Multi-atlas pancreas segmentation: Atlas selection based on vessel structure

Automated organ segmentation from medical images is an indispensable component for clinical applications such as computer-aided diagnosis (CAD) and computer-assisted surgery (CAS). We utilize a multi-atlas segmentation scheme, which has recently been used in different approaches in the literature to achieve more accurate and robust segmentation of anatomical structures in computed tomography (CT) volume data. Among abdominal organs, the pancreas has large inter-patient variability in its position, size and shape. Moreover, the CT intensity of the pancreas closely resembles adjacent tissues, rendering its segmentation a challenging task. Due to this, conventional intensity-based atlas selection for pancreas segmentation often fails to select atlases that are similar in pancreas position and shape to those of the unlabeled target volume. In this paper, we propose a new atlas selection strategy based on vessel structure around the pancreatic tissue and demonstrate its application to a multi-atlas pancreas segmentation. Our method utilizes vessel structure around the pancreas to select atlases with high pancreatic resemblance to the unlabeled volume. Also, we investigate two types of applications of the vessel structure information to the atlas selection. Our segmentations were evaluated on 150 abdominal contrast-enhanced CT volumes. The experimental results showed that our approach can segment the pancreas with an average Jaccard index of 66.3% and an average Dice overlap coefficient of 78.5%.     

Efficient multi-atlas abdominal segmentation on clinically acquired CT with SIMPLE context learning

Abdominal segmentation on clinically acquired computed tomography (CT) has been a challenging problem given the inter-subject variance of human abdomens and complex 3-D relationships among organs. Multi-atlas segmentation (MAS) provides a potentially robust solution by leveraging label atlases via image registration and statistical fusion. We posit that the efficiency of atlas selection requires further exploration in the context of substantial registration errors. The selective and iterative method for performance level estimation (SIMPLE) method is a MAS technique integrating atlas selection and label fusion that has proven effective for prostate radiotherapy planning. Herein, we revisit atlas selection and fusion techniques for segmenting 12 abdominal structures using clinically acquired CT. Using a re-derived SIMPLE algorithm, we show that performance on multi-organ classification can be improved by accounting for exogenous information through Bayesian priors (so called context learning). These innovations are integrated with the joint label fusion (JLF) approach to reduce the impact of correlated errors among selected atlases for each organ, and a graph cut technique is used to regularize the combined segmentation. In a study of 100 subjects, the proposed method outperformed other comparable MAS approaches, including majority vote, SIMPLE, JLF, and the Wolz locally weighted vote technique. The proposed technique provides consistent improvement over state-of-the-art approaches (median improvement of 7.0% and 16.2% in DSC over JLF and Wolz, respectively) and moves toward efficient segmentation of large-scale clinically acquired CT data for biomarker screening, surgical navigation, and data mining.     

FocusNetv2: Imbalanced large and small organ segmentation with adversarial shape constraint for head and neck CT images

Radiotherapy is a treatment where radiation is used to eliminate cancer cells. The delineation of organs-at-risk (OARs) is a vital step in radiotherapy treatment planning to avoid damage to healthy organs. For nasopharyngeal cancer, more than 20 OARs are needed to be precisely segmented in advance. The challenge of this task lies in complex anatomical structure, low-contrast organ contours, and the extremely imbalanced size between large and small organs. Common segmentation methods that treat them equally would generally lead to inaccurate small-organ labeling. We propose a novel two-stage deep neural network, FocusNetv2, to solve this challenging problem by automatically locating, ROI-pooling, and segmenting small organs with specifically designed small-organ localization and segmentation sub-networks while maintaining the accuracy of large organ segmentation. In addition to our original FocusNet, we employ a novel adversarial shape constraint on small organs to ensure the consistency between estimated small-organ shapes and organ shape prior knowledge. Our proposed framework is extensively tested on both self-collected dataset of 1,164 CT scans and the MICCAI Head and Neck Auto Segmentation Challenge 2015 dataset, which shows superior performance compared with state-of-the-art head and neck OAR segmentation methods.     

Interactive segmentation of abdominal aortic aneurysms in CTA images

A model-based approach to interactive segmentation of abdominal aortic aneurysms from CTA data is presented. After manual delineation of the aneurysm sac in the first slice, the method automatically detects the contour in subsequent slices, using the result from the previous slice as a reference. If an obtained contour is not sufficiently accurate, the user can intervene and provide an additional manual reference contour. The method is inspired by the active shape model (ASM) segmentation scheme (), in which a statistical shape model, derived from corresponding landmark points in manually labeled training images, is fitted to the image in an iterative manner. In our method, a shape model of the contours in two adjacent image slices is progressively fitted to the entire volume. The contour obtained in one slice thus constrains the possible shapes in the next slice. The optimal fit is determined on the basis of multi-resolution gray level models constructed from gray value patches sampled around each landmark. We propose to use the similarity of adjacent image slices for this gray level model, and compare these to single-slice features that are more generally used with ASM. The performance of various image features is evaluated in leave-one-out experiments on 23 data sets. Features that use the similarity of adjacent image slices outperform measures based on single-slice features in all cases. The average number of slices in our datasets is 51, while on average eight manual initializations are required, which decreases operator segmentation time by a factor of 6.     

Skull stripping using graph cuts

Removal of non-brain tissues, particularly dura, is an important step in enabling accurate measurement of brain structures. Many popular methods rely on iterative surface deformation to fit the brain boundary and tend to leave residual dura. Similar to other approaches, the method proposed here uses intensity thresholding followed by removal of narrow connections to obtain a brain mask. However, instead of using morphological operations to remove narrow connections, a graph theoretic image segmentation technique was used to position cuts that isolate and remove dura. This approach performed well on both the standardized IBSR test data sets and empirically derived data. Compared to the Hybrid Watershed Algorithm (HWA; (Segonne et al., 2004)) the novel approach achieved an additional 10–30% of dura removal without incurring further brain tissue erosion. The proposed method is best used in conjunction with HWA as the errors produced by the two approaches often occur at different locations and cancel out when their masks are combined. Our experiments indicate that this combination can substantially decrease and often fully avoid cortical surface overestimation in subsequent segmentation.     

Bayesian logistic shape model inference: Application to cochlear image segmentation

Incorporating shape information is essential for the delineation of many organs and anatomical structures in medical images. While previous work has mainly focused on parametric spatial transformations applied to reference template shapes, in this paper, we address the Bayesian inference of parametric shape models for segmenting medical images with the objective of providing interpretable results. The proposed framework defines a likelihood appearance probability and a prior label probability based on a generic shape function through a logistic function. A reference length parameter defined in the sigmoid controls the trade-off between shape and appearance information. The inference of shape parameters is performed within an Expectation-Maximisation approach in which a Gauss-Newton optimization stage provides an approximation of the posterior probability of the shape parameters. This framework is applied to the segmentation of cochlear structures from clinical CT images constrained by a 10-parameter shape model. It is evaluated on three different datasets, one of which includes more than 200 patient images. The results show performances comparable to supervised methods and better than previously proposed unsupervised ones. It also enables an analysis of parameter distributions and the quantification of segmentation uncertainty, including the effect of the shape model.     

Low-rank and sparse decomposition based shape model and probabilistic atlas for automatic pathological organ segmentation

One major limiting factor that prevents the accurate delineation of human organs has been the presence of severe pathology and pathology affecting organ borders. Overcoming these limitations is exactly what we are concerned in this study. We propose an automatic method for accurate and robust pathological organ segmentation from CT images. The method is grounded in the active shape model (ASM) framework. It leverages techniques from low-rank and sparse decomposition (LRSD) theory to robustly recover a subspace from grossly corrupted data. We first present a population-specific LRSD-based shape prior model, called LRSD-SM, to handle non-Gaussian gross errors caused by weak and misleading appearance cues of large lesions, complex shape variations, and poor adaptation to the finer local details in a unified framework. For the shape model initialization, we introduce a method based on patient-specific LRSD-based probabilistic atlas (PA), called LRSD-PA, to deal with large errors in atlas-to-target registration and low likelihood of the target organ. Furthermore, to make our segmentation framework more efficient and robust against local minima, we develop a hierarchical ASM search strategy. Our method is tested on the SLIVER07 database for liver segmentation competition, and ranks 3rd in all the published state-of-the-art automatic methods. Our method is also evaluated on some pathological organs (pathological liver and right lung) from 95 clinical CT scans and its results are compared with the three closely related methods. The applicability of the proposed method to segmentation of the various pathological organs (including some highly severe cases) is demonstrated with good results on both quantitative and qualitative experimentation; our segmentation algorithm can delineate organ boundaries that reach a level of accuracy comparable with those of human raters.     

Prior-aware autoencoders for lung pathology segmentation

Segmentation of lung pathology in Computed Tomography (CT) images is of great importance for lung disease screening. However, the presence of different types of lung pathologies with a wide range of heterogeneities in size, shape, location, and texture, on one side, and their visual similarity with respect to surrounding tissues, on the other side, make it challenging to perform reliable automatic lesion segmentation. To leverage segmentation performance, we propose a deep learning framework comprising a Normal Appearance Autoencoder (NAA) model to learn the distribution of healthy lung regions and reconstruct pathology-free images from the corresponding pathological inputs by replacing the pathological regions with the characteristics of healthy tissues. Detected regions that represent prior information regarding the shape and location of pathologies are then integrated into a segmentation network to guide the attention of the model into more meaningful delineations. The proposed pipeline was tested on three types of lung pathologies, including pulmonary nodules, Non-Small Cell Lung Cancer (NSCLC), and Covid-19 lesion on five comprehensive datasets. The results show the superiority of the proposed prior model, which outperformed the baseline segmentation models in all the cases with significant margins. On average, adding the prior model improved the Dice coefficient for the segmentation of lung nodules by 0.038, NSCLCs by 0.101, and Covid-19 lesions by 0.041. We conclude that the proposed NAA model produces reliable prior knowledge regarding the lung pathologies, and integrating such knowledge into a prior segmentation network leads to more accurate delineations.     

LMISA: A lightweight multi-modality image segmentation network via domain adaptation using gradient magnitude and shape constraint

In medical image segmentation, supervised machine learning models trained using one image modality (e.g. computed tomography (CT)) are often prone to failure when applied to another image modality (e.g. magnetic resonance imaging (MRI)) even for the same organ. This is due to the significant intensity variations of different image modalities. In this paper, we propose a novel end-to-end deep neural network to achieve multi-modality image segmentation, where image labels of only one modality (source domain) are available for model training and the image labels for the other modality (target domain) are not available. In our method, a multi-resolution locally normalized gradient magnitude approach is firstly applied to images of both domains for minimizing the intensity discrepancy. Subsequently, a dual task encoder-decoder network including image segmentation and reconstruction is utilized to effectively adapt a segmentation network to the unlabeled target domain. Additionally, a shape constraint is imposed by leveraging adversarial learning. Finally, images from the target domain are segmented, as the network learns a consistent latent feature representation with shape awareness from both domains. We implement both 2D and 3D versions of our method, in which we evaluate CT and MRI images for kidney and cardiac tissue segmentation. For kidney, a public CT dataset (KiTS19, MICCAI 2019) and a local MRI dataset were utilized. The cardiac dataset was from the Multi-Modality Whole Heart Segmentation (MMWHS) challenge 2017. Experimental results reveal that our proposed method achieves significantly higher performance with a much lower model complexity in comparison with other state-of-the-art methods. More importantly, our method is also capable of producing superior segmentation results than other methods for images of an unseen target domain without model retraining. The code is available at GitHub (https://github.com/MinaJf/LMISA) to encourage method comparison and further research.     

Boundary-aware context neural network for medical image segmentation

Medical image segmentation can provide a reliable basis for further clinical analysis and disease diagnosis. With the development of convolutional neural networks (CNNs), medical image segmentation performance has advanced significantly. However, most existing CNN-based methods often produce unsatisfactory segmentation masks without accurate object boundaries. This problem is caused by the limited context information and inadequate discriminative feature maps after consecutive pooling and convolution operations. Additionally, medical images are characterized by high intra-class variation, inter-class indistinction and noise, extracting powerful context and aggregating discriminative features for fine-grained segmentation remain challenging. In this study, we formulate a boundary-aware context neural network (BA-Net) for 2D medical image segmentation to capture richer context and preserve fine spatial information, which incorporates encoder-decoder architecture. In each stage of the encoder sub-network, a proposed pyramid edge extraction module first obtains multi-granularity edge information. Then a newly designed mini multi-task learning module for jointly learning segments the object masks and detects lesion boundaries, in which a new interactive attention layer is introduced to bridge the two tasks. In this way, information complementarity between different tasks is achieved, which effectively leverages the boundary information to offer strong cues for better segmentation prediction. Finally, a cross feature fusion module acts to selectively aggregate multi-level features from the entire encoder sub-network. By cascading these three modules, richer context and fine-grain features of each stage are encoded and then delivered to the decoder. The results of extensive experiments on five datasets show that the proposed BA-Net outperforms state-of-the-art techniques.     

Inferior vena cava segmentation with parameter propagation and graph cut

Purpose

The inferior vena cava (IVC) is one of the vital veins inside the human body. Accurate segmentation of the IVC from contrast-enhanced CT images is of great importance. This extraction not only helps the physician understand its quantitative features such as blood flow and volume, but also it is helpful during the hepatic preoperative planning. However, manual delineation of the IVC is time-consuming and poorly reproducible.

Methods

In this paper, we propose a novel method to segment the IVC with minimal user interaction. The proposed method performs the segmentation block by block between user-specified beginning and end masks. At each stage, the proposed method builds the segmentation model based on information from image regional appearances, image boundaries, and a prior shape. The intensity range and the prior shape for this segmentation model are estimated based on the segmentation result from the last block, or from user- specified beginning mask if at first stage. Then, the proposed method minimizes the energy function and generates the segmentation result for current block using graph cut. Finally, a backward tracking step from the end of the IVC is performed if necessary.

Results

We have tested our method on 20 clinical datasets and compared our method to three other vessel extraction approaches. The evaluation was performed using three quantitative metrics: the Dice coefficient (Dice), the mean symmetric distance (MSD), and the Hausdorff distance (MaxD). The proposed method has achieved a Dice of \(89.56 \pm 3.71\%\), an MSD of \(0.80 \pm 0.33\) mm, and a MaxD of \(11.48 \pm 3.04\) mm, respectively, in our experiments.

Conclusion

The proposed approach can achieve a sound performance with a relatively low computational cost and a minimal user interaction. The proposed algorithm has high potential to be applied for the clinical applications in the future.

     

Incorporating the hybrid deformable model for improving the performance of abdominal CT segmentation via multi-scale feature fusion network

Automated multi-organ abdominal Computed Tomography (CT) image segmentation can assist the treatment planning, diagnosis, and improve many clinical workflows’ efficiency. The 3-D Convolutional Neural Network (CNN) recently attained state-of-the-art accuracy, which typically relies on supervised training with many manual annotated data. Many methods used the data augmentation strategy with a rigid or affine spatial transformation to alleviate the over-fitting problem and improve the network’s robustness. However, the rigid or affine spatial transformation fails to capture the complex voxel-based deformation in the abdomen, filled with many soft organs. We developed a novel Hybrid Deformable Model (HDM), which consists of the inter-and intra-patient deformation for more effective data augmentation to tackle this issue. The inter-patient deformations were extracted from the learning-based deformable registration between different patients, while the intra-patient deformations were formed using the random 3-D Thin-Plate-Spline (TPS) transformation. Incorporating the HDM enabled the network to capture many of the subtle deformations of abdominal organs. To find a better solution and achieve faster convergence for network training, we fused the pre-trained multi-scale features into the a 3-D attention U-Net. We directly compared the segmentation accuracy of the proposed method to the previous techniques on several centers’ datasets via cross-validation. The proposed method achieves the average Dice Similarity Coefficient (DSC) 0.852, which outperformed the other state-of-the-art on multi-organ abdominal CT segmentation results.     

Holistic multitask regression network for multiapplication shape regression segmentation

A holistic multitask regression approach was implemented to tackle the limitations of clinical image analysis. Standard practice requires identifying multiple anatomic structures in multiple planes from multiple anatomic regions using multiple modalities. The proposed novel holistic multitask regression network (HMR-Net) formulates organ segmentation as a multitask learning problem. Multitask learning leverages the strength of joint task problem solving from capturing task correlations. HMR-Net performs multitask regression by estimating an organ’s class, regional location, and precise contour coordinates. The estimation of each coordinate point also corresponds to another regression task. HMR-Net leverages hierarchical multiscale and fused organ features to handle nonlinear relationships between image appearance and distinct organ properties. Simultaneously, holistic shape information is captured by encoding coordinate correlations. The multitask pipeline enables the capturing of holistic organ information (e.g. class, location, shape) to perform shape regression for medical image segmentation. HMR-Net was validated on eight representative datasets obtained from a total of 222 subjects. A mean average precision and dice score reaching up to 0.81 and 0.93, respectively, was achieved on the representative multiapplication database. The generalized model demonstrates comparable or superior performance compared to state-of-the-art algorithms. The high-performance accuracy demonstrates our model as an effective general framework to perform organ shape regression in multiple applications. This method was proven to provide high-contrast sensitivity to delineate even the smallest and oddly shaped organs. HMR-Net’s flexible framework holds great potential in providing a fully automatic preliminary analysis for multiple types of medical images.     

Bilateral adaptive graph convolutional network on CT based Covid-19 diagnosis with uncertainty-aware consensus-assisted multiple instance learning

Coronavirus disease (COVID-19) has caused a worldwide pandemic, putting millions of people’s health and lives in jeopardy. Detecting infected patients early on chest computed tomography (CT) is critical in combating COVID-19. Harnessing uncertainty-aware consensus-assisted multiple instance learning (UC-MIL), we propose to diagnose COVID-19 using a new bilateral adaptive graph-based (BA-GCN) model that can use both 2D and 3D discriminative information in 3D CT volumes with arbitrary number of slices. Given the importance of lung segmentation for this task, we have created the largest manual annotation dataset so far with 7,768 slices from COVID-19 patients, and have used it to train a 2D segmentation model to segment the lungs from individual slices and mask the lungs as the regions of interest for the subsequent analyses. We then used the UC-MIL model to estimate the uncertainty of each prediction and the consensus between multiple predictions on each CT slice to automatically select a fixed number of CT slices with reliable predictions for the subsequent model reasoning. Finally, we adaptively constructed a BA-GCN with vertices from different granularity levels (2D and 3D) to aggregate multi-level features for the final diagnosis with the benefits of the graph convolution network’s superiority to tackle cross-granularity relationships. Experimental results on three largest COVID-19 CT datasets demonstrated that our model can produce reliable and accurate COVID-19 predictions using CT volumes with any number of slices, which outperforms existing approaches in terms of learning and generalisation ability. To promote reproducible research, we have made the datasets, including the manual annotations and cleaned CT dataset, as well as the implementation code, available at https://doi.org/10.5281/zenodo.6361963.     

Random walks with shape prior for cochlea segmentation in ex vivo $$\mu \hbox {CT}$$

Purpose

Cochlear implantation is a safe and effective surgical procedure to restore hearing in deaf patients. However, the level of restoration achieved may vary due to differences in anatomy, implant type and surgical access. In order to reduce the variability of the surgical outcomes, we previously proposed the use of a high-resolution model built from \(\mu \hbox {CT}\) images and then adapted to patient-specific clinical CT scans. As the accuracy of the model is dependent on the precision of the original segmentation, it is extremely important to have accurate \(\mu \hbox {CT}\) segmentation algorithms.

Methods

We propose a new framework for cochlea segmentation in ex vivo \(\mu \hbox {CT}\) images using random walks where a distance-based shape prior is combined with a region term estimated by a Gaussian mixture model. The prior is also weighted by a confidence map to adjust its influence according to the strength of the image contour. Random walks is performed iteratively, and the prior mask is aligned in every iteration.

Results

We tested the proposed approach in ten \(\mu \hbox {CT}\) data sets and compared it with other random walks-based segmentation techniques such as guided random walks (Eslami et al. in Med Image Anal 17(2):236–253, 2013) and constrained random walks (Li et al. in Advances in image and video technology. Springer, Berlin, pp 215–226, 2012). Our approach demonstrated higher accuracy results due to the probability density model constituted by the region term and shape prior information weighed by a confidence map.

Conclusion

The weighted combination of the distance-based shape prior with a region term into random walks provides accurate segmentations of the cochlea. The experiments suggest that the proposed approach is robust for cochlea segmentation.

     

Spine detection in CT and MR using iterated marginal space learning

Examinations of the spinal column with both, Magnetic Resonance (MR) imaging and Computed Tomography (CT), often require a precise three-dimensional positioning, angulation and labeling of the spinal disks and the vertebrae. A fully automatic and robust approach is a prerequisite for an automated scan alignment as well as for the segmentation and analysis of spinal disks and vertebral bodies in Computer Aided Diagnosis (CAD) applications. In this article, we present a novel method that combines Marginal Space Learning (MSL), a recently introduced concept for efficient discriminative object detection, with a generative anatomical network that incorporates relative pose information for the detection of multiple objects. It is used to simultaneously detect and label the spinal disks. While a novel iterative version of MSL is used to quickly generate candidate detections comprising position, orientation, and scale of the disks with high sensitivity, the anatomical network selects the most likely candidates using a learned prior on the individual nine dimensional transformation spaces. Finally, we propose an optional case-adaptive segmentation approach that allows to segment the spinal disks and vertebrae in MR and CT respectively. Since the proposed approaches are learning-based, they can be trained for MR or CT alike. Experimental results based on 42 MR and 30 CT volumes show that our system not only achieves superior accuracy but also is among the fastest systems of its kind in the literature. On the MR data set the spinal disks of a whole spine are detected in 11.5 s on average with 98.6% sensitivity and 0.073 false positive detections per volume. On the CT data a comparable sensitivity of 98.0% with 0.267 false positives is achieved. Detected disks are localized with an average position error of 2.4 mm/3.2 mm and angular error of 3.9°/4.5° in MR/CT, which is close to the employed hypothesis resolution of 2.1 mm and 3.3°.     

基于双源CT图像的冠状动脉分割

背景：在计算机辅助下,从双源CT图像中把三维冠状动脉分割出来能为其定量评价提供基础。但冠状动脉的三维形态复杂多变,且其管径细小,因而实现冠状动脉的高精度分割是一项有挑战性的课题。目的：解决冠状动脉难以实现高精度分割的问题。方法：采用三步数据处理策略实现冠状动脉分割。先采用阈值方法对三维双源CT图像进行预分割;然后,采用交互式的策略分割出与主动脉相连的左、右冠状动脉始端;最后,根据冠状动脉始端的位置,利用形态学方法和三维断层图像相邻层间的关系分割出三维冠状动脉。结果与结论：提出的基于形态学与断层图像层间关系的分割方法能较精确地从双源CT图像中分割出左、右冠状动脉,说明该方法适用于三维冠状动脉的分割。     

Volumetric memory network for interactive medical image segmentation

Despite recent progress of automatic medical image segmentation techniques, fully automatic results usually fail to meet clinically acceptable accuracy, thus typically require further refinement. To this end, we propose a novel Volumetric Memory Network, dubbed as VMN, to enable segmentation of 3D medical images in an interactive manner. Provided by user hints on an arbitrary slice, a 2D interaction network is firstly employed to produce an initial 2D segmentation for the chosen slice. Then, the VMN propagates the initial segmentation mask bidirectionally to all slices of the entire volume. Subsequent refinement based on additional user guidance on other slices can be incorporated in the same manner. To facilitate smooth human-in-the-loop segmentation, a quality assessment module is introduced to suggest the next slice for interaction based on the segmentation quality of each slice produced in the previous round. Our VMN demonstrates two distinctive features: First, the memory-augmented network design offers our model the ability to quickly encode past segmentation information, which will be retrieved later for the segmentation of other slices; Second, the quality assessment module enables the model to directly estimate the quality of each segmentation prediction, which allows for an active learning paradigm where users preferentially label the lowest-quality slice for multi-round refinement. The proposed network leads to a robust interactive segmentation engine, which can generalize well to various types of user annotations (e.g., scribble, bounding box, extreme clicking). Extensive experiments have been conducted on three public medical image segmentation datasets (i.e., MSD, KiTS₁₉, CVC-ClinicDB), and the results clearly confirm the superiority of our approach in comparison with state-of-the-art segmentation models. The code is made publicly available at https://github.com/0liliulei/Mem3D.     

Posterior shape models

We present a method to compute the conditional distribution of a statistical shape model given partial data. The result is a “posterior shape model”, which is again a statistical shape model of the same form as the original model. This allows its direct use in the variety of algorithms that include prior knowledge about the variability of a class of shapes with a statistical shape model. Posterior shape models then provide a statistically sound yet easy method to integrate partial data into these algorithms. Usually, shape models represent a complete organ, for instance in our experiments the femur bone, modeled by a multivariate normal distribution. But because in many application certain parts of the shape are known a priori, it is of great interest to model the posterior distribution of the whole shape given the known parts. These could be isolated landmark points or larger portions of the shape, like the healthy part of a pathological or damaged organ. However, because for most shape models the dimensionality of the data is much higher than the number of examples, the normal distribution is singular, and the conditional distribution not readily available. In this paper, we present two main contributions: First, we show how the posterior model can be efficiently computed as a statistical shape model in standard form and used in any shape model algorithm. We complement this paper with a freely available implementation of our algorithms. Second, we show that most common approaches put forth in the literature to overcome this are equivalent to probabilistic principal component analysis (PPCA), and Gaussian Process regression. To illustrate the use of posterior shape models, we apply them on two problems from medical image analysis: model-based image segmentation incorporating prior knowledge from landmarks, and the prediction of anatomically correct knee shapes for trochlear dysplasia patients, which constitutes a novel medical application. Our experiments confirm that the use of conditional shape models for image segmentation improves the overall segmentation accuracy and robustness.