We review methods designed to compute correspondences between geometric shapes represented by triangle meshes, contours, or point sets. This survey is motivated in part by recent developments in space-time registration, where one seeks a correspondence between non-rigid and time-varying surfaces, and semantic shape analysis, which underlines a recent trend to incorporate shape understanding into the analysis pipeline. Establishing a meaningful correspondence between shapes is often difficult since it generally requires an understanding of the structure of the shapes at both the local and global levels, and sometimes the functionality of the shape parts as well. Despite its inherent complexity, shape correspondence is a recurrent problem and an essential component of numerous geometry processing applications. In this survey, we discuss the different forms of the correspondence problem and review the main solution methods, aided by several classification criteria arising from the problem definition. The main categories of classification are defined in terms of the input and output representation, objective function, and solution approach. We conclude the survey by discussing open problems and future perspectives.

In this paper, we propose a level set method for shape-driven object extraction. We introduce a voxel-wise probabilistic level set formulation to account for prior knowledge. To this end, objects are represented in an implicit form. Constraints on the segmentation process are imposed by seeking a projection to the image plane of the prior model modulo a similarity transformation. The optimization of a statistical metric between the evolving contour and the model leads to motion equations that evolve the contour toward the desired image properties while recovering the pose of the object in the new image. Upon convergence, a solution that is similarity invariant with respect to the model and the corresponding transformation are recovered. Promising experimental results demonstrate the potential of such an approach.

Abstract — Registration and modeling of shapes are two important problems in computer vision and pattern recognition. Despite enormous progress made over the past decade, still these problems are open. In this paper, we advance the state of the art in both directions. First we consider an efficient registration method that aims to recover a one-to-one correspondence between shapes as well as measures of uncertainties driven from the data and explain the local support of the recovered transformations. To this end, a free form deformation is used to describe the deformation model that is combined with an objective function defined in the space of implicit functions used to represent shapes in 2D and 3D. Once the registration parameters have been recovered, we introduce a novel technique for model building and statistical interpretation of the training examples based on a variable bandwidth kernel approach. The support on the kernels varies spatially and is determined according to the uncertainties of the registration process. Such a technique introduces the ability to account for potential registration errors in the model. Handwritten character recognition, knowledge-based object extraction and reproduction of transitions between facial animations are examples of applications that demonstrate the potentials of the proposed framework. Index Terms — Shape registration, free form deformation, implicit shape representation, distance transforms, uncertainty, non parametric densities, variable metric kernels, region based segmentation, Gaussian mixture density estimation, facial animations. I.

In this paper, we introduce the concept of isosurface similarity maps for the visualization of volume data. Isosurface similarity maps present structural information of a volume data set by depicting similarities between individual isosurfaces quantified by a robust information-theoretic measure. Unlike conventional histograms, they are not based on the frequency of isovalues and/or derivatives and therefore provide complementary information. We demonstrate that this new representation can be used to guide transfer function design and visualization parameter specification. Furthermore, we use isosurface similarity to develop an automatic parameter-free method for identifying representative isovalues. Using real-world data sets, we show that isosurface similarity maps can be a useful addition to conventional classification techniques. Categories and Subject Descriptors (according to ACM CCS): Generation—Display algorithms I.3.3 [Computer Graphics]: Picture/Image 1.

In this paper, we examine the use of implicit shape representations for nonrigid registration of serial CT liver examinations. Using ground truth in the form of corresponding landmarks manually labeled by a radiotherapist, we carry out an experiment to determine whether nonrigid registration performs better when applied to the original image data or to images constructed from implicit representations of the liver. We compare a variety of standard regularizers (elastic, diffusion, and curvature), similarity measures (sum of squared differences and mutual information), and weighting factors, using three different implicit shape representations: the Euclidean Distance Transform, the Poisson Transform (based on the expected hitting time of a random walk), and a new transform designed to highlight concavities in the shape. Index Terms — Image registration, shape, biomedical imaging 1.

Abstract—Dendritic spines form postsynaptic contact sites in the central nervous system. The rapid and spontaneous morphology changes of spines have been widely observed by neurobiologists. Determining the relationship between dendritic spine morphology change and its functional properties such as memory learning is a fundamental yet challenging problem in neurobiology research. In this paper, we propose a novel algorithm to track the morphology change of multiple spines simultaneously in time-lapse neuronal images based on nonrigid registration and integer programming. We also propose a robust scheme to link disappearing-and-reappearing spines. Performance comparisons with other state-of-the-art cell and spine tracking algorithms, and the ground truth show that our approach is more accurate and robust, and it is capable of tracking a large number of neuronal spines in time-lapse confocal microscopy images. Index Terms—Dendritic spine, free form deformation, global similarity, integer programming, time-lapse images. I.

Dendritic spines form postsynaptic contact sites in the central nervous system. The rapid and spontaneous morphology changes of spines have been widely observed by neurobiologists. Determining the relationship between dendritic spine morphology change and its functional properties such as memory learning is a fundamental yet challenging problem in neurobiology research. In this paper, we propose a novel algorithm to track the morphology change of multiple spines simultaneously in time-lapse neuronal images based on non-rigid registration and integer programming. We also propose a robust scheme to link disappearing-and-reappearing spines. Performance comparisons with other state-of-the-art cell and spine tracking algorithms, and the ground truth show that our approach is more accurate and robust, and it is capable of tracking a large number of neuronal spines in time-lapse confocal microscopy images. 1

Abstract. We propose a novel shape and appearance based spatiotemporal constraint and combine it with a level set based deformable model, which can be used for Left Ventricle segmentation in 4D gated cardiac SPECT, particularly in the presence of perfusion defects. The model incorporates appearance in addition to shape information into a soft-tohard probabilistic constraint, and utilizes spatiotemporal regularization via a Maximum A Posteriori framework. This constraint force allows more flexibility than the rigid forces of shape constraint-only schemes, as well as other state-of-the-art joint shape and appearance constraints. We present comparative results to illustrate the improvement gain. Key words: spatiotemporal 4D segmentation, constrained deformable model, gated cardiac SPECT

We present an implicit approach for pair-wise non-rigid registration of moving and deforming objects. Shapes of interest are implicitly embedded in the 3D implicit vector space. In this implicit embedding space, registration is performed using a global-to-local framework. Firstly, a non-linear optimization functional defined on the vector distance function is used to find the global alignment between shapes. Secondly, an incremental cubic B-spline free form deformation is used to recover the non-rigid transformation parameters. Local non-rigid registration is posed in terms of minimising an energy functional, for which we give a closed-form linear system and solve it using an improved iterative Gauss-Seidel method. Our approach can consistently produce smooth and continuous registration fields, and correctly establish dense one-toone correspondences. It can naturally deal with both open partial and closed shapes, and imperfect models with gaps and noise, through its use of the implicit vector representation. Experimental results on several datasets demonstrate the robustness of the proposed method.

We present a review of the correspondence problem and its solution methods, targeting the computer graphics audience. With this goal in mind, we focus on the correspondence of geometric shapes represented by point sets, contours or triangle meshes. This survey is motivated by recent developments in the field such as those requiring the correspondence of non-rigid or time-varying surfaces and a recent trend towards semantic shape analysis, of which shape correspondence is one of the central tasks. Establishing a meaningful shape correspondence is a difficult problem since it typically relies on an understanding of the structure of the shapes in question at both a local and global level, and sometimes also the shapes ’ functionality. However, despite its inherent complexity, shape correspondence is a recurrent problem and an essential component in numerous geometry processing applications. In this report, we discuss the different forms of the correspondence problem and review the main solution methods, aided by several classification criteria which can be used by the reader to objectively compare the methods. We finalize the report by discussing open problems and future perspectives. 1.