Image Segmentation Using Weak Shape Priors

The problem of image segmentation is known to become particularly challenging in the case of partial occlusion of the object(s) of interest, background clutter, and the presence of strong noise. To overcome this problem, the present paper introduces a novel approach segmentation through the use of "weak" shape priors. Specifically, in the proposed method, an segmenting active contour is constrained to converge to a configuration at which its geometric parameters attain their empirical probability densities closely matching the corresponding model densities that are learned based on training samples. It is shown through numerical experiments that the proposed shape modeling can be regarded as "weak" in the sense that it minimally influences the segmentation, which is allowed to be dominated by data-related forces. On the other hand, the priors provide sufficient constraints to regularize the convergence of segmentation, while requiring substantially smaller training sets to yield less biased results as compared to the case of PCA-based regularization methods. The main advantages of the proposed technique over some existing alternatives is demonstrated in a series of experiments.Comment: 27 pages, 8 figure

Geometric Data Analysis: Advancements of the Statistical Methodology and Applications

Data analysis has become fundamental to our society and comes in multiple facets and approaches. Nevertheless, in research and applications, the focus was primarily on data from Euclidean vector spaces. Consequently, the majority of methods that are applied today are not suited for more general data types. Driven by needs from fields like image processing, (medical) shape analysis, and network analysis, more and more attention has recently been given to data from non-Euclidean spaces–particularly (curved) manifolds. It has led to the field of geometric data analysis whose methods explicitly take the structure (for example, the topology and geometry) of the underlying space into account. This thesis contributes to the methodology of geometric data analysis by generalizing several fundamental notions from multivariate statistics to manifolds. We thereby focus on two different viewpoints. First, we use Riemannian structures to derive a novel regression scheme for general manifolds that relies on splines of generalized Bézier curves. It can accurately model non-geodesic relationships, for example, time-dependent trends with saturation effects or cyclic trends. Since Bézier curves can be evaluated with the constructive de Casteljau algorithm, working with data from manifolds of high dimensions (for example, a hundred thousand or more) is feasible. Relying on the regression, we further develop a hierarchical statistical model for an adequate analysis of longitudinal data in manifolds, and a method to control for confounding variables. We secondly focus on data that is not only manifold- but even Lie group-valued, which is frequently the case in applications. We can only achieve this by endowing the group with an affine connection structure that is generally not Riemannian. Utilizing it, we derive generalizations of several well-known dissimilarity measures between data distributions that can be used for various tasks, including hypothesis testing. Invariance under data translations is proven, and a connection to continuous distributions is given for one measure. A further central contribution of this thesis is that it shows use cases for all notions in real-world applications, particularly in problems from shape analysis in medical imaging and archaeology. We can replicate or further quantify several known findings for shape changes of the femur and the right hippocampus under osteoarthritis and Alzheimer's, respectively. Furthermore, in an archaeological application, we obtain new insights into the construction principles of ancient sundials. Last but not least, we use the geometric structure underlying human brain connectomes to predict cognitive scores. Utilizing a sample selection procedure, we obtain state-of-the-art results

MR to Ultrasound Registration for Image-Guided Prostate Biopsy

Transrectal ultrasound (TRUS) guided prostate biopsy is the standard approach for diagnosis of prostate cancer (PCa). However, due to the lack of image contrast of prostate tumors, it often results in false negatives. Magnetic Resonance Imaging (MRI) has been considered to be a promising imaging modality for noninvasive identification of PCa, since it can provide a high sensitivity and specificity for the detection of early stage PCa. Our main objective is to develop a registration method of 3D MR-TRUS images, allowing generation of volumetric 3D maps of targets identified in 3D MR images to be biopsied using 3D TRUS images. We proposed an image-based non-rigid registration approach which employs the modality independent neighborhood descriptor (MIND) as the local similarity feature. An efficient duality-based convex optimization-based algorithmic scheme was introduced to extract the deformations. The registration accuracy was evaluated using 20 patient images by calculating the target registration error (TRE) using manually identified corresponding intrinsic fiducials. Additional performance metrics (DSC, MAD, and MAXD) were also calculated by comparing the MR and TRUS manually segmented prostate surfaces in the registered images. Experimental results showed that the proposed method yielded an overall median TRE of 1.76 mm. In addition, we proposed a surface-based registration method, which first makes use of an initial rigid registration of 3D MR to TRUS using 6 manually placed corresponding landmarks in each image. Following the manual initialization, two prostate surfaces are segmented from 3D MR and TRUS images and then non-rigidly registered using a thin-plate spline algorithm. The registration accuracy was evaluated using 17 patient images by measuring TRE. Experimental results show that the proposed method yielded an overall mean TRE of 2.24 mm, which is favorably comparable to a clinical requirement for an error of less than 2.5 mm

Improvement of Geometric Quality Inspection and Process Efficiency in Additive Manufacturing

Additive manufacturing (AM) has been known for its ability of producing complex geometries in flexible production environments. In recent decades, it has attracted increasing attention and interest of different industrial sectors. However, there are still some technical challenges hindering the wide application of AM. One major barrier is the limited dimensional accuracy of AM produced parts, especially for industrial sectors such as aerospace and biomedical engineering, where high geometric accuracy is required. Nevertheless, traditional quality inspection techniques might not perform well due to the complexity and flexibility of AM fabricated parts. Another issue, which is brought up from the growing demand for large-scale 3D printing in these industry sectors, is the limited fabrication speed of AM processes. However, how to improve the fabrication efficiency without sacrificing the geometric quality is still a challenging problem that has not been well addressed. In this work, new geometric inspection methods are proposed for both offline and online inspection paradigms, and a layer-by-layer toolpath optimization model is proposed to further improve the fabrication efficiency of AM processes without degrading the resolution. First, a novel Location-Orientation-Shape (LOS) distribution derived from 3D scanning output is proposed to improve the offline inspection in detecting and distinguishing positional and dimensional non-conformities of features. Second, the online geometric inspection is improved by a multi-resolution alignment and inspection framework based on wavelet decomposition and design of experiments (DOE). The new framework is able to improve the alignment accuracy and to distinguish different sources of error based on the shape deviation of each layer. In addition, a quickest change point detection method is used to identify the layer where the earliest change of systematic deviation distribution occurs during the printing process. Third, to further improve the printing efficiency without sacrificing the quality of each layer, a toolpath allocation and scheduling optimization model is proposed based on a concurrent AM process that allows multiple extruders to work collaboratively on the same layer. For each perspective of improvements, numerical studies are provided to emphasize the theoretical and practical meanings of proposed methodologies

Proceedings of the First International Workshop on Mathematical Foundations of Computational Anatomy (MFCA'06) - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceNon-linear registration and shape analysis are well developed research topic in the medical image analysis community. There is nowadays a growing number of methods that can faithfully deal with the underlying biomechanical behaviour of intra-subject shape deformations. However, it is more difficult to relate the anatomical shape of different subjects. The goal of computational anatomy is to analyse and to statistically model this specific type of geometrical information. In the absence of any justified physical model, a natural attitude is to explore very general mathematical methods, for instance diffeomorphisms. However, working with such infinite dimensional space raises some deep computational and mathematical problems. In particular, one of the key problem is to do statistics. Likewise, modelling the variability of surfaces leads to rely on shape spaces that are much more complex than for curves. To cope with these, different methodological and computational frameworks have been proposed. The goal of the workshop was to foster interactions between researchers investigating the combination of geometry and statistics for modelling biological shape variability from image and surfaces. A special emphasis was put on theoretical developments, applications and results being welcomed as illustrations. Contributions were solicited in the following areas: * Riemannian and group theoretical methods on non-linear transformation spaces * Advanced statistics on deformations and shapes * Metrics for computational anatomy * Geometry and statistics of surfaces 26 submissions of very high quality were recieved and were reviewed by two members of the programm committee. 12 papers were finally selected for oral presentations and 8 for poster presentations. 16 of these papers are published in these proceedings, and 4 papers are published in the proceedings of MICCAI'06 (for copyright reasons, only extended abstracts are provided here)

Probabilistic modeling of texture transition for fast tracking and delineation

In this thesis a probabilistic approach to texture boundary detection for tracking applications is presented. We have developed a novel fast algorithm for Bayesian estimation of texture transition locations from a short sequence of pixels on a scanline that combines the desirable speed of edge-based line search and the sophistication of Bayesian texture analysis given a small set of observations. For the cases where the given observations are too few for reliable Bayesian estimation of probability of texture change we propose an innovative machine learning technique to generate a probabilistic texture transition model. This is achieved by considering a training dataset containing small patches of blending textures. By encompassing in the training set enough examples to accurately model texture transitions of interest we can construct a predictor that can be used for object boundary tracking that can deal with few observations and demanding cases of tracking of arbitrary textured objects against cluttered background. Object outlines are then obtained by combining the texture crossing probabilities across a set of scanlines. We show that a rigid geometric model of the object to be tracked or smoothness constraints in the absence of such a model can be used to coalesce the scanline texture crossing probabilities obtained using the methods mentioned above. We propose a Hidden Markov Model to aggregate robustly the sparse transition probabilities of scanlines sampled along the projected hypothesis model contour. As a result continuous object contours can be extracted using a posteriori maximization of texture transition probabilities. On the other hand, stronger geometric constraints such as available rigid models of the target are directly enforced by robust stochastic optimization. In addition to being fast, the allure of the proposed probabilistic framework is that it accommodates a unique infrastructure for tracking of heterogeneous objects which utilizes the machine learning-based predictor as well as the Bayesian estimator interchangeably in conjunction with robust optimization to extract object contours robustly. We apply the developed methods to tracking of textured and non textured rigid objects as well as deformable body outlines and monocular articulated human motion in challenging conditions. Finally, because it is fast, our method can also serve as an interactive texture segmentation tool

Part-based recognition of 3-D objects with application to shape modeling in hearing aid manufacturing

In order to meet the needs of people with hearing loss today hearing aids are custom designed. Increasingly accurate 3-D scanning technology has contributed to the transition from conventional production scenarios to software based processes. Nonetheless, there is a tremendous amount of manual work involved to transform an input 3-D surface mesh of the outer ear into a final hearing aid shape. This manual work is often cumbersome and requires lots of experience which is why automatic solutions are of high practical relevance. This work is concerned with the recognition of 3-D surface meshes of ear implants. In particular we present a semantic part-labeling framework which significantly outperforms existing approaches for this task. We make at least three contributions which may also be found useful for other classes of 3-D meshes. Firstly, we validate the discriminative performance of several local descriptors and show that the majority of them performs poorly on our data except for 3-D shape contexts. The reason for this is that many local descriptor schemas are not rich enough to capture subtle variations in form of bends which is typical for organic shapes. Secondly, based on the observation that the left and the right outer ear of an individual look very similar we raised the question how similar the ear shapes among arbitrary individuals are? In this work, we define a notion of distance between ear shapes as building block of a non-parametric shape model of the ear to better handle the anatomical variability in ear implant labeling. Thirdly, we introduce a conditional random field model with a variety of label priors to facilitate the semantic part-labeling of 3-D meshes of ear implants. In particular we introduce the concept of a global parametric transition prior to enforce transition boundaries between adjacent object parts with an a priori known parametric form. In this way we were able to overcome the issue of inadequate geometric cues (e.g., ridges, bumps, concavities) as natural indicators for the presence of part boundaries. The last part of this work offers an outlook to possible extensions of our methods, in particular the development of 3-D descriptors that are fast to compute whilst at the same time rich enough to capture the characteristic differences between objects residing in the same class