Statistics of populations of images and its embedded objects: driving applications in neuroimaging

journal articleWork in progress towards modeling shape statistics of multi-object complexes is presented. Constraints defined by the set of objects such as a compact representation of object shape relationships and correlation of shape changes might have advantages for automatic segmentation and group discrimination. We present a concept for statistical multi-object modeling and discuss the major challenges which are a reduction to a small set of descriptive features, calculation of mean and variability via curved statistics, the choice of aligning sets of multiple objects, and the problem of describing the statistics of object pose and object shape and their interrelationship. Shape modeling and analysis is demonstrated with an application to a longitudinal autism study, with shape modeling of sets of 10 subcortical structures in a population of 20 subjects

Ball-Scale Based Hierarchical Multi-Object Recognition in 3D Medical Images

This paper investigates, using prior shape models and the concept of ball scale (b-scale), ways of automatically recognizing objects in 3D images without performing elaborate searches or optimization. That is, the goal is to place the model in a single shot close to the right pose (position, orientation, and scale) in a given image so that the model boundaries fall in the close vicinity of object boundaries in the image. This is achieved via the following set of key ideas: (a) A semi-automatic way of constructing a multi-object shape model assembly. (b) A novel strategy of encoding, via b-scale, the pose relationship between objects in the training images and their intensity patterns captured in b-scale images. (c) A hierarchical mechanism of positioning the model, in a one-shot way, in a given image from a knowledge of the learnt pose relationship and the b-scale image of the given image to be segmented. The evaluation results on a set of 20 routine clinical abdominal female and male CT data sets indicate the following: (1) Incorporating a large number of objects improves the recognition accuracy dramatically. (2) The recognition algorithm can be thought as a hierarchical framework such that quick replacement of the model assembly is defined as coarse recognition and delineation itself is known as finest recognition. (3) Scale yields useful information about the relationship between the model assembly and any given image such that the recognition results in a placement of the model close to the actual pose without doing any elaborate searches or optimization. (4) Effective object recognition can make delineation most accurate.Comment: This paper was published and presented in SPIE Medical Imaging 201

Consistent estimation of shape parameters in statistical shape model by symmetric EM algorithm

In order to fit an unseen surface using statistical shape model (SSM), a correspondence between the unseen surface and the model needs to be established, before the shape parameters can be estimated based on this correspondence. The correspondence and parameter estimation problem can be modeled probabilistically by a Gaussian mixture model (GMM), and solved by expectation-maximization iterative closest points (EM-ICP) algorithm. In this paper, we propose to exploit the linearity of the principal component analysis (PCA) based SSM, and estimate the parameters for the unseen shape surface under the EM-ICP framework. The symmetric data terms are devised to enforce the mutual consistency between the model reconstruction and the shape surface. The a priori shape information encoded in the SSM is also included as regularization. The estimation method is applied to the shape modeling of the hippocampus using a hippocampal SSM

Knowledge-Based Deformable Surface Model with Application to Segmentation of Brain Structures in MRI

We have developed a knowledge-based deformable surface for segmentation of medical images. This work has been done in the context of segmentation of hippocampus from brain MRI, due to its challenge and clinical importance. The model has a polyhedral discrete structure and is initialized automatically by analyzing brain MRI sliced by slice, and finding few landmark features at each slice using an expert system. The expert system decides on the presence of the hippocampus and its general location in each slice. The landmarks found are connected together by a triangulation method, to generate a closed initial surface. The surface deforms under defined internal and external force terms thereafter, to generate an accurate and reproducible boundary for the hippocampus. The anterior and posterior (AP) limits of the hippocampus is estimated by automatic analysis of the location of brain stem, and some of the features extracted in the initialization process. These data are combined together with a priori knowledge using Bayes method to estimate a probability density function (pdf) for the length of the structure in sagittal direction. The hippocampus AP limits are found by optimizing this pdf. The model is tested on real clinical data and the results show very good model performance.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85930/1/Fessler166.pd

Enhanced cortical thickness measurements for rodent brains via Lagrangian-based RK4 streamline computation

The cortical thickness of the mammalian brain is an important morphological characteristic that can be used to investigate and observe the brain's developmental changes that might be caused by biologically toxic substances such as ethanol or cocaine. Although various cortical thickness analysis methods have been proposed that are applicable for human brain and have developed into well-validated open-source software packages, cortical thickness analysis methods for rodent brains have not yet become as robust and accurate as those designed for human brains. Based on a previously proposed cortical thickness measurement pipeline for rodent brain analysis,1 we present an enhanced cortical thickness pipeline in terms of accuracy and anatomical consistency. First, we propose a Lagrangian-based computational approach in the thickness measurement step in order to minimize local truncation error using the fourth-order Runge-Kutta method. Second, by constructing a line object for each streamline of the thickness measurement, we can visualize the way the thickness is measured and achieve sub-voxel accuracy by performing geometric post-processing. Last, with emphasis on the importance of an anatomically consistent partial differential equation (PDE) boundary map, we propose an automatic PDE boundary map generation algorithm that is specific to rodent brain anatomy, which does not require manual labeling. The results show that the proposed cortical thickness pipeline can produce statistically significant regions that are not observed in the previous cortical thickness analysis pipeline

Statistical shape analysis of Multi-Object complexes

journal articleAn important goal of statistical shape analysis is the discrimination between populations of objects, exploring group differences in morphology not explained by standard volumetric analysis. Certain applications additionally require analysis of objects in their embedding context by joint statistical analysis of sets of interrelated objects. In this paper, we present a framework for discriminant analysis of populations of 3-D multi-object sets. In view of the driving medical applications, a skeletal object parametrization of shape is chosen since it naturally encodes thickening, bending and twisting. In a multi-object setting, we not only consider a joint analysis of sets of shapes but also must take into account differences in pose. Statistics on features of medial descriptions and pose parameters, which include rotational frames and distances, uses a Riemannian symmetric space instead of the standard Euclidean metric. Our choice of discriminant method is the distance weighted discriminant (DWD) because of its generalization ability in high dimensional, low sample size settings. Joint analysis of 10 sub-cortical brain structures in a pediatric autism study demonstrates that multi-object analysis of shape results in a better group discrimination than pose, and that the combination of pose and shape performs better than shape alone. Finally, given a discriminating axis of shape and pose, we can visualize the differences between the populations

Skeletal Shape Correspondence Through Entropy

We present a novel approach for improving the shape statistics of medical image objects by generating correspondence of skeletal points. Each object's interior is modeled by an s-rep, i.e., by a sampled, folded, two-sided skeletal sheet with spoke vectors proceeding from the skeletal sheet to the boundary. The skeleton is divided into three parts: the up side, the down side, and the fold curve. The spokes on each part are treated separately and, using spoke interpolation, are shifted along that skeleton in each training sample so as to tighten the probability distribution on those spokes' geometric properties while sampling the object interior regularly. As with the surface/boundary-based correspondence method of Cates et al., entropy is used to measure both the probability distribution tightness and the sampling regularity, here of the spokes' geometric properties. Evaluation on synthetic and real world lateral ventricle and hippocampus data sets demonstrate improvement in the performance of statistics using the resulting probability distributions. This improvement is greater than that achieved by an entropy-based correspondence method on the boundary points