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Formmodellbasierte Segmentierung des Unterkiefers aus Dental-CT-Aufnahmen
Abstract
Dental-CT-Aufnahmen leiden unter einer vergleichsweise schlechten Bildqualität bezüglich des Signal-zu-Rausch Verhältnisses. Aus diesem Grund benutzen wir ein statistisches Formmodell (SFM) zur robusten Segmentierung des Unterkiefers. Im Gegensatz zu bisherigen Arbeiten ist das von uns vorgestellte Verfahren vollautomatisch – sowohl was die Korrespondenzfindung angeht, als auch bezüglich der Segmentierung an sich. Obwohl unsere Trainingspopulation weniger als 30 % des Umfangs ähnlicher Arbeiten aufweist, erzielen wir vergleichbare Ergebnisse. Ein wesentlicher Grund hierfür ist die Korrespondenzfindung mittels Optimierung einer modellbasierten Ziefunktion: Unsere Ergebnisse zeigen, dass dies eine deutliche Verbesserung der Segmentierungsergebnisse erlaubt und belegen damit erstmals die Bedeutung dieses Ansatz unmittelbar in einer Anwendung zur Segmentierung.
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Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closed-form solution to the least-squares problem for three or more points. Currently various empirical, graphical, and numerical iterative methods are in use. Derivation of the solution is simplified by use of unit quaternions to represent rotation. I emphasize a symmetry property that a solution to this problem ought to possess. The best translational offset is the difference between the centroid of the coordinates in one system and the rotated and scaled centroid of the coordinates in the other system. The best scale is equal to the ratio of the root-mean-square deviations of the coordinates in the two systems from their respective centroids. These exact results are to be preferred to approximate methods based on measurements of a few selected points. The unit quaternion representing the best rotation is the eigenvector associated with the most positive eigenvalue of a symmetric 4 × 4 matrix. The elements of this matrix are combinations of sums of products of corresponding coordinates of the points.
The identification of corresponding landmarks across a set of training shapes is a prerequisite for statistical shape model (SSM) construction. We automatically establish 3D correspondence using one new and several known alternative approaches for consistent, shape-preserving, spherical parameterization. The initial correspondence determined by all employed methods is refined by optimizing a groupwise objective function. The quality of all models before and after optimization is thoroughly evaluated using several data sets of clinically relevant, anatomical objects of varying complexity. Correspondence quality is benchmarked in terms of the SSMs’ specificity and generalization ability, which are measured using different surface based distance functions.
We find that our new approach performs best for complex objects. Furthermore, all new and previously published methods of our own allow for (i) building SSMs that are significantly better than the well-known SPHARM method, (ii) establishing quasi-optimal correspondence for low and moderately complex objects without additional optimization, and (iii) considerably speeding up convergence, thus, providing means for practical, fast, and accurate SSM construction.
Preoperative planning systems are commonly used for oral implant surgery. One of the objectives is to determine if the quantity and quality of bone is sufficient to sustain an implant while avoiding critical anatomic structures. We aim to automate the segmentation of jaw tissues on CT images: cortical bone, trabecular core and especially the mandibular canal containing the dental nerve. This nerve must be avoided during implant surgery to prevent lip numbness. Previous work in this field used thresholds or filters and needed manual initialization. An automated system based on the use of Active Appearance Models (AAMs) is proposed. Our contribution is a completely automated segmentation of tissues and a semi-automatic landmarking process necessary to create the AAM model. The AAM is trained using 215 images and tested with a leave-4-out scheme. Results obtained show an initialization error of 3.25% and a mean error of 1.63mm for the cortical bone, 2.90 mm for the trabecular core, 4.76 mm for the mandibular canal and 3.40 mm for the dental nerve.
Active Shape Models are a popular method for segmenting three-dimensional medical images. To obtain the required landmark correspondences, various automatic approaches have been proposed. In this work, we present an improved version of minimizing the description length (MDL) of the model. To initialize the algorithm, we describe a method to distribute landmarks on the training shapes using a conformal parameterization function. Next, we introduce a novel procedure to modify landmark positions locally without disturbing established correspondences. We employ a gradient descent optimization to minimize the MDL cost function, speeding up automatic model building by several orders of magnitude when compared to the original MDL approach. The necessary gradient information is estimated from a singular value decomposition, a more accurate technique to calculate the PCA than the commonly used eigendecomposition of the covariance matrix. Finally, we present results for several synthetic and real-world datasets demonstrating that our procedure generates models of significantly better quality in a fraction of the time needed by previous approaches.
The authors describe a general-purpose, representation-independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces. The method handles the full six degrees of freedom and is based on the iterative closest point (ICP) algorithm, which requires only a procedure to find the closest point on a geometric entity to a given point. The ICP algorithm always converges monotonically to the nearest local minimum of a mean-square distance metric, and the rate of convergence is rapid during the first few iterations. Therefore, given an adequate set of initial rotations and translations for a particular class of objects with a certain level of `shape complexity', one can globally minimize the mean-square distance metric over all six degrees of freedom by testing each initial registration. One important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model, prior to shape inspection. Experimental results show the capabilities of the registration algorithm on point sets, curves, and surfaces
Model-based vision is firmly established as a robust approach to recognizing and locating known rigid objects in the presence of noise, clutter, and occlusion. It is more problematic to apply model-based methods to images of objects whose appearance can vary, though a number of approaches based on the use of flexible templates have been proposed. The problem with existing methods is that they sacrifice model specificity in order to accommodate variability, thereby compromising robustness during image interpretation. We argue that a model should only be able to deform in ways characteristic of the class of objects it represents. We describe a method for building models by learning patterns of variability from a training set of correctly annotated images. These models can be used for image search in an iterative refinement algorithm analogous to that employed by Active Contour Models (Snakes). The key difference is that our Active Shape Models can only deform to fit the data in ways consistent with the training set. We show several practical examples where we have built such models and used them to locate partially occluded objects in noisy, cluttered images.
This paper presents procedures for the explicit parametric representation and global description of surfaces of simply connected 3-D objects. The novel techniques overcome severe limitations of earlier methods (restriction to star-shaped objects (D. H. Ballard and Ch. M. Brown, Computer Vision, Prentice-Hall, Englewood Cliffs, NJ, 1981), constraints on positioning and shape of cross-sections (F. Solina and R. Bajcsy, IEEE Trans. Pattern Anal. Much. Intell. 12(2), 1990, 131-147; L. H. Staib and J. S. Duncan, in Visualization in Biomedical Computing 1992 (R. A. Robb, Ed.), Vol. Proc. SPIE 108, pp. 90-104, 1992), and nonhomogeneous distribution of parameter space). We parametrize the surface by defining a continuous, one-to-one mapping from the surface of the original object to the surface of a unit sphere. The parametrization is formulated as a constrained optimization problem. Practicable starting values are obtained by an initial mapping based on a heat conduction model. The parametrization enables us to expand the object surface into a series of spherical harmonic functions, extending to 3-D the concept of elliptical Fourier descriptors for 2-D closed curves (E. Persoon and K. S. Fu, IEEE Trans. Syst. Man Cybernetics 7(3), 1977, 388-397; F. P. Kuhl and Ch. R. Giardina, Comput. Graphics Image Process. 18(3), 1982, 236-258). Invariant, object-centered descriptors are obtained by rotating the parameter net and the object into standard positions. The new methods are illustrated with 3-D test objects. Potential applications are recognition, classification, and comparison of convoluted surfaces or parts of surfaces of 3-D shapes.
The exact localization of the mandibular nerve with respect to the bone is important for applications in dental implantology and maxillofacial surgery. Cone beam computed tomography (CBCT), often also called digital volume tomography (DVT), is increasingly utilized in maxillofacial or dental imaging. Compared to conventional CT, however, soft tissue discrimination is worse due to a reduced dose. Thus, small structures like the alveolar nerves are even harder recognizable within the image data. We show that it is nonetheless possible to accurately reconstruct the 3D bone surface and the course of the nerve in a fully automatic fashion, with a method that is based on a combined statistical shape model of the nerve and the bone and a Dijkstra-based optimization procedure. Our method has been validated on 106 clinical datasets: the average reconstruction error for the bone is 0.5 +/- 0.1 mm, and the nerve can be detected with an average error of 1.0 +/- 0.6 mm.
Statistical shape models (SSMs) have by now been firmly established as a robust tool for segmentation of medical images. While 2D models have been in use since the early 1990 s, wide-spread utilization of three-dimensional models appeared only in recent years, primarily made possible by breakthroughs in automatic detection of shape correspondences. In this article, we review the techniques required to create and employ these 3D SSMs. While we concentrate on landmark-based shape representations and thoroughly examine the most popular variants of Active Shape and Active Appearance models, we also describe several alternative approaches to statistical shape modeling. Structured into the topics of shape representation, model construction, shape correspondence, local appearance models and search algorithms, we present an overview of the current state of the art in the field. We conclude with a survey of applications in the medical field and a discussion of future developments.
A new approach to the problem of automatic construction of eigenshape models is presented. Eigenshape models have proved to be successful in a variety of medical image analysis problems. However, automatic construction of eigenshape models has proved to be a difficult problem, and in many applications the models are built by hand-a painstaking process. We show that the fundamental problem is a choice of the correct pose and parametrization of each shape in the training set. Eigenshape models are not invariant under reparametrizations and pose transformations of the training shapes. Since there is no a priori correct choice for the pose and parametrization of each shape, their value should be chosen so as to produce a model that is compact and specific. This problem can be solved by finding an objective function that measures these properties and varying the pose and parametrization of each shape to optimize this function. We show that the appropriate objective function is the determinant of the covariance matrix. We go on to show how this objective function can be optimized by a genetic algorithm (GA) and thus give a practical method for building eigenshape models. The models produced are often better than hand-built ones. The advantages of a GA over other choices of optimization method are that no assumptions about the nature of the shapes being modelled is required and that the global minimum of the objective function can, in principle, be found.