Stefka Gueorguieva

3D surface reconstruction using HMH algorithm

3D surface reconstruction using the half maximum height (HMH) algorithm is a method to extract a surface of interest from a voxel data set. It is based on the original HMH method applied to each voxel of the segmented surface to reconstruct. From a 3D voxel grid, an initial segmentation is computed to extract a discrete surface of interest. For each of these voxels, HMH computes a segmentation and an orientation. The result of this step is then processed using a marching cube-like algorithm. The two major advantages of this method are the precision of the surface extraction and its non user-dependancy.

Automated trimmed iterative closest point algorithm

A novel method for automatic registration based on Iterative Closest Point (ICP) approach is proposed. This method uses geometric bounding containers to evaluate the optimum overlap rate of the data and model point sets.

Nibble meshing: incremental triangulation of non-manifold solid boundary

Abstract A computational method, called Nibble algorithm, for triangulation of non-manifold solid boundary is proposed. The algorithm is based on an incremental boundary traversal technique. The mesh generator creates a mesh element-by-element until the whole region is covered no matter the domain complexity (faces with non-convex shapes and multi-connected boundaries are treated). At each step of the algorithm, a surface boundary called active boundary is evaluated in such a way that it nibbles the surface to be triangulated. The fundamental feature of this process is the definition of an area, called influence zone , which controls the node insertion and thus avoids edge intersection tests. Further, the generated mesh is refined through an extension of the Laplacian smoothing . It allows an optimization of the smoothing quality without saturating the time complexity. A new technique for adaptive smoothing is also applied in order to speed up the mesh refinement.

Trochlear surface reconstruction and evaluation based on laser scanner acquisition

The purpose of this study is to investigate the accuracy, reproducibility and validation of linear measurements on digital reconstruction of the trochlear articular surface. Surface reconstruction is produced by a laser scanner acquisition pipeline that preserves rough data. Arc and chord measurements between chosen landmarks on physical specimens are simulated by geodesic path length evaluation on the corresponding digital models. The osteological specimens are issued from an archaeological series emerging from the “Soeurs Grises”s cemetery (medieval sample, XV-XVIII century) located in Beauvais (Oise, France).

CW complexes: topological mainframe for numerical representations of objects

Dimensionally non-homogeneous pointsets with internal structure are the focus in a consequent number of studies in both computational geometry and discrete (or digital) geometry, and lead to various practical applications in geometric modeling and computer imagery. Our motivation is to revisit the well known notion of algebraic topology, the cell CW complex, and to use it as an abstract framework for numerical representation of inhomogeneous objects. Two representational issues, respectively in non-manifold solid modeling and in discrete object boundary reconstruction, are discussed in illustration of this general setting.

A note on non-manifold object sweeping

Sweeping in a non-manifold environment is a more powerful modeling tool than its manifold counterpart. The interest towards non-manifold processing gives rise to active research in the field. Some of the proposed data structures are reported as internal representations of geometric modelers and are implemented for the realization of modeling operations. In particular with respect to non-manifold sweeping, basic ideas are given by (Ferrucci and Paoluzzi, 1993), (Paoluzzi, Bernardini, Cattani and Ferrucci, 1993), (Weiler, 1990). First due to the generality of the representation domain there are no restrictions either on the sweeping operands or on the resulting objects. Any combination of wireframes, shells and volumes could be processed. The “degenerate” cases of dimensionally non-homogeneous parts or self-intersection are also supported. Second non-manifold sweeping is a selective multi-step operation. Using traditional extrusion as an example, the elements are swept to a higher dimension. Thus a curve is swept to a shell and a face is transformed into a volume. In contrast, non-manifold sweeping allows elements to be swept in one of three ways: to a higher dimension (as the classic algorithm), to the same dimension or to remain in place. Moreover, just chosen portions of the object could be transformed while maintaining the connectivity between swept and unswept elements. Further, elements created in one step could be candidates to be swept in another step of the sweep operation. This level of generality is supported by the non-manifold environment in a quite natural and simple way.

Teaching geometric modeling algorithms and data structures through laser scanner acquisition pipeline

Experience from geometric modeling course based on a specific teaching medium, namely trochlear surface reconstruction from laser scans, its evaluation in terms of shape feature measurements and finally its instantiation through 3D printing, are presented. Laser scanner acquisition, reconstruction and 3D printing lend well to teaching general concepts in geometric modeling for several reasons. First, starting and ending with real physical 3D objects (the talus and its 3D print) provide in addition to the classical visual feedback a material feedback for correctness of treatments all over the pipeline. Second, the notion of error during each step of the pipeline is illustrated in a very intuitive way through length measurements, manual ones with callipers on the tali, and numerical ones with arc and chord lengths on the numerical reconstructions. Third, students are involved with challenging scientific problems and produce semester-long projects included in larger scaled project of cultural heritage preservation. Our believe is that this approach gives a deeper understanding of both theoretical and application issues in geometric modeling.