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

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.     

The solid-state rearrangement of the Wells-Dawson K6P2W18O62·10H2O to a stable Keggin-type heteropolyanion phase: a catalyst for the selective oxidation of isobutane to isobutene

The thermal and structural stability of the Wells-Dawson-type heteropoly compound K₆P₂W₁₈O₆₂·10H₂O was examined by FT-IR spectroscopy, X-ray powder diffraction, thermogravimetric analysis and HRTEM. It was found that calcination at temperatures higher than 850 K led to the formation of a Keggin-type compound K₃PW₁₂O₄₀, containing small amounts of an additional phase originated from the high-temperature interaction between potassium phosphate (K₃PO₄ formed during the decomposition of the K₆P₂W₁₈O₆₂·10H₂O) and the Keggin-type compound itself. The Keggin-type product showed a higher activity in the selective oxidative dehydrogenation of isobutane to isobutene compared to both the Wells-Dawson precursor and to pure, authentic K₃PW₁₂O₄₀. This higher activity can be tentatively attributed to the presence of an amorphous layer of unknown stoichiometry at the surface of the thermally rearranged Wells-Dawson compound.     

Linking the von Kries model to Wien’s law for the estimation of an illuminant invariant image

Modeling the color variation due to an illuminant change is an important task for many computer vision applications, like color constancy, object recognition, shadow removal and image restoration. The von Kries diagonal model and Wien’s law are widely assumed by many algorithms for solving these problems. In this work we combine these two hypotheses and we show that under Wien’s law, the parameters of the von Kries model are related to each other through the color temperatures of the illuminants and the spectral sensitivities of the acquisition device. Based on this result, we provide a method for estimating some camera cues that are used to compute the illuminant invariant intrinsic image proposed by Finlayson and others. This is obtained by projecting the log-chromaticities of an input color image onto a vector depending only on the spectral cues of the acquisition device.     

Computer-aided detection of lung nodules based on decision fusion techniques

We adopted decision fusion techniques to develop a computer-aided detection (CAD) system for automatic detection of pulmonary nodules in low-dose CT images. Two distinct phases, aimed, respectively, at detecting volumes of interests (VOIs) within the CT scan, and at classifying VOIs into nodules and non-nodules, were considered. Three algorithms, namely thresholding, region growing and robust fuzzy clustering, were used as VOI detectors. For the classification phase, we built multi-classifier systems, which aggregate the decisions of three statistical classifiers, a neural network and a decision tree. Finally, the receiver operating characteristic convex hull method was used to build the final classifier, which results to be the aggregation of the best local behaviors of both classifiers and combiners. All the CAD modules were tested on CT scans analyzed by two expert radiologists. In the experiments, we achieved a sensitivity of 92.5% against a specificity of 83.5%.     

Nexus 2012: Relationships Between Architecture and Mathematics

The ninth edition of the biennial conference series “Nexus: Relationships Between Architecture and Mathematics” took place at the Politecnico di Milan in June 2012. There are many connections between architecture and mathematics: mathematic principles may be used as a basis for an architectural design, or as a tool for analyzing an existing monument; architecture may be a concrete expression of mathematical ideas, becoming, in a sense, “visual mathematics”. The purpose of the Nexus conference series is to bring together all those working with ideas related to both architecture and mathematics, and to allow researchers to exchange ideas first-hand. Papers presented at the conference are published in the Nexus Network Journal, providing a permanent archive of studies in architecture and mathematics, and in 2012 a special volume of papers from the Ph.D. Day and the poster session was published.     

Allocation and scheduling of Conditional Task Graphs

We propose an original, complete and efficient approach to the allocation and scheduling of Conditional Task Graphs (CTGs). In CTGs, nodes represent activities, some of them are branches and are labeled with a condition, arcs rooted in branch nodes are labeled with condition outcomes and a corresponding probability. A task is executed at run time if the condition outcomes that label the arcs in the path to the task hold at schedule execution time; this can be captured off-line by adopting a stochastic model. Tasks need for their execution either unary or cumulative resources and some tasks can be executed on alternative resources. The solution to the problem is a single assignment of a resource and of a start time to each task so that the allocation and schedule is feasible in each scenario and the expected value of a given objective function is optimized. For this problem we need to extend traditional constraint-based scheduling techniques in two directions: (i) compute the probability of sets of scenarios in polynomial time, in order to get the expected value of the objective function; (ii) define conditional constraints that ensure feasibility in all scenarios. We show the application of this framework on problems with objective functions depending either on the allocation of resources to tasks or on the scheduling part. Also, we present the conditional extension to the timetable global constraint. Experimental results show the effectiveness of the approach on a set of benchmarks taken from the field of embedded system design. Comparing our solver with a scenario based solver proposed in the literature, we show the advantages of our approach both in terms of execution time and solution quality.