Giuseppe Patanè

Mesh Segmentation - A Comparative Study

Mesh segmentation has become an important component in many applications in computer graphics. In the last several years, many algorithms have been proposed in this growing area, offering a diversity of methods and various evaluation criteria. This paper provides a comparative study of some of the latest algorithms and results, along several axes. We evaluate only algorithms whose code is available to us, and thus it is not a comprehensive study. Yet, it sheds some light on the vital properties of the methods and on the challenges that future algorithms should face

The enhanced LBG algorithm

Clustering applications cover several fields such as audio and video data compression, pattern recognition, computer vision, medical image recognition, etc. In this paper, we present a new clustering algorithm called Enhanced LBG (ELBG). It belongs to the hard and K-means vector quantization groups and derives directly from the simpler LBG. The basic idea we have developed is the concept of utility of a codeword, a powerful instrument to overcome one of the main drawbacks of clustering algorithms: generally, the results achieved are not good in the case of a bad choice of the initial codebook. We will present our experimental results showing the ELBG is able to find better codebooks than previous clustering techniques and the computational complexity is virtually the same as the simpler LBG.

Parallel CRC realization

This paper presents a theoretical result in the context of realizing high-speed hardware for parallel CRC checksums. Starting from the serial implementation widely reported in the literature, we have identified a recursive formula from which our parallel implementation is derived. In comparison with previous works, the new scheme is faster and more compact and is independent of the technology used in its realization. In our solution, the number of bits processed in parallel can be different from the degree of the polynomial generator. Last, we have also developed high-level parametric codes that are capable of generating the circuits autonomously when only the polynomial is given.

Blowing Bubbles for Multi-Scale Analysis and Decomposition of Triangle Meshes

Abstract Tools for the automatic decomposition of a surface into shape features will facilitate the editing, matching, texturing, morphing, compression and simplification of three-dimensional shapes. Different features, such as flats, limbs, tips, pits and various blending shapes that transition between them, may be characterized in terms of local curvature and other differential properties of the surface or in terms of a global skeletal organization of the volume it encloses. Unfortunately, both solutions are extremely sensitive to small perturbations in surface smoothness and to quantization effects when they operate on triangulated surfaces. Thus, we propose a multi-resolution approach, which not only estimates the curvature of a vertex over neighborhoods of variable size, but also takes into account the topology of the surface in that neighborhood. Our approach is based on blowing a spherical bubble at each vertex and studying how the intersection of that bubble with the surface evolves. We describe an efficient approach for computing these characteristics for a sampled set of bubble radii and for using them to identify features, based on easily formulated filters, that may capture the needs of a particular application.

Archeomagnetic dating of Mediterranean volcanics of the last 2100 years: validity and limits

Abstract Archeomagnetic dating developed at St. Maur laboratory has been applied to the Mediterranean volcanoes Etna, Vesuvius and Ischia. The method involves samples from lava flows or high temperature emplaced pyroclasts (welded scoriae, pumice, etc.) weighing 0.5–1 kg each, that allows reaching a precision of a few tenths of a degree on the direction of their thermoremanent magnetization, and hence a semi-angle of the Fisher 95% confidence cone between 0.6 and 1.8° for every volcanic unit. Among the factors reducing precision on the mean magnetic direction, the most important appears to be a distortion of the ambient field induced by magnetization of the cooling lava, which means that a number of samples should be collected over a large area. Age determination is based upon similarity between variation curves of the Direction of Earth’s Magnetic Field (DEMF) reconstructed in France from 120 well-dated archeological sites, and on Italian volcanoes from historically dated eruptions. A total of 63 lava flows and pyroclastic units, such as cinder cones or nuee ardente deposits, are shown to be dated with an overall precision of ±40 years for the last 1500 years, and ±50 to ±100 years from AD 500 to 150 BC, this lesser precision resulting from both an increasing uncertainty on the shape of the DEMF curve and a smaller variation of the DEMF itself. This irregularity of the DEMF path plus an increasing number of ambiguities, related to similarity of the DEMF at different times further into the past, are the most serious limitations of the method. Though well-dated eruptions are known for the last two millennia, retrieval of their products is often misleading and about 50% of volcanics presumed of known date prior to the 17th century are in fact of older age, discrepancies usually reaching several hundreds of years. Owing to good agreement between the DEMF curves of France and southern Italy, the method may confidently be extended to volcanic materials from the whole of Mediterranean Europe, provided there are firm constraints that they were erupted within the last 2100 years.

3D Shape Matching through Topological Structures

This paper introduces a framework for the matching of 3D shapes represented by topological graphs. The method proposes as comparison algorithm an error tolerant graph isomorphism that includes a structured process for identifying matched areas on the input objects. Finally, we provide a series of experiments showing its capability to automatically compare complex objects starting from different skeletal representations used in Shape Modeling.

Spectral-Driven Isometry-Invariant Matching of 3D Shapes

This paper presents a matching method for 3D shapes, which comprises a new technique for surface sampling and two algorithms for matching 3D shapes based on point-based statistical shape descriptors. Our sampling technique is based on critical points of the eigenfunctions related to the smaller eigenvalues of the Laplace-Beltrami operator. These critical points are invariant to isometries and are used as anchor points of a sampling technique, which extends the farthest point sampling by using statistical criteria for controlling the density and number of reference points. Once a set of reference points has been computed, for each of them we construct a point-based statistical descriptor (PSSD, for short) of the input surface. This descriptor incorporates an approximation of the geodesic shape distribution and other geometric information describing the surface at that point. Then, the dissimilarity between two surfaces is computed by comparing the corresponding sets of PSSDs with bipartite graph matching or measuring the L1-distance between the reordered feature vectors of a proximity graph. Here, the reordering is given by the Fiedler vector of a Laplacian matrix associated to the proximity graph. Our tests have shown that both approaches are suitable for online retrieval of deformed objects and our sampling strategy improves the retrieval performances of isometry-invariant matching methods. Finally, the approach based on the Fiedler vector is faster than using the bipartite graph matching and it has a similar retrieval effectiveness.

Three-dimensional P-wave velocity structure of Mt. Etna, Italy

The three-dimensional P-wave velocity structure of Mt. Etna is determined to depths of 15 km by tomographic inversion of first arrival times from local earthquakes recorded by a network of 29 permanent and temporary seismographs. Results show a near-vertical low-velocity zone that extends from beneath the central craters to a depth of 10 km. This low-velocity region is coincident with a band of steeply-dipping seismicity, suggesting a magmatic conduit that feeds the summit eruptions. The most prominent structure is an approximately 8-km-diameter high-velocity body located between 2 and 12 km depth below the southeast flank of the volcano. This high-velocity body is interpreted as a remnant mafic intrusion that is an important structural feature influencing both volcanism and east flank slope stability and faulting.

What’s in an image?

There are many possible 2D views of a given 3D object and most people would agree that some views are more aesthetic and/or more “informative” than others. Thus, it would be very useful, in many applications, to be able to automatically compute these “best” views. Although all measures of the quality of a view will ultimately be subjective, hence difficult to quantify, we propose some general principles which may be used to address this challenge. In particular, we describe a number of different ways to measure the goodness of a view, and show how to optimize these measures by reducing the size of the search space.

Seismic tomography of Etna volcano

Abstract A 3-D velocity model beneath Etna volcano has been obtained through inversion of P-wave arrivals of local earthquakes. About 300 seismic events distributed around this volcano from surface up to a depth of 20 km have been used to infer the P-wave velocity structure. High P-wave velocity bodies have been found in the upper portion of the volcanic edifice, in a region where positive values of Bouguer anomalies have previously been found. Low-velocity bodies are identified at depths lower than 10 km and may be related to magmatic reservoirs. The spatial pattern of these deeper velocity anomalies appears to be correlated at surface with the distribution of spatter cones. In the NW quadrant, a high-velocity anomaly is correlated to the presence of a deeper seismicity. The distribution of relocated hypocenters is not homogeneous but shows some features apparently related to the presence of magmatic bodies.