Shape Matching and Registration by Data-driven EM

Accurate and Robust Non-rigid Point Set Registration using Student's-t Mixture Model with Prior Probability Modeling

A new accurate and robust non-rigid point set registration method, named DSMM, is proposed for non-rigid point set registration in the presence of significant amounts of missing correspondences and outliers. The key idea of this algorithm is to consider the relationship between the point sets as random variables and model the prior probabilities via Dirichlet distribution. We assign the various prior probabilities of each point to its correspondences in the Student's-t mixture model. We later incorporate the local spatial representation of the point sets by representing the posterior probabilities in a linear smoothing filter and get closed-form mixture proportions, leading to a computationally efficient registration algorithm comparing to other Student's-t mixture model based methods. Finally, by introducing the hidden random variables in the Bayesian framework, we propose a general mixture model family for generalizing the mixture-model-based point set registration, where the existing methods can be considered as members of the proposed family. We evaluate DSMM and other state-of-the-art finite mixture models based point set registration algorithms on both artificial point set and various 2D and 3D point sets, where DSMM demonstrates its statistical accuracy and robustness, outperforming the competing algorithms.

Discriminatively Trained And-Or Graph Models for Object Shape Detection

In this paper, we investigate a novel reconfigurable part-based model, namely And-Or graph model, to recognize object shapes in images. Our proposed model consists of four layers: leaf-nodes at the bottom are local classifiers for detecting contour fragments; or-nodes above the leaf-nodes function as the switches to activate their child leaf-nodes, making the model reconfigurable during inference; and-nodes in a higher layer capture holistic shape deformations; one root-node on the top, which is also an or-node, activates one of its child and-nodes to deal with large global variations (e.g. different poses and views). We propose a novel structural optimization algorithm to discriminatively train the And-Or model from weakly annotated data. This algorithm iteratively determines the model structures (e.g. the nodes and their layouts) along with the parameter learning. On several challenging datasets, our model demonstrates the effectiveness to perform robust shape-based object detection against background clutter and outperforms the other state-of-the-art approaches. We also release a new shape database with annotations, which includes more than 1500 challenging shape instances, for recognition and detection.

Segmentation, Inference and Classification of Partially Overlapping Nanoparticles

This paper presents a method that enables automated morphology analysis of partially overlapping nanoparticles in electron micrographs. In the undertaking of morphology analysis, three tasks appear necessary: separate individual particles from an agglomerate of overlapping nano-objects; infer the particle's missing contours; and ultimately, classify the particles by shape based on their complete contours. Our specific method adopts a two-stage approach: the first stage executes the task of particle separation, and the second stage conducts simultaneously the tasks of contour inference and shape classification. For the first stage, a modified ultimate erosion process is developed for decomposing a mixture of particles into markers, and then, an edge-to-marker association method is proposed to identify the set of evidences that eventually delineate individual objects. We also provided theoretical justification regarding the separation capability of the first stage. In the second stage, the set of evidences become inputs to a Gaussian mixture model on B-splines, the solution of which leads to the joint learning of the missing contour and the particle shape. Using twelve real electron micrographs of overlapping nanoparticles, we compare the proposed method with seven state-of-the-art methods. The results show the superiority of the proposed method in terms of particle recognition rate.

Nonlinear shape registration without correspondences

In this paper, we propose a novel framework to estimate the parameters of a diffeomorphism that aligns a known shape and its distorted observation. Classical registration methods first establish correspondences between the shapes and then compute the transformation parameters from these landmarks. Herein, we trace back the problem to the solution of a system of nonlinear equations which directly gives the parameters of the aligning transformation. The proposed method provides a generic framework to recover any diffeomorphic deformation without established correspondences. It is easy to implement, not sensitive to the strength of the deformation, and robust against segmentation errors. The method has been applied to several commonly used transformation models. The performance of the proposed framework has been demonstrated on large synthetic data sets as well as in the context of various applications.

Automatic detection and quantification of tree-in-bud (TIB) opacities from CT scans

This study presents a novel computer-assisted detection (CAD) system for automatically detecting and precisely quantifying abnormal nodular branching opacities in chest computed tomography (CT), termed tree-in-bud (TIB) opacities by radiology literature. The developed CAD system in this study is based on 1) fast localization of candidate imaging patterns using local scale information of the images, and 2) Möbius invariant feature extraction method based on learned local shape and texture properties of TIB patterns. For fast localization of candidate imaging patterns, we use ball-scale filtering and, based on the observation of the pattern of interest, a suitable scale selection is used to retain only small size patterns. Once candidate abnormality patterns are identified, we extract proposed shape features from regions where at least one candidate pattern occupies. The comparative evaluation of the proposed method with commonly used CAD methods is presented with a dataset of 60 chest CTs (laboratory confirmed 39 viral bronchiolitis human parainfluenza CTs and 21 normal chest CTs). The quantitative results are presented as the area under the receiver operator characteristics curves and a computer score (volume affected by TIB) provided as an output of the CAD system. In addition, a visual grading scheme is applied to the patient data by three well-trained radiologists. Interobserver and observer-computer agreements are obtained by the relevant statistical methods over different lung zones. Experimental results demonstrate that the proposed CAD system can achieve high detection rates with an overall accuracy of 90.96%. Moreover, correlations of observer-observer (R(2)=0.8848, and observer-CAD agreements (R(2)=0.824, validate the feasibility of the use of the proposed CAD system in detecting and quantifying TIB patterns.

Image-guided intraoperative cortical deformation recovery using game theory: application to neocortical epilepsy surgery

During neurosurgery, nonrigid brain deformation prevents preoperatively-acquired images from accurately depicting the intraoperative brain. Stereo vision systems can be used to track intraoperative cortical surface deformation and update preoperative brain images in conjunction with a biomechanical model. However, these stereo systems are often plagued with calibration error, which can corrupt the deformation estimation. In order to decouple the effects of camera calibration from the surface deformation estimation, a framework that can solve for disparate and often competing variables is needed. Game theory, which was developed to handle decision making in this type of competitive environment, has been applied to various fields from economics to biology. In this paper, game theory is applied to cortical surface tracking during neocortical epilepsy surgery and used to infer information about the physical processes of brain surface deformation and image acquisition. The method is successfully applied to eight in vivo cases, resulting in an 81% decrease in mean surface displacement error. This includes a case in which some of the initial camera calibration parameters had errors of 70%. Additionally, the advantages of using a game theoretic approach in neocortical epilepsy surgery are clearly demonstrated in its robustness to initial conditions.