Prior model evaluation from Null Space Compensation perspective with application to surface reconstruction from single images

Prior model is widely applied in the area of computer vision and computer graphics. However, there is still a lack of a general theoretical scheme for evaluating the performance of the priors and a guidance for choosing suitable models. In this paper, a general scheme is proposed for linear singular problems based on the idea of Null Space Compensation. It is proved that for a linear prior model the principal directions obtained from the singular value decomposition of the model shall not be parallel to those of the system matrix determined by the problem. It is also suggested that for a nonlinear prior, higher correlation between the null space components of the estimate data based on the given prior and those of the ground truth or controlled data indicate the better suitability of the prior. The proposed evaluation scheme is demonstrated through an application to a linearized shape from shading problem, where surface shall be reconstructed from single 2D images. Both linear model and nonlinear constraints are evaluated with experiments on both synthetic images and real images. The results validate the proposed evaluation scheme and its capability for guiding in choosing a good prior model structure.     

An extension of Geman and Reynolds' approach to constrainedrestoration and the recovery of discontinuities

Geman and Reynolds (ibid., vol.14, 1992) present an approach to linear image restoration which provides for recovery of horizontal and vertical gray-level discontinuities from blurred and noisy observations. We extend their model and parameter selection method to include diagonal discontinuities. A hazard of this modeling approach is identified and addressed. We also comment on the truncated Gibbs sampler suggested in the paper     

A parallel approach to the picture restoration algorithm of Geman and Geman on an SIMD machine

This paper considers how the image restoration technique of Geman and Geman, which involves searching for the maximum a posteriori distribution of an image modelled as bounded Markov random fields using simulated annealing, can be approximated on a parallel SIMD processor array, the ICL Distributed Array Processor (DAP). For the version implemented, the potential speed-up over an equivalent serial processor is equal to half the number of processors in the array, or 2048 for the 64×64 DAP. The time taken by the DAP for one updating cycle is about 30 ms, and the typical complete picture restoration consisting of 1000 annealing cycles takes around 30 s. A method of increasing the efficiency of the present algorithm is suggested and the possibility of making the algorithm work with several frames of data collected over time is discussed.     

An external field prior for the hidden Potts model with application to cone-beam computed tomography

In images with low contrast-to-noise ratio (CNR), the information gain from the observed pixel values can be insufficient to distinguish foreground objects. A Bayesian approach to this problem is to incorporate prior information about the objects into a statistical model. A method for representing spatial prior information as an external field in a hidden Potts model is introduced. This prior distribution over the latent pixel labels is a mixture of Gaussian fields, centred on the positions of the objects at a previous point in time. It is particularly applicable in longitudinal imaging studies, where the manual segmentation of one image can be used as a prior for automatic segmentation of subsequent images. The method is demonstrated by application to cone-beam computed tomography (CT), an imaging modality that exhibits distortions in pixel values due to X-ray scatter. The external field prior results in a substantial improvement in segmentation accuracy, reducing the mean pixel misclassification rate for an electron density phantom from 87% to 6%. The method is also applied to radiotherapy patient data, demonstrating how to derive the external field prior in a clinical context.     

Ultrasound image restoration based on a learned dictionary and a higher-order MRF

The restoration of images degraded by blur and multiplicative noise is a critical preprocessing step in medical ultrasound images which exhibit clinical diagnostic features of interest. This paper proposes a novel non-smooth non-convex variational model for ultrasound images denoising and deblurring motivated by the successes of sparse representation of images and FoE based approaches. Dictionaries are well adapted to textures and extended to arbitrary image sizes by defining a global image prior, while FoE image prior explicitly characterizes the statistics properties of natural image. Following these ideas, the new model is composed of the data-fidelity term, the sparse and redundant representations via learned dictionaries, and the FoE image prior model. The iPiano algorithm can efficiently deal with this optimization problem. The new proposed model is applied to several simulated images and real ultrasound images. The experimental results of denoising and deblurring show that proposed method gives a better visual effect by efficiently removing noise and preserving details well compared with two state-of-the-art methods.     

基于单幅图像景深和大气散射模型的去雾方法

为恢复雾天图像对比度和颜色,更好地提取图像中的信息,根据海上开阔海域的特点,利用3维到2维透视投影模型,推导了海上图像任意像素点景深的计算公式,并结合暗原色先验知识,有效解决基准景深点的选取和天空亮度的选取问题,最后基于相对景深模型和大气散射模型,对单幅雾天图像进行清晰化处理。通过大量雾天降质图像的实验验证,该算法的去雾效果优于基于暗原色先验统计方法的效果。     

A Coupled Minimization Problem for Medical Image Segmentation with Priors

We present a coupled minimization problem for image segmentation using prior shape and intensity profile. One part of the model minimizes a shape related energy and the energy of geometric active contour with a parameter that balances the influence from these two. The minimizer corresponding to a fixed parameter in this minimization gives a segmentation and an alignment between the segmentation and prior shape. The second part of this model optimizes the selection of the parameter by maximizing the mutual information of image geometry between the prior and the aligned novel image over all the alignments corresponding to different parameters in the first part. By this coupling the segmentation arrives at higher image gradient, forms a shape similar to the prior, and captures the prior intensity profile. We also propose using mutual information of image geometry to generate intensity model from a set of training images. Experimental results on cardiac ultrasound images are presented. These results indicate that the proposed model provides close agreement with expert traced borders, and the parameter determined in this model for one image can be used for images with similar properties.     

一种基于暗通道优先和双边滤波的遥感图像 增强方法

提出了一种基于暗通道原理和双边滤波的遥感图像增强算法。由于暗通道模型的softmatting过程计算复杂性高,本文使用双边滤波代替softmatting以用于透射图的优化,提高了计算效率。针对将暗通道原理应用于遥感图像增强时所产生的色彩失真现象,提出了透射图的改进算法,提高景深图像的取值,同时约束其最大值不大于1。实验结果表明,本文的算法能够有效地增加图像对比度,使图像更符合视觉特性,适用于遥感图像的可视化增强。     

基于多节点拓扑重叠测度高阶MRF模型的图像分割

针对低阶马尔科夫随机场(Markov random field, MRF)模型难以有效表达自然图像中复杂的先验知识而造成误分割问题, 提出一种基于多节点拓扑重叠测度高阶MRF模型(Higher-order MRF model with multi-node topological overlap measure, MTOM-HMRF)的图像分割方法. 首先, 为描述图像局部区域内多像素蕴含的复杂空间拓扑结构信息, 利用多节点拓扑重叠测度建立图像局部区域的高阶先验模型; 其次, 利用较大的局部区域包含更多的标签节点信息能力, 基于Pairwise MRF模型建立基于局部区域的部分二阶Potts先验模型, 提高分割模型的抗噪能力; 再次, 为有效描述观察图像场与其标签场的似然特征分布, 研究利用局部区域内邻接像素的Hamming距离引入图像局部空间相关性, 建立局部空间一致性约束的高斯混合分布; 最后, 基于MRF框架建立用于图像分割的多节点拓扑重叠测度高阶MRF模型, 采用Gibbs采样算法对提出模型进行优化. 实验结果表明, 提出模型不仅能有效抵抗图像强噪声和复杂的纹理突变干扰, 鲁棒性更好, 而且具有更准确的图像分割结果.     

Random walks with statistical shape prior for cochlea and inner ear segmentation in micro-CT images

A cochlear implant is an electronic device which can restore sound to completely or partially deaf patients. For surgical planning, a patient-specific model of the inner ear must be built using high-resolution images accurately segmented. We propose a new framework for segmentation of micro-CT cochlear images using random walks, where a region term estimated by a Gaussian mixture model is combined with a shape prior initially obtained by a statistical shape model (SSM). The region term can then take advantage of the high contrast between the background and foreground, while the shape prior guides the segmentation to the exterior of the cochlea and to less contrasted regions inside the cochlea. The prior is obtained via a non-rigid registration regularized by a statistical shape model. The SSM constrains the inner parts of the cochlea and ensures valid output shapes of the inner ear.     

用于图像分割的局部区域一致性流形约束MRF模型

针对区域马尔可夫随机场(MRF)模型难以有效描述图像复杂先验知识的问题,提出一种基于局部区域一致性流形约束MRF(LRCMC-MRF)模型.首先,所提模型利用高维数据的低维流形分布表征图像局部区域的复杂几何结构先验,建立图像局部区域的流形先验约束;其次,基于Pairwise MRF模型,建立一种包含更多图像局部信息的局部空间自适应MRF模型;最后,基于贝叶斯理论,将复杂局部区域几何结构先验和局部空间自适应统计特征融合,利用Gibbs采样算法对所提出模型进行优化.实验结果表明,与基于常规区域的MRF模型相比,所提出的分割算法具有较好的分割效果.     

一种保边缘影像超分辨率重建方法

提出了一种基于方向性平滑测度的保边缘加权马尔可夫先验模型,并将其应用到基于最大后验估计的影像超分辨率重建中.该模型对邻域内不同方向的平滑测度使用不同的权值,以此减小对影像高频成分的惩罚约束,进而保护影像的边缘.利用不同影像对本文方法进行了验证,并用MSE影像评价方法对重建影像进行了定量评价.实验结果表明,与传统马尔可夫先验模型相比,加权马尔可夫先验模型能有效保护影像的边缘,取得更好的重建结果.     

基于水平集的牙齿CT图像分割技术

牙齿的计算机断层扫描(CT)图像中存在边界模糊、相邻牙齿粘连等情况,且拓扑结构较为复杂,要实现准确的牙齿分割非常困难。对传统的牙齿CT图像分割方法,特别是近年来用于牙齿分割的水平集方法进行介绍,对其水平集函数中各能量项进行研究,并通过对比实验体现水平集方法的优越性。基于水平集的牙齿CT图像分割方法中水平集函数的能量项主要包括:竞争能量项、梯度能量项、形状约束能量项、全局先验灰度能量项、局部灰度能量项。实验结果表明基于混合模型的水平集方法分割效果最佳,切牙与磨牙分割准确率分别为88.92%和92.34%,相比自适应阈值和传统水平集方法,分割准确率总体提升10%以上。在综合利用图像信息和先验知识的基础上,通过对水平集函数中能量项进行优化和创新,有望进一步提高分割的准确率。     

基于HMRF先验模型的超分辨率重建

针对基于最大后验概率(MAP)的超分辨率重建算法在重建图像过程中存在的问题,提出一种基于Huber-马尔可夫随机场(HMRF)先验模型的超分辨率重建方法,采用HMRF作为图像先验模型,对图像进行分段超分辨率重建。仿真实验结果表明,与传统的MAP算法相比,该方法能更好地保存重建图像的边缘细节,有效提高重建图像的质量。     

基于相对透射率估计的快速图像去雾算法

针对暗通道先验算法中恢复效果偏暗以及运算时间过久的问题,提出一种基于相对透射率估计的单幅图像快速去雾算法。该算法在分析雾霾条件下场景深度与最小值图像关系的基础上,依据景深相对量初步估计透射率,利用改进的均值滤波器作精确化调整,最后根据大气散射模型复原清晰图像,并通过亮度增强改善其视觉效果。该算法对透射率的估计简单、有效,复原图像清晰、自然,并且具有较高的细节可见度和层次感。实验结果表明,该算法在去雾效果和处理速度方面均有很大改善,有利于实现实时性应用。     

基于条件先验人体模型的人体姿态估计

人体姿态估计算法中的人体模型是对人体部位或关节间外观和空间关联情况的数学描述。虽然当前已经有部分人体模型在建立时考虑到了部位或关节的空间定位会满足一定的先验分布，但却都将基于同样先验分布建立的人体模型用于不同待处理图片进行人体姿态估计，并没有考虑到不同图片中的实际定位对先验分布服从程度的不同。为此，提出了一种基于条件先验的人体模型，在人体模型中添加自适应调节参数，参数值根据待处理图片中关节可能定位与外观模型相似度的大小来确定，从而达到根据待处理图片自适应调节先验分布在计算关节定位概率时所起作用大小的目的。将基于条件先验的人体模型用于人体姿态估计，仿真实验表明，与现有基于先验的人体模型相比，所提人体模型用于人体姿态估计时获得了更高的估计准确度。     

基于主成分迭代支集检测的多对比度 磁共振快速成像

很多磁共振成像应用(如 T1、T2 参数成像)需要连续采集一系列不同对比度的图像。丰富的对比度机制反映了 人体组织的内在特性,为临床提供了有效的定量诊断手段。然而,由于扫描时间过长,这种方法在临床上的应用受到一 定的限制。近几年兴起的压缩感知理论在磁共振快速成像方面显示了巨大的潜能。其中,学者们提出一种基于主成分分 析的快速磁共振成像方法。该方法从已知的解析物理模型和参数范围中训练主成分,并通过截断的方式利用图像序列的 时域稀疏性。但是,当这种截断先验信息不准确时,上述方法可能会产生模型误差。 本文通过采用迭代支集检测的方法 实现主成分系数支集的适应性估计。文章最后通过两组人体膝盖数据的重建实验,验证了该方法的有效性。     

Unsupervised multi-class segmentation of SAR images using fuzzy triplet Markov fields model

Triplet Markov fields (TMF) model proposed recently is suitable for nonstationary image segmentation. For synthetic aperture radar (SAR) image segmentation, TMF model can adopt diverse statistical models for SAR data related to diverse radar backscattering sources. However, TMF model does not take into account the inherent imprecision associated with SAR images. In this paper, we propose a statistical fuzzy TMF (FTMF) model, which is a fuzzy clustering type treatment of TMF model, for unsupervised multi-class segmentation of SAR images. This paper contributes to SAR image segmentation in four aspects: (1) Nonstationarity of the statistical distribution of SAR intensity/amplitude data is taken into account to improve the spatial modeling capability of fuzzy TMF model. (2) Mean field theory is generalized to deal with planar variables to derive prior probability in fuzzy TMF model, which resolves the problem in Gibbs sampler in terms of computation cost. (3) A fuzzy objective function with regularization by Kullback–Leibler information of fuzzy TMF model is constructed for SAR image segmentation. The introduction of fuzziness for the belongingness of SAR image pixel makes fuzzy TMF model be able to retain more information from SAR image. (4) Fuzzy iterative conditional estimation (ICE) method, as an extension of the general ICE method is proposed to perform the model parameters estimation. The effectiveness of the proposed algorithm is demonstrated by application to simulated data and real SAR images.     

Graph cut segmentation with a statistical shape model in cardiac MRI

Segmenting the right ventricle (RV) in magnetic resonance (MR) images is required for cardiac function assessment. The segmentation of the RV is a difficult task due to low contrast with surrounding tissues and high shape variability. To overcome these problems, we introduce a segmentation method based on a statistical shape model obtained with a principal component analysis (PCA) on a set of representative shapes of the RV. Shapes are not represented by a set of points, but by distance maps to their contour, relaxing the need for a costly landmark detection and matching process. A shape model is thus obtained by computing a PCA on the shape variations. This prior is registered onto the image via a very simple user interaction and then incorporated into the well-known graph cut framework in order to guide the segmentation. Our semi-automatic segmentation method has been applied on 248 MR images of a publicly available dataset (from MICCAI’12 Right Ventricle Segmentation Challenge). We show that encouraging results can be obtained for this challenging application.     

Circulant preconditioning technique for barrier options pricing under fractional diffusion models

In recent years, considerable literature has proposed the more general class of exponential Lévy processes as the underlying model for prices of financial quantities, which thus better explain many important empirical facts of financial markets. Finite moment log stable, Carr–Geman–Madan–Yor and KoBoL models are chosen from those above-mentioned models as the dynamics of underlying equity prices in this paper. With such models pricing barrier options, one kind of financial derivatives is transformed to solve specific fractional partial differential equations (FPDEs). This study focuses on numerically solving these FPDEs via the fully implicit scheme, with the shifted Grünwald approximation. The circulant preconditioned generalized minimal residual method which converges very fast with theoretical proof is incorporated for solving resultant linear systems. Numerical examples are given to demonstrate the effectiveness of the proposed preconditioner and show the accuracy of our method compared with that done by the Fourier cosine expansion method as a benchmark.