Non-rigid registration by geometry-constrained diffusion.

. Assume that only partial knowledge about a non-rigid registration is given so that certain points, curves, or surfaces in one 3D image map to certain certain points, curves, or surfaces in another 3D image. We are facing the aperture problem because along the curves and surfaces, point correspondences are not given. We will advocate the viewpoint that the aperture and the 3D interpolation problem may be solved simultaneously by finding the simplest displacement field. This is obtained by a geometry-constrained diffusion which yields the simplest displacement field in a precise sense. The point registration obtained may be used for growth modelling, shape statistics, or kinematic interpolation. The algorithm applies to geometrical objects of any dimensionality. We may thus keep any number of fiducial points, curves, and/or surfaces fixed while finding the simplest registration. Examples of inferred point correspondences in a longitudinal growth study of the mandible are g..

Surface-bounded growth modeling applied to human mandibles

From a set of longitudinal three-dimensional scans of the same anatomical structure, we have accurately modeled the temporal shape and size changes using a linear shape model. On a total of 31 computed tomography scans of the mandible from six patients, 14851 semilandmarks are found automatically using shape features and a new algorithm called geometry-constrained diffusion. The semilandmarks are mapped into Procrustes space. Principal component analysis extracts a one-dimensional subspace, which is used to construct a linear growth model. The worst case mean modeling error in a cross validation study is 3.7 mm

Building and Testing a Statistical Shape Model of the Human Ear Canal

Abstract. Today the design of custom in-the-ear hearing aids is based on personal experience and skills and not on a systematic description of the variation of the shape of the ear canal. In this paper it is described how a dense surface point distribution model of the human ear canal is built based on a training set of laser scanned ear impressions and a sparse set of anatomical landmarks placed by an expert. The landmarks are used to warp a template mesh onto all shapes in the training set. Using the vertices from the warped meshes, a 3D point distribution model is made. The model is used for testing for gender related differences in size and shape of the ear canal.

Multimodal Three Dimensional Scene Reconstruction, The Gaussian Fields Framework

The focus of this research is on building 3D representations of real world scenes and objects using different imaging sensors. Primarily range acquisition devices (such as laser scanners and stereo systems) that allow the recovery of 3D geometry, and multi-spectral image sequences including visual and thermal IR images that provide additional scene characteristics. The crucial technical challenge that we addressed is the automatic point-sets registration task. In this context our main contribution is the development of an optimization-based method at the core of which lies a unified criterion that solves simultaneously for the dense point correspondence and transformation recovery problems. The new criterion has a straightforward expression in terms of the datasets and the alignment parameters and was used primarily for 3D rigid registration of point-sets. However it proved also useful for feature-based multimodal image alignment. We derived our method from simple Boolean matching principles by approximation and relaxation. One of the main advantages of the proposed approach, as compared to the widely used class of Iterative Closest Point (ICP) algorithms, is convexity in the neighborhood of the registration parameters and continuous differentiability, allowing for the use of standard gradient-based optimization techniques. Physically the criterion is interpreted in terms of a Gaussian Force Field exerted by one point-set on the other. Such formulation proved useful for controlling and increasing the region of convergence, and hence allowing for more autonomy in correspondence tasks. Furthermore, the criterion can be computed with linear complexity using recently developed Fast Gauss Transform numerical techniques. In addition, we also introduced a new local feature descriptor that was derived from visual saliency principles and which enhanced significantly the performance of the registration algorithm. The resulting technique was subjected to a thorough experimental analysis that highlighted its strength and showed its limitations. Our current applications are in the field of 3D modeling for inspection, surveillance, and biometrics. However, since this matching framework can be applied to any type of data, that can be represented as N-dimensional point-sets, the scope of the method is shown to reach many more pattern analysis applications

Model and Appearance Based Analysis of Neuronal Morphology from Different Microscopy Imaging Modalities

The neuronal morphology analysis is key for understanding how a brain works. This process requires the neuron imaging system with single-cell resolution; however, there is no feasible system for the human brain. Fortunately, the knowledge can be inferred from the model organism, Drosophila melanogaster, to the human system. This dissertation explores the morphology analysis of Drosophila larvae at single-cell resolution in static images and image sequences, as well as multiple microscopy imaging modalities. Our contributions are on both computational methods for morphology quantification and analysis of the influence of the anatomical aspect. We develop novel model-and-appearance-based methods for morphology quantification and illustrate their significance in three neuroscience studies. Modeling of the structure and dynamics of neuronal circuits creates understanding about how connectivity patterns are formed within a motor circuit and determining whether the connectivity map of neurons can be deduced by estimations of neuronal morphology. To address this problem, we study both boundary-based and centerline-based approaches for neuron reconstruction in static volumes. Neuronal mechanisms are related to the morphology dynamics; so the patterns of neuronal morphology changes are analyzed along with other aspects. In this case, the relationship between neuronal activity and morphology dynamics is explored to analyze locomotion procedures. Our tracking method models the morphology dynamics in the calcium image sequence designed for detecting neuronal activity. It follows the local-to-global design to handle calcium imaging issues and neuronal movement characteristics. Lastly, modeling the link between structural and functional development depicts the correlation between neuron growth and protein interactions. This requires the morphology analysis of different imaging modalities. It can be solved using the part-wise volume segmentation with artificial templates, the standardized representation of neurons. Our method follows the global-to-local approach to solve both part-wise segmentation and registration across modalities. Our methods address common issues in automated morphology analysis from extracting morphological features to tracking neurons, as well as mapping neurons across imaging modalities. The quantitative analysis delivered by our techniques enables a number of new applications and visualizations for advancing the investigation of phenomena in the nervous system