Recent developments in techniques for modeling, digitizing and visualizing 3D shapes has led to an explosion in the number of available 3D models on the Internet and in domain-specific databases. This has led to the development of 3D shape retrieval systems that, given a query object, retrieve similar 3D objects. For visualization, 3D shapes are often represented as a surface, in particular polygonal meshes, for example in VRML format. Often these models contain holes, intersecting polygons, are not manifold, and do not enclose a volume unambiguously. On the contrary, 3D volume models, such as solid models produced by CAD systems, or voxels models, enclose a volume properly. This paper surveys the literature on methods for content based 3D retrieval, taking into account the applicability to surface models as well as to volume models. The methods are evaluated with respect to several requirements of content based 3D shape retrieval, such as: (1) shape representation requirements, (2) properties of dissimilarity measures, (3) efficiency, (4) discrimination abilities, (5) ability to perform partial matching, (6) robustness, and (7) necessity of pose normalization. Finally, the advantages and limits of the several approaches in content based 3D shape retrieval are discussed. 1.

The automatic co-registration of point clouds, representing 3D surfaces, is a relevant problem in 3D modeling. This multiple registration problem can be defined as a surface matching task. We treat it as least squares matching of overlapping surfaces. The surface may have been digitized/sampled point by point using a laser scanner device, a photogrammetric method or other surface measurement techniques. Our proposed method estimates the transformation parameters of one or more 3D search surfaces with respect to a 3D template surface, using the Generalized Gauss-Markoff model, minimizing the sum of squares of the Euclidean distances between the surfaces. This formulation gives the opportunity of matching arbitrarily oriented 3D surface patches. It fully considers 3D geometry. Besides the mathematical model and execution aspects we address the further extensions of the basic model. We also show how this method can be used for curve matching in 3D space and matching of curves to surfaces. Some practical examples based on the registration of close-range laser scanner and photogrammetric point clouds are presented for the demonstration of the method. This surface matching technique is a generalization of the least squares image matching concept and offers high flexibility for any kind of 3D surface correspondence problem, as well as statistical tools for the analysis of the quality of final matching results.

This paper presents a method for automatically registering multiple three dimensional (3D) data sets. Previous approaches required manual specification of initial pose estimates or relied on external pose measurement systems. In contrast, our method does not assume any knowledge of initial poses or even which data sets overlap. Our automatic registration algorithm begins by converting the input data into surface meshes, which are pair-wise registered using a surface matching engine. The resulting matches are tested for surface consistency, but some incorrect matches may be locally undetectable. A global optimization process searches a graph constructed from these potentially faulty pair-wise matches for a connected sub-graph containing only correct matches, employing a global consistency measure to detect incorrect, but locally consistent matches. From this sub-graph, the final poses of all views can be computed directly. We apply our algorithm to the problem of 3D digital reconstruction of real world objects and show results for a collection of automatically digitized objects.

The development of effective content-based multimedia search systems is an important research issue due to the growing amount of digital audio-visual information. In the case of images and video, the growth of digital data has been observed since the introduction of 2D capture devices. A similar development is expected for 3D data as

Due to the recent improvements in laser scanning technology, 3D visualization and modelling, there is an increasing need for tools supporting the automatic search for 3D objects in archives. In this paper we describe a new geometric approach to 3D shape comparison and retrieval for arbitrary objects described by 3D polyhedral models that may contain gaps. In contrast with existing approaches, our approach takes the overall relative spatial location into account by representing the 3D shape as a weighted point set. To compare two objects geometrically we first apply principal components analysis to bring the objects in a standard pose, and enclose each object by a 3D grid. Then we generate for each object a signature representing a weighted point set, that contains for each non-empty grid cell a salient point. We compare three methods to select in each grid cell a salient point and a weight: (1) choose the vertex in the cell with the highest Gaussian curvature, and choose as weight a measure for that curvature, (2) choose the area-weighted mean of the vertices in the cell, and choose as weight a measure denoting the normal variation of the facets in the cell and (3) choose the centre of mass of all vertices in the cell, and choose as weight one. Finally, we compute the similarity between two shapes by comparing their signatures using a new shape similarity measure based on weight transportation that is a variation on the Earth Mover's Distance. Unlike the Earth Mover's Distance, the new shape similarity measure satisfies the triangle inequality.

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In this article we present the integration of 3-D shape knowledge into a variational model for level set based image segmentation and tracking. Given a 3-D surface model of an object that is visible in the image of one or multiple cameras calibrated to the same world coordinate system, the object contour extracted by the segmentation method is applied to estimate the 3-D pose parameters of the object. Vice-versa, the surface model projected to the image plane helps in a top-down manner to improve the extraction of the contour. While common alternative segmentation approaches, which integrate 2-D shape knowledge, face the problem that an object can look very differently from various viewpoints, a 3-D free form model ensures that for each view the model can fit the data in the image very well. Moreover, one additionally solves the higher level problem of determining the object pose in 3-D space. Due to the variational formulation, the approach clearly states all model assumptions in a single energy functional that is locally minimized by our method. Its performance is demonstrated by experiments with a monocular and a stereo camera system. 1 1

This paper explores a view-based approach to recognize free-form objects in range images. We are using a set of local features that are easy to calculate and robust to partial occlusions. By combining those features in a multidimensional histogram, we can obtain highly discriminant classifiers without the need for segmentation. Recognition is performed using either histogram matching or a probabilistic recognition algorithm. We compare the performance of both methods in the presence of occlusions and test the system on a database of almost 2000 full-sphere views of 30 free-form objects. The system achieves a recognition accuracy above 93% on ideal images, and of 89% with 20% occlusion.

A statistical representation of three-dimensional shapes is introduced, based on a novel four-dimensional feature. The feature parameterizes the intrinsic geometrical relation of an oriented surface-point pair. The set of all such features represents both local and global characteristics of the surface. We compress this set into a histogram. A database of histograms, one per object, is sampled in a training phase. During recognition, sensed surface data, as may be acquired by stereo vision, a laser range-scanner, etc., are processed and compared to the stored histograms. We evaluate the match quality by six different criteria that are commonly used in statistical settings. Experiments with artificial data containing varying levels of noise and occlusion of the objects show that Kullback-Leibler and likelihood matching yield robust recognition rates. The present study proposes histograms of the geometric relation between two oriented surface points (surflets) as a compact yet distinctive representation of arbitrary three-dimensional shapes.

We consider the use of medial surfaces to represent symmetries of 3-D objects. This allows for a qualitative abstraction based on a directed acyclic graph of components and also a degree of invariance to a variety of transformations including the articulation of parts. We demonstrate the use of this representation for 3-D object model retrieval. Our formulation uses the geometric information