such as logistic regression often outperforms more sophisticated methods. Further, it is shown that the interpretability of the linear model offers great advantage in many applications. Model validation and automatic feature selection by means of L1 regularized parameter estimation have a significant role in this thesis. It is shown that a combination of a careful model assessment scheme and automatic feature selection by means of logistic regression model and coefficient regularization create a powerful, yet simple and practical, tool chain for applications of supervised learning and classification

Recognizing deviations from normalcy for brain tumor segmentation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003.Includes bibliographical references (p. 180-189).A framework is proposed for the segmentation of brain tumors from MRI. Instead of training on pathology, the proposed method trains exclusively on healthy tissue. The algorithm attempts to recognize deviations from normalcy in order to compute a fitness map over the image associated with the presence of pathology. The resulting fitness map may then be used by conventional image segmentation techniques for honing in on boundary delineation. Such an approach is applicable to structures that are too irregular, in both shape and texture, to permit construction of comprehensive training sets. We develop the method of diagonalized nearest neighbor pattern recognition, and we use it to demonstrate that recognizing deviations from normalcy requires a rich understanding of context. Therefore, we propose a framework for a Contextual Dependency Network (CDN) that incorporates context at multiple levels: voxel intensities, neighborhood coherence, intra-structure properties, inter-structure relationships, and user input. Information flows bi-directionally between the layers via multi-level Markov random fields or iterated Bayesian classification. A simple instantiation of the framework has been implemented to perform preliminary experiments on synthetic and MRI data.by David Thomas Gering.Ph.D

An attention model and its application in man-made scene interpretation

The ultimate aim of research into computer vision is designing a system which interprets its surrounding environment in a similar way the human can do effortlessly. However, the state of technology is far from achieving such a goal. In this thesis different components of a computer vision system that are designed for the task of interpreting man-made scenes, in particular images of buildings, are described. The flow of information in the proposed system is bottom-up i.e., the image is first segmented into its meaningful components and subsequently the regions are labelled using a contextual classifier. Starting from simple observations concerning the human vision system and the gestalt laws of human perception, like the law of “good (simple) shape” and “perceptual grouping”, a blob detector is developed, that identifies components in a 2D image. These components are convex regions of interest, with interest being defined as significant gradient magnitude content. An eye tracking experiment is conducted, which shows that the regions identified by the blob detector, correlate significantly with the regions which drive the attention of viewers. Having identified these blobs, it is postulated that a blob represents an object, linguistically identified with its own semantic name. In other words, a blob may contain a window a door or a chimney in a building. These regions are used to identify and segment higher order structures in a building, like facade, window array and also environmental regions like sky and ground. Because of inconsistency in the unary features of buildings, a contextual learning algorithm is used to classify the segmented regions. A model which learns spatial and topological relationships between different objects from a set of hand-labelled data, is used. This model utilises this information in a MRF to achieve consistent labellings of new scenes