Stochastic Algorithm For Parameter Estimation For Dense Deformable Template Mixture Model

Estimating probabilistic deformable template models is a new approach in the fields of computer vision and probabilistic atlases in computational anatomy. A first coherent statistical framework modelling the variability as a hidden random variable has been given by Allassonni\`ere, Amit and Trouv\'e in [1] in simple and mixture of deformable template models. A consistent stochastic algorithm has been introduced in [2] to face the problem encountered in [1] for the convergence of the estimation algorithm for the one component model in the presence of noise. We propose here to go on in this direction of using some "SAEM-like" algorithm to approximate the MAP estimator in the general Bayesian setting of mixture of deformable template model. We also prove the convergence of this algorithm toward a critical point of the penalised likelihood of the observations and illustrate this with handwritten digit images

Learning Active Basis Models by EM-Type Algorithms

EM algorithm is a convenient tool for maximum likelihood model fitting when the data are incomplete or when there are latent variables or hidden states. In this review article we explain that EM algorithm is a natural computational scheme for learning image templates of object categories where the learning is not fully supervised. We represent an image template by an active basis model, which is a linear composition of a selected set of localized, elongated and oriented wavelet elements that are allowed to slightly perturb their locations and orientations to account for the deformations of object shapes. The model can be easily learned when the objects in the training images are of the same pose, and appear at the same location and scale. This is often called supervised learning. In the situation where the objects may appear at different unknown locations, orientations and scales in the training images, we have to incorporate the unknown locations, orientations and scales as latent variables into the image generation process, and learn the template by EM-type algorithms. The E-step imputes the unknown locations, orientations and scales based on the currently learned template. This step can be considered self-supervision, which involves using the current template to recognize the objects in the training images. The M-step then relearns the template based on the imputed locations, orientations and scales, and this is essentially the same as supervised learning. So the EM learning process iterates between recognition and supervised learning. We illustrate this scheme by several experiments.Comment: Published in at http://dx.doi.org/10.1214/09-STS281 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

MAP Estimation of Statistical Deformable Templates Via Nonlinear Mixed Effects Models : Deterministic and Stochastic Approaches

International audienceIn [1], a new coherent statistical framework for estimating statistical deformable templates relevant to computational anatomy (CA) has been proposed. This paper addresses the problem of population av- erage and estimation of the underlying geometrical variability as a MAP computation problem for which deterministic and stochastic approxima- tion schemes have been proposed. We illustrate some of the numerical issues with handwritten digit and 2D medical images and apply the es- timated models to classification through maximum likelihood

Segmentation and Fracture Detection in CT Images for Traumatic Pelvic Injuries

In recent decades, more types and quantities of medical data have been collected due to advanced technology. A large number of significant and critical information is contained in these medical data. High efficient and automated computational methods are urgently needed to process and analyze all available medical data in order to provide the physicians with recommendations and predictions on diagnostic decisions and treatment planning. Traumatic pelvic injury is a severe yet common injury in the United States, often caused by motor vehicle accidents or fall. Information contained in the pelvic Computed Tomography (CT) images is very important for assessing the severity and prognosis of traumatic pelvic injuries. Each pelvic CT scan includes a large number of slices. Meanwhile, each slice contains a large quantity of data that may not be thoroughly and accurately analyzed via simple visual inspection with the desired accuracy and speed. Hence, a computer-assisted pelvic trauma decision-making system is needed to assist physicians in making accurate diagnostic decisions and determining treatment planning in a short period of time. Pelvic bone segmentation is a vital step in analyzing pelvic CT images and assisting physicians with diagnostic decisions in traumatic pelvic injuries. In this study, a new hierarchical segmentation algorithm is proposed to automatically extract multiplelevel bone structures using a combination of anatomical knowledge and computational techniques. First, morphological operations, image enhancement, and edge detection are performed for preliminary bone segmentation. The proposed algorithm then uses a template-based best shape matching method that provides an entirely automated segmentation process. This is followed by the proposed Registered Active Shape Model (RASM) algorithm that extracts pelvic bone tissues using more robust training models than the Standard ASM algorithm. In addition, a novel hierarchical initialization process for RASM is proposed in order to address the shortcoming of the Standard ASM, i.e. high sensitivity to initialization. Two suitable measures are defined to evaluate the segmentation results: Mean Distance and Mis-segmented Area to quantify the segmentation accuracy. Successful segmentation results indicate effectiveness and robustness of the proposed algorithm. Comparison of segmentation performance is also conducted using both the proposed method and the Snake method. A cross-validation process is designed to demonstrate the effectiveness of the training models. 3D pelvic bone models are built after pelvic bone structures are segmented from consecutive 2D CT slices. Automatic and accurate detection of the fractures from segmented bones in traumatic pelvic injuries can help physicians detect the severity of injuries in patients. The extraction of fracture features (such as presence and location of fractures) as well as fracture displacement measurement, are vital for assisting physicians in making faster and more accurate decisions. In this project, after bone segmentation, fracture detection is performed using a hierarchical algorithm based on wavelet transformation, adaptive windowing, boundary tracing and masking. Also, a quantitative measure of fracture severity based on pelvic CT scans is defined and explored. The results are promising, demonstrating that the proposed method not only capable of automatically detecting both major and minor fractures, but also has potentials to be used for clinical applications