3D Object Comparison Based on Shape Descriptors

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Comparing Features of Three-Dimensional Object Models Using Registration Based on Surface Curvature Signatures

This dissertation presents a technique for comparing local shape properties for similar three-dimensional objects represented by meshes. Our novel shape representation, the curvature map, describes shape as a function of surface curvature in the region around a point. A multi-pass approach is applied to the curvature map to detect features at different scales. The feature detection step does not require user input or parameter tuning. We use features ordered by strength, the similarity of pairs of features, and pruning based on geometric consistency to efficiently determine key corresponding locations on the objects. For genus zero objects, the corresponding locations are used to generate a consistent spherical parameterization that defines the point-to-point correspondence used for the final shape comparison

A feature-based shape similarity assessment framework

The popularity of 3D CAD systems is resulting in a large number of CAD models being generated. Availability of these CAD models is opening up new ways in which information can be archived, analyzed, and reused. 3D geometric information is one of the main components of CAD models. Therefore shape similarity assessment is a fundamental geometric reasoning problem that finds several different applications. In many design and manufacturing applications, the gross shape of the 3D parts does not play an important role in the similarity assessment. Instead certain attributes of part features play a dominant role in determining the similarity between two parts. Different feature-based models are usually created using their own coordinate systems. Therefore, feature-based shape similarity assessment involves finding the optimal alignment transformations for two sets of feature vectors. The optimal alignment corresponds to the minimum value of a distance function that is computed between the two sets of feature vectors being aligned. In order to compute the distance function the closest neighbor to each feature vector needs to be identified. We have developed optimal feature alignment algorithms based on the partitioning of the transformation space into regions such that the closest neighbors are invariant within each region. These algorithms can work with customizable distance functions. We have shown that they have polynomial time complexity. For higher dimension transformation spaces it is harder to design algorithms based on the partitioning of transformation spaces because the data structures involved are very complex. In those cases, feature alignment algorithms based on iterative strategies have been developed. Iterative strategies make use of optimal feature alignment algorithms based on the partitioning of lower dimension transformation spaces. Extensive experiments have been carried out to provide empirical evidence that iterative strategies can find the optimal solution for feature alignment problems. A feature-based shape similarity analysis framework has been built based on the feature alignment algorithms. This framework has been demonstrated with the two following applications. A machining feature based alignment algorithm has been developed to automatically search databases for parts that are similar to a newly designed part in terms of machining features. We expect that the retrieved parts can be used as a basis to perform cost estimation of the newly designed part. A surface feature based alignment algorithm has been developed to automatically search databases for parts that are similar to a newly designed part in terms of surface features. We expect that the retrieved parts can be used as a basis to choose the most appropriate tool maker for the newly designed part. We believe that the feature-based shape similarity assessment algorithms developed in this thesis will provide the foundations for designing new feature-based shape similarity algorithms that will enable designers to efficiently retrieve archived geometric information. We expect that these tools will facilitate information reuse and therefore decrease product development time and cost

3D Shape Similarity Through Structural Descriptors

Due to the recent improvements to 3D object acquisition, visualization and modeling techniques, the number of 3D models available is more and more growing, and there is an increasing demand for tools supporting the automatic search for 3D objects and their sub-parts in digital archives. Whilst there are already techniques for rapidly extracting knowledge from massive volumes of texts (like Google [htt]) it is harder to structure, filter, organize, retrieve and maintain archives of digital shapes like images, 3D objects, 3D animations and virtual or augmented reality. This situations suggests that in the future a primary challenge in computer graphics will be how to find models having a similar global and/or local appearance. Shape descriptors and the methodologies used to compare them, occupy an important role for achieving this task. For this reason a first contribution of this thesis is to provide a critical analysis of the most representative geometric and structural shape descriptors with respect to a set of properties that shape descriptors should have. This analysis is targeted at highlighting the differences between descriptors in order to better understand where a descriptor fails and another succeed. As a second contribution, the thesis investigates the problem of using a structural descriptor for shape comparison purposes. A large class of structural shape descriptors can be easily encoded as directed, a-cyclic and attributed graphs, thus the problem of comparing structural descriptors is approached as a graph matching problem. The techniques used for graph comparison have an exponential computational complexity and it is therefore necessary to define an algorithmic approximation of the optimal solution. The methods for structural descriptors comparison, commonly used in the computer graphics community, consist of heuristic graph matching algorithms for specific application tasks, while it is lacking a general approach suitable for incorporating different heuristics applicable in different application tasks. The second contribution presented in this thesis is aimed at defining a framework for expressing the optimal algorithm for the computation of the maximal common subgraph in a formalization which makes it straightforward usable for plugging heuristics in it, in order to achieving different approximations of the optimal solution according to the specific case. Implemented heuristics for robust graph matching with respect to graph structural noise are discussed and experimented on sub-part correspondence between similar 3D objects, and shape retrieval application with respect to different structural graph descriptors

Scale-Space Representation of 3D Models and Topological Matching

Reeb graphs have been shown to be effective for topology matching of 3D objects. Their effectiveness breaks down, however, when the individual models become very geometrically and topologically detaileas is the case for complex machined parts. The result is that Reeb graph techniques, as developed for matching general shape and computer graphics models, produce poor results when directly applied to create engineering databases