Level Set Representations, the pioneering framework introduced by Osher and Sethian [14] is the most common choice for the implementation of variational frameworks in Computer Vision since it is implicit, intrinsic, parameter and topology free. However, many Computer vision applications refer to entities with physical meanings that follow a shape form with a certain degree of variability. In this paper, we propose a novel energetic form to introduce shape constraints to level set representations. This formulation exploits all advantages of these representations resulting on a very elegant approach that can deal with a large number of parametric as well as continuous transformations. Furthermore, it can be combined with existing well known level set-based segmentation approaches leading to paradigms that can deal with noisy, occluded and missing or physically corrupted data. Encouraging experimental results are obtained using synthetic and real images.

this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is simpler than traditional shape matching methods that require pose registration, feature correspondence, or model fitting

Abstract not found

In this paper, we describe a novel method for searching and comparing 3D objects. The method encodes the geometric and topological information in the form of a skeletal graph and uses graph matching techniques to match the skeletons and to compare them. The skeletal graphs can be manually annotated to refine or restructure the search. This helps in choosing between a topological similarity and a geometric (shape) similarity. A feature of skeletal matching is the ability to perform part-matching, and its inherent intuitiveness, which helps in defining the search and in visualizing the results. Also, the matching results, which are presented in a per-node basis can be used for driving a number of registration algorithms, most of which require a good initial guess to perform registration. In this paper, we also describe a visualization tool to aid in the selection and specification of the matched objects.

This paper presents an algorithm for full 3D shape reconstruction of indoor and outdoor environments with mobile robots. Data is acquired by a fastmoving robot equipped with two 2D laser range finders. Our approach combines an efficient scan matching routine for robot pose estimation with an algorithm for approximating environments using flat surfaces. On top of that, our approach includes a mesh simplification technique to reduce the complexity of the resulting models. In extensive experiments, our method is shown to produce accurate models of indoor and outdoor environments that compare favorably to other methods.

Abstract not found

Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists.

We present a novel variational and statistical approach for shape registration. Shapes of interest are implicitly embedded in a higher dimensional space of distance transforms. In this implicit embedding space, registration is formulated in a hierarchical manner: the Mutual Information criterion supports various transformation models and is optimized to perform global registration; then a B-spline based Incremental Free Form Deformations (IFFD) model is used to minimize a Sum-of-Squared-Differences (SSD) measure and further recover a dense local nonrigid registration field. The key advantage of such framework is twofold: (1) it naturally deals with shapes of arbitrary dimension (2D, 3D or higher) and arbitrary topology (multiple parts, closed/open), and (2) it preserves shape topology during local deformation, and produces local registration fields that are smooth, continuous and establish one-to-one correspondences. Its invariance to initial conditions is evaluated through empirical validation, and various hard 2D/3D geometric shape registration examples are used to show its robustness to noise, severe occlusion and missing parts. We demonstrate the power of the proposed framework using two applications: one for statistical modeling of anatomical structures, another for 3D face scan registration and expression tracking. We also compare the performance of our algorithm with that of several other well-known shape registration algorithms.

The generalized Hough transform constitutes a wellknown approach to object recognition and pose detection. To attain reliable detection results, however, a very large number of candidate object poses and scale factors need to be considered. In this paper we employ an inexpensive, consumer-market graphics card as the "poor man's" parallel processing system. We describe the implementation of a fast and enhanced version of the generalized Hough transform on graphics hardware. Thanks to the high bandwidth of on-board texture memory, a single pose can be evaluated in less than 3 ms, independent of the number of edge pixels in the image. From known object geometry, our hardwareaccelerated generalized Hough transform algorithm is capable of detecting an object's 3D pose, scale, and position in the image within less than one minute.

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.