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

Hierarchical Object Parsing from Structured Noisy Point Clouds

Object parsing and segmentation from point clouds are challenging tasks because the relevant data is available only as thin structures along object boundaries or other features, and is corrupted by large amounts of noise. To handle this kind of data, flexible shape models are desired that can accurately follow the object boundaries. Popular models such as Active Shape and Active Appearance models lack the necessary flexibility for this task, while recent approaches such as the Recursive Compositional Models make model simplifications in order to obtain computational guarantees. This paper investigates a hierarchical Bayesian model of shape and appearance in a generative setting. The input data is explained by an object parsing layer, which is a deformation of a hidden PCA shape model with Gaussian prior. The paper also introduces a novel efficient inference algorithm that uses informed data-driven proposals to initialize local searches for the hidden variables. Applied to the problem of object parsing from structured point clouds such as edge detection images, the proposed approach obtains state of the art parsing errors on two standard datasets without using any intensity information.Comment: 13 pages, 16 figure

Optical techniques for 3D surface reconstruction in computer-assisted laparoscopic surgery

One of the main challenges for computer-assisted surgery (CAS) is to determine the intra-opera- tive morphology and motion of soft-tissues. This information is prerequisite to the registration of multi-modal patient-specific data for enhancing the surgeon’s navigation capabilites by observ- ing beyond exposed tissue surfaces and for providing intelligent control of robotic-assisted in- struments. In minimally invasive surgery (MIS), optical techniques are an increasingly attractive approach for in vivo 3D reconstruction of the soft-tissue surface geometry. This paper reviews the state-of-the-art methods for optical intra-operative 3D reconstruction in laparoscopic surgery and discusses the technical challenges and future perspectives towards clinical translation. With the recent paradigm shift of surgical practice towards MIS and new developments in 3D opti- cal imaging, this is a timely discussion about technologies that could facilitate complex CAS procedures in dynamic and deformable anatomical regions

Computer analysis of objects’ movement in image sequences: methods and applications

Computer analysis of objects’ movement in image sequences is a very complex problem, considering that it usually involves tasks for automatic detection, matching, tracking, motion analysis and deformation estimation. In spite of its complexity, this computational analysis has a wide range of important applications; for instance, in surveillance systems, clinical analysis of human gait, objects recognition, pose estimation and deformation analysis. Due to the extent of the purposes, several difficulties arise, such as the simultaneous tracking of manifold objects, their possible temporary occlusion or definitive disappearance from the image scene, changes of the viewpoints considered in images acquisition or of the illumination conditions, or even nonrigid deformations that objects may suffer in image sequences. In this paper, we present an overview of several methods that may be considered to analyze objects’ movement; namely, for their segmentation, tracking and matching in images, and for estimation of the deformation involved between images.This paper was partially done in the scope of project “Segmentation, Tracking and Motion Analysis of Deformable (2D/3D) Objects using Physical Principles”, with reference POSC/EEA-SRI/55386/2004, financially supported by FCT -Fundação para a Ciência e a Tecnologia from Portugal. The fourth, fifth and seventh authors would like to thank also the support of their PhD grants from FCT with references SFRH/BD/29012/2006, SFRH/BD/28817/2006 and SFRH/BD/12834/2003, respectively