A Combinatorial Solution to Non-Rigid 3D Shape-to-Image Matching

We propose a combinatorial solution for the problem of non-rigidly matching a 3D shape to 3D image data. To this end, we model the shape as a triangular mesh and allow each triangle of this mesh to be rigidly transformed to achieve a suitable matching to the image. By penalising the distance and the relative rotation between neighbouring triangles our matching compromises between image and shape information. In this paper, we resolve two major challenges: Firstly, we address the resulting large and NP-hard combinatorial problem with a suitable graph-theoretic approach. Secondly, we propose an efficient discretisation of the unbounded 6-dimensional Lie group SE(3). To our knowledge this is the first combinatorial formulation for non-rigid 3D shape-to-image matching. In contrast to existing local (gradient descent) optimisation methods, we obtain solutions that do not require a good initialisation and that are within a bound of the optimal solution. We evaluate the proposed method on the two problems of non-rigid 3D shape-to-shape and non-rigid 3D shape-to-image registration and demonstrate that it provides promising results.Comment: 10 pages, 7 figure

Variational shape matching for shape classification and retrieval

International audienceIn this paper we define a multi-scale distance between shapes based on geodesics in the shape space. The proposed distance, robust to outliers, uses shape matching to compare shapes locally. The multi-scale analysis is introduced in order to address local and global variabilities. The resulting similarity measure is invariant to translation, rotation and scaling independently of constraints or landmarks, but constraints can be added to the approach formulation when needed. An evaluation of the proposed approach is reported for shape classification and shape retrieval on the part B of the MPEG-7 shape database. The proposed approach is shown to significantly outperform previous works and reaches 89.05% of retrieval accuracy and 98.86% of correct classification rate

Elastic Shape Models for Face Analysis Using Curvilinear Coordinates

International audienceThis paper studies the problem of analyzing variability in shapes of facial surfaces using a Rie- mannian framework, a fundamental approach that allows for joint matchings, comparisons, and deformations of faces under a chosen metric. The starting point is to impose a curvilinear coordinate system, named the Darcyan coordinate system, on facial surfaces; it is based on the level curves of the surface distance function measured from the tip of the nose. Each facial surface is now represented as an indexed collection of these level curves. The task of finding optimal deformations, or geodesic paths, between facial surfaces reduces to that of finding geodesics between level curves, which is accomplished using the theory of elastic shape analy- sis of 3D curves. Elastic framework allows for nonlinear matching between curves and between points across curves. The resulting geodesics provide optimal elastic deformations between faces and an elastic metric for comparing facial shapes. We demonstrate this idea using examples from FSU face databas

Concepts for a theoretical and experimental study of lifting rotor random loads and vibrations. Phase 6-B: Experiments with progressing/regressing forced rotor flapping modes

A two bladed 16-inch hingeless rotor model was built and tested outside and inside a 24 by 24 inch wind tunnel test section at collective pitch settings up to 5 deg and rotor advance ratios up to .4. The rotor model has a simple eccentric mechanism to provide progressing or regressing cyclic pitch excitation. The flapping responses were compared to analytically determined responses which included flap-bending elasticity but excluded rotor wake effects. Substantial systematic deviations of the measured responses from the computed responses were found, which were interpreted as the effects of interaction of the blades with a rotating asymmetrical wake

A Second Order Variational Approach For Diffeomorphic Matching Of 3D Surfaces

In medical 3D-imaging, one of the main goals of image registration is to accurately compare two observed 3D-shapes. In this dissertation, we consider optimal matching of surfaces by a variational approach based on Hilbert spaces of diffeomorphic transformations. We first formulate, in an abstract setting, the optimal matching as an optimal control problem, where a vector field flow is sought to minimize a cost functional that consists of the kinetic energy and the matching quality. To make the problem computationally accessible, we then incorporate reproducing kernel Hilbert spaces with the Gaussian kernels and weighted sums of Dirac measures. We propose a second order method based the Bellman's optimality principle and develop a dynamic programming algorithm. We apply successfully the second order method to diffeomorphic matching of anterior leaflet and posterior leaflet snapshots. We obtain a quadratic convergence for data sets consisting of hundreds of points. To further enhance the computational efficiency for large data sets, we introduce new representations of shapes and develop a multi-scale method. Finally, we incorporate a stretching fraction in the cost function to explore the elastic model and provide a computationally feasible algorithm including the elasticity energy. The performance of the algorithm is illustrated by numerical results for examples from medical 3D-imaging of the mitral valve to reduce excessive contraction and stretching.Mathematics, Department o

Using contour information and segmentation for object registration, modeling and retrieval

This thesis considers different aspects of the utilization of contour information and syntactic and semantic image segmentation for object registration, modeling and retrieval in the context of content-based indexing and retrieval in large collections of images. Target applications include retrieval in collections of closed silhouettes, holistic w ord recognition in handwritten historical manuscripts and shape registration. Also, the thesis explores the feasibility of contour-based syntactic features for improving the correspondence of the output of bottom-up segmentation to semantic objects present in the scene and discusses the feasibility of different strategies for image analysis utilizing contour information, e.g. segmentation driven by visual features versus segmentation driven by shape models or semi-automatic in selected application scenarios. There are three contributions in this thesis. The first contribution considers structure analysis based on the shape and spatial configuration of image regions (socalled syntactic visual features) and their utilization for automatic image segmentation. The second contribution is the study of novel shape features, matching algorithms and similarity measures. Various applications of the proposed solutions are presented throughout the thesis providing the basis for the third contribution which is a discussion of the feasibility of different recognition strategies utilizing contour information. In each case, the performance and generality of the proposed approach has been analyzed based on extensive rigorous experimentation using as large as possible test collections

Elastic Metrics on Spaces of Euclidean Curves: Theory and Algorithms

A main goal in the field of statistical shape analysis is to define computable and informative metrics on spaces of immersed manifolds, such as the space of curves in a Euclidean space. The approach taken in the elastic shape analysis framework is to define such a metric by starting with a reparameterization-invariant Riemannian metric on the space of parameterized shapes and inducing a metric on the quotient by the group of diffeomorphisms. This quotient metric is computed, in practice, by finding a registration of two shapes over the diffeomorphism group. For spaces of Euclidean curves, the initial Riemannian metric is frequently chosen from a two-parameter family of Sobolev metrics, called elastic metrics. Elastic metrics are especially convenient because, for several parameter choices, they are known to be locally isometric to Riemannian metrics for which one is able to solve the geodesic boundary problem explictly -- well-known examples of these local isometries include the complex square root transform of Younes, Michor, Mumford and Shah and square root velocity (SRV) transform of Srivastava, Klassen, Joshi and Jermyn. In this paper, we show that the SRV transform extends to elastic metrics for all choices of parameters, for curves in any dimension, thereby fully generalizing the work of many authors over the past two decades. We give a unified treatment of the elastic metrics: we extend results of Trouv\'{e} and Younes, Bruveris as well as Lahiri, Robinson and Klassen on the existence of solutions to the registration problem, we develop algorithms for computing distances and geodesics, and we apply these algorithms to metric learning problems, where we learn optimal elastic metric parameters for statistical shape analysis tasks