Automatic construction of 3-D statistical deformation models of the brain using nonrigid registration

In this paper, we show how the concept of statistical deformation models (SDMs) can be used for the construction of average models of the anatomy and their variability. SDMs are built by performing a statistical analysis of the deformations required to map anatomical features in one subject into the corresponding features in another subject. The concept of SDMs is similar to statistical shape models (SSMs) which capture statistical information about shapes across a population, but offers several advantages over SSMs. First, SDMs can be constructed directly from images such as three-dimensional (3-D) magnetic resonance (MR) or computer tomography volumes without the need for segmentation which is usually a prerequisite for the construction of SSMs. Instead, a nonrigid registration algorithm based on free-form deformations and normalized mutual information is used to compute the deformations required to establish dense correspondences between the reference subject and the subjects in the population class under investigation. Second, SDMs allow the construction of an atlas of the average anatomy as well as its variability across a population of subjects. Finally, SDMs take the 3-D nature of the underlying anatomy into account by analysing dense 3-D deformation fields rather than only information about the surface shape of anatomical structures. We show results for the construction of anatomical models of the brain from the MR images of 25 different subjects. The correspondences obtained by the nonrigid registration are evaluated using anatomical landmark locations and show an average error of 1.40 mm at these anatomical landmark positions. We also demonstrate that SDMs can be constructed so as to minimize the bias toward the chosen reference subject.     

A model-based, semi-global segmentation approach for automatic 3-D point landmark localization in neuroimages

The existing differential approaches for localization of 3-D anatomic point landmarks in 3-D images are sensitive to noise and usually extract numerous spurious landmarks. The parametric model-based approaches are not practically usable for localization of landmarks that can not be modeled by simple parametric forms. Some dedicated methods using anatomic knowledge to identify particular landmarks are not general enough to cope with other landmarks. In this paper, we propose a model-based, semi-global segmentation approach to automatically localize 3-D point landmarks in neuroimages. To localize a landmark, the semi-global segmentation (meaning the segmentation of a part of the studied structure in a certain neighborhood of the landmark) is first achieved by an active surface model, and then the landmark is localized by analyzing the segmented part only. The joint use of global model-to-image registration, semi-global structure registration, active surface-based segmentation, and point-anchored surface registration makes our method robust to noise and shape variation. To evaluate the method, we apply it to the localization of ventricular landmarks including curvature extrema, centerline intersections, and terminal points. Experiments with 48 clinical and 18 simulated magnetic resonance (MR) volumetric images show that the proposed approach is able to localize these landmarks with an average accuracy of 1 mm (i.e., at the level of image resolution). We also illustrate the use of the proposed approach to cortical landmark identification and discuss its potential applications ranging from computer-aided radiology and surgery to atlas registration with scans.      

Automated 3-D PDM construction from segmented images using deformable models

In recent years, several methods have been proposed for constructing statistical shape models to aid image analysis tasks by providing a priori knowledge. Examples include principal component analysis of manually or semiautomatically placed corresponding landmarks on the learning shapes [point distribution models (PDMs)], which is time consuming and subjective. However, automatically establishing surface correspondences continues to be a difficult problem. This paper presents a novel method for the automated construction of three-dimensional PDM from segmented images. Corresponding surface landmarks are established by adapting a triangulated learning shape to segmented volumetric images of the remaining shapes. The adaptation is based on a novel deformable model technique. We illustrate our approach using computed tomography data of the vertebra and the femur. We demonstrate that our method accurately represents and predicts shapes.     

Estimation of mouse organ locations through registration of a statistical mouse atlas with micro-CT images

Micro-CT is widely used in preclinical studies of small animals. Due to the low soft-tissue contrast in typical studies, segmentation of soft tissue organs from noncontrast enhanced micro-CT images is a challenging problem. Here, we propose an atlas-based approach for estimating the major organs in mouse micro-CT images. A statistical atlas of major trunk organs was constructed based on 45 training subjects. The statistical shape model technique was used to include inter-subject anatomical variations. The shape correlations between different organs were described using a conditional Gaussian model. For registration, first the high-contrast organs in micro-CT images were registered by fitting the statistical shape model, while the low-contrast organs were subsequently estimated from the high-contrast organs using the conditional Gaussian model. The registration accuracy was validated based on 23 noncontrast-enhanced and 45 contrast-enhanced micro-CT images. Three different accuracy metrics (Dice coefficient, organ volume recovery coefficient, and surface distance) were used for evaluation. The Dice coefficients vary from 0.45 ± 0.18 for the spleen to 0.90 ± 0.02 for the lungs, the volume recovery coefficients vary from 0.96 ± 0.10 for the liver to 1.30 ± 0.75 for the spleen, the surface distances vary from 0.18 ± 0.01 mm for the lungs to 0.72 ± 0.42 mm for the spleen. The registration accuracy of the statistical atlas was compared with two publicly available single-subject mouse atlases, i.e., the MOBY phantom and the DIGIMOUSE atlas, and the results proved that the statistical atlas is more accurate than the single atlases. To evaluate the influence of the training subject size, different numbers of training subjects were used for atlas construction and registration. The results showed an improvement of the registration accuracy when more training subjects were used for the atlas construction. The statistical atlas-based registration was also compared with the thin-plate spline based deformable registration, commonly used in mouse atlas registration. The results revealed that the statistical atlas has the advantage of improving the estimation of low-contrast organs.     

Geodesic morphometry with applications to 3-D morpho-functional anatomy

The quantitative analysis of three-dimensional (3-D) shapes in terms of morphology and functionality is one of the most challenging problems in medical image analysis. This paper proposes a general methodology that aims at solving part of this problem. It introduces a nonparametric hierarchical partitioning approach that operates on any arbitrary 3-D shape described as a triangle mesh. It first extends the concept of basin districts to the case of curved spaces through a partitioning process on a valuation representing the main curvatures over a polyhedral support. A hierarchical construction of basin districts is obtained from a watershed transform. The speed of the front propagation on the polyhedral surface is controlled by the local characteristics of the surface geometry. As a prerequisite, a set of co-processing tools has been developed that operates directly on a triangulated domain. This includes classical signal processing tasks (e.g., re-sampling, filtering) on a polyhedral support performing a trade-off between accuracy and efficiency. The ability to provide an intrinsic shape partition from any triangular mesh is useful in a wide range of applications from accurate geometric modeling, and hierarchical shape dissection to robust mesh compression. Examples are presented in the paper to illustrate the principles and methodology.     

Parameter space warping: shape-based correspondence between morphologically different objects

This paper presents a novel and comprehensive method for the automated determination of correspondences between two morphologically different two-dimensional (2-D) or three-dimensional (3-D) objects. Correspondences are determined by warping parametric representations of the objects to be matched. The warp is guided by the minimization of a similarity criterion function that measures features related to structural correspondence, including Euclidian point-to-point distance and differences in normals and curvature. The method uses a continuous harmonic parameterization for both the object and the warp, which provides: 1) a high degree of computational efficiency; 2) robust extraction of differential features, not subject to discretization errors or noise amplification in differentiation; 3) direct formulation of constraints to avoid overlaps in the resulting correspondence set; and 4) a scale-space paradigm of object shape and warp. The new method does not search for individual landmarks, but operates with a complete, integrated representation of the object geometry. The method was tested on 2-D and 3-D objects with substantial shape differences. Results demonstrated substantial improvements of 2%-33% in correspondence accuracy and 15%-59% in correspondence quality compared with direct registration methods.     

Diffeomorphic sulcal shape analysis on the cortex

We present a diffeomorphic approach for constructing intrinsic shape atlases of sulci on the human cortex. Sulci are represented as square-root velocity functions of continuous open curves in R3, and their shapes are studied as functional representations of an infinite-dimensional sphere. This spherical manifold has some advantageous properties--it is equipped with a Riemannian L2 metric on the tangent space and facilitates computational analyses and correspondences between sulcal shapes. Sulcal shape mapping is achieved by computing geodesics in the quotient space of shapes modulo scales, translations, rigid rotations, and reparameterizations. The resulting sulcal shape atlas preserves important local geometry inherently present in the sample population. The sulcal shape atlas is integrated in a cortical registration framework and exhibits better geometric matching compared to the conventional euclidean method. We demonstrate experimental results for sulcal shape mapping, cortical surface registration, and sulcal classification for two different surface extraction protocols for separate subject populations.     

基于非均匀采样的多模型红外三维目标跟踪

针对红外三维目标跟踪过程中目标姿态变化导致跟踪器失效的问题,提出了一种基于非均匀采样的多模型方法.首先用若干个原型视图表征三维目标,将这些原型视图对应的原型形状作为目标的多模型形状表示,并建立了这些原型形状之间的转移概率矩阵.在粒子滤波框架下,以对数极坐标变换下的原型视图中目标的灰度分布特征作为参考目标模型.通过对形状转移概率采样,实现了样本形状的转移与传播.此方法提高了跟踪器对于姿态变化的鲁棒性,同时具有非均匀采样特性的对数极坐标变换可以抑制图像尺度、旋转造成的畸变,并起到压缩周边的计算量的作用.仿真结果表明,这种算法对三维目标有较好的跟踪效果.     

Morphological iterative closest point algorithm

This work presents a method for the registration of three-dimensional (3-D) shapes. The method is based on the iterative closest point (ICP) algorithm and improves it through the use of a 3-D volume containing the shapes to be registered. The Voronoi diagram of the "model" shape points is first constructed in the volume. Then this is used for the calculation of the closest point operator. This way a dramatic decrease of the computational cost is achieved.     

A comparison framework for breathing motion estimation methods from 4-D imaging

Motion estimation is an important issue in radiation therapy of moving organs. In particular, motion estimates from 4-D imaging can be used to compute the distribution of an absorbed dose during the therapeutic irradiation. We propose a strategy and criteria incorporating spatiotemporal information to evaluate the accuracy of model-based methods capturing breathing motion from 4-D CT images. This evaluation relies on the identification and tracking of landmarks on the 4-D CT images by medical experts. Three different experts selected more than 500 landmarks within 4-D CT images of lungs for three patients. Landmark tracking was performed at four instants of the expiration phase. Two metrics are proposed to evaluate the tracking performance of motion-estimation models. The first metric cumulates over the four instants the errors on landmark location. The second metric integrates the error over a time interval according to an a priori breathing model for the landmark spatiotemporal trajectory. This latter metric better takes into account the dynamics of the motion. A second aim of this paper is to estimate the impact of considering several phases of the respiratory cycle as compared to using only the extreme phases (end-inspiration and end-expiration). The accuracy of three motion estimation models (two image registration-based methods and a biomechanical method) is compared through the proposed metrics and statistical tools. This paper points out the interest of taking into account more frames for reliably tracking the respiratory motion.     

Assessment of the 3-d reconstruction and high-resolution geometrical modeling of the human skeletal trunk from 2-D radiographic images

This paper presents an in vivo validation of a method for the three-dimensional (3-D) high-resolution modeling of the human spine, rib cage, and pelvis for the study of spinal deformities. The method uses an adaptation of a standard close-range photogrammetry method called direct linear transformation to reconstruct the 3-D coordinates of anatomical landmarks from three radiographic images of the subject's trunk. It then deforms in 3-D 1-mm-resolution anatomical primitives (reference bones) obtained by serial computed tomography-scan reconstruction of a dry specimen. The free-form deformation is calculated using dual kriging equations. In vivo validation of this method on 40 scoliotic vertebrae gives an overall accuracy of 3.3 +/- 3.8 mm, making it an adequate tool for clinical studies and mechanical analysis purposes.     

Reconstruction of serially acquired slices using physics-based modeling

This paper presents an accurate, computationally efficient, fast, and fully automated algorithm for the alignment of two-dimensional (2-D) serially acquired sections forming a 3-D volume. The approach relies on the determination of interslice correspondences. The features used for correspondence are extracted by a 2-D physics-based deformable model parameterizing the object shape. Correspondence affinities and global constrains render the method efficient and reliable. The method accounts for one of the major shortcomings of 2-D slices alignment of a 3-D volume, namely variable and nonuniform thickness of the slices. Moreover, no particular alignment direction is privileged, avoiding global offsets, biases, and error propagation. The method was evaluated on real images and the experimental results demonstrated its accuracy, as reconstruction errors were smaller than I degree in rotation and smaller than 1 pixel in translation.     

A global energy function for the alignment of serially acquired slices

An accurate, computationally efficient, and fully automated algorithm for the alignment of two-dimensional (2-D) serially acquired sections forming a three-dimensional (3-D) volume is presented. The approach relies on the optimization of a global energy function, based on the object shape, measuring the similarity between a slice and its neighborhood in the 3-D volume. Slice similarity is computed using the distance transform measure in both directions. No particular direction is privileged in the method avoiding global offsets, biases in the estimation and error propagation. The method was evaluated on real images [medical, biological, and other computerized tomography (CT) scanned 3-D data] and the experimental results demonstrated its accuracy as reconstuction errors are less than one degree in rotation and less than one pixel in translation.     

Coupled nonparametric shape and moment-based intershape pose priors for multiple basal ganglia structure segmentation

This paper presents a new active contour-based, statistical method for simultaneous volumetric segmentation of multiple subcortical structures in the brain. In biological tissues, such as the human brain, neighboring structures exhibit co-dependencies which can aid in segmentation, if properly analyzed and modeled. Motivated by this observation, we formulate the segmentation problem as a maximum a posteriori estimation problem, in which we incorporate statistical prior models on the shapes and intershape (relative) poses of the structures of interest. This provides a principled mechanism to bring high level information about the shapes and the relationships of anatomical structures into the segmentation problem. For learning the prior densities we use a nonparametric multivariate kernel density estimation framework. We combine these priors with data in a variational framework and develop an active contour-based iterative segmentation algorithm. We test our method on the problem of volumetric segmentation of basal ganglia structures in magnetic resonance images. We present a set of 2-D and 3-D experiments as well as a quantitative performance analysis. In addition, we perform a comparison to several existent segmentation methods and demonstrate the improvements provided by our approach in terms of segmentation accuracy.     

Learning-based segmentation framework for tissue images containing gene expression data

Associating specific gene activity with functional locations in the brain results in a greater understanding of the role of the gene. To perform such an association for the more than 20 000 genes in the mammalian genome, reliable automated methods that characterize the distribution of gene expression in relation to a standard anatomical model are required. In this paper, we propose a new automatic method that results in the segmentation of gene expression images into distinct anatomical regions in which the expression can be quantified and compared with other images. Our contribution is a novel hybrid atlas that utilizes a statistical shape model based on a subdivision mesh, texture differentiation at region boundaries, and features of anatomical landmarks to delineate boundaries of anatomical regions in gene expression images. This atlas, which provides a common coordinate system for internal brain data, is being used to create a searchable database of gene expression patterns in the adult mouse brain. Our framework annotates the images about four times faster and has achieved a median spatial overlap of up to 0.92 compared with expert segmentation in 64 images tested. This tool is intended to help scientists interpret large-scale gene expression patterns more efficiently.     

较少标定点条件下的主动形状模型研究

主动形状模型(ASM)的核心部分包括两个子模型,全局形状模型和局部纹理模型,两者均由标定人脸的许多关键点经过统计方法构建而成.本文研究了在只有少量关键标定点情况下,如何有效的进行主动形状建模的问题.通过充分利用面部轮廓标定点的信息,提出了一种将面部轮廓质心动态变化和传统主动形状模型相结合的策略,解决了在少量标定点条件下主动形状建模所遇到的问题.实验表明,改进方法在定位人脸图像关键点时耗时更短,而且具有更广范围的搜索能力和性能良好的搜索精度.     

Neighbor-constrained segmentation with level set based 3-D deformable models

A novel method for the segmentation of multiple objects from three-dimensional (3-D) medical images using interobject constraints is presented. Our method is motivated by the observation that neighboring structures have consistent locations and shapes that provide configurations and context that aid in segmentation. We define a maximum a posteriori (MAP) estimation framework using the constraining information provided by neighboring objects to segment several objects simultaneously. We introduce a representation for the joint density function of the neighbor objects, and define joint probability distributions over the variations of the neighboring shape and position relationships of a set of training images. In order to estimate the MAP shapes of the objects, we formulate the model in terms of level set functions, and compute the associated Euler-Lagrange equations. The contours evolve both according to the neighbor prior information and the image gray level information. This method is useful in situations where there is limited interobject information as opposed to robust global atlases. In addition, we compare our level set representation of the object shape to the point distribution model. Results and validation from experiments on synthetic data and medical imagery in two-dimensional and 3-D are demonstrated.