Visibility-Related Problems on Parallel Computational Models

Visibility-related problems find applications in seemingly unrelated and diverse fields such as computer graphics, scene analysis, robotics and VLSI design. While there are common threads running through these problems, most existing solutions do not exploit these commonalities. With this in mind, this thesis identifies these common threads and provides a unified approach to solve these problems and develops solutions that can be viewed as template algorithms for an abstract computational model. A template algorithm provides an architecture independent solution for a problem, from which solutions can be generated for diverse computational models. In particular, the template algorithms presented in this work lead to optimal solutions to various visibility-related problems on fine-grain mesh connected computers such as meshes with multiple broadcasting and reconfigurable meshes, and also on coarse-grain multicomputers. Visibility-related problems studied in this thesis can be broadly classified into Object Visibility and Triangulation problems. To demonstrate the practical relevance of these algorithms, two of the fundamental template algorithms identified as powerful tools in almost every algorithm designed in this work were implemented on an IBM-SP2. The code was developed in the C language, using MPI, and can easily be ported to many commercially available parallel computers

A design flow for performance planning : new paradigms for iteration free synthesis

In conventional design, higher levels of synthesis produce a netlist, from which layout synthesis builds a mask specification for manufacturing. Timing anal ysis is built into a feedback loop to detect timing violations which are then used to update specifications to synthesis. Such iteration is undesirable, and for very high performance designs, infeasible. The problem is likely to become much worse with future generations of technology. To achieve a non-iterative design flow, early synthesis stages should use wire planning to distribute delays over the functional elements and interconnect, and layout synthesis should use its degrees of freedom to realize those delays

A practical and robust method to compute the boundary of three-dimensional axis-aligned boxes

The union of axis-aligned boxes results in a constrained structure that is advantageous for solving certain geometrical problems. A widely used scheme for solid modelling systems is the boundary representation (Brep). We present a method to obtain the B-rep of a union of axis-aligned boxes. Our method computes all boundary vertices, and additional information for each vertex that allows us to apply already existing methods to extract the B-rep. It is based on dividing the three-dimensional problem into two-dimensional boundary computations and combining their results. The method can deal with all geometrical degeneracies that may arise. Experimental results prove that our approach outperforms existing general methods, both in efficiency and robustness.)Peer ReviewedPostprint (author’s final draft

Skeletal representations of orthogonal shapes

In this paper we present two skeletal representations applied to orthogonal shapes of R^n : the cube axis and a family of skeletal representations provided by the scale cube axis. Orthogonal shapes are a subset of polytopes, where the hyperplanes of the bounding facets are restricted to be axis aligned. Both skeletal representations rely on the L∞ metric and are proven to be homotopically equivalent to its shape. The resulting skeleton is composed of n − 1 dimensional facets. We also provide an efficient and robust algorithm to compute the scale cube axis in the plane and compare the resulting skeleton with other skeletal representations.Postprint (published version

From 3D Models to 3D Prints: an Overview of the Processing Pipeline

Due to the wide diffusion of 3D printing technologies, geometric algorithms for Additive Manufacturing are being invented at an impressive speed. Each single step, in particular along the Process Planning pipeline, can now count on dozens of methods that prepare the 3D model for fabrication, while analysing and optimizing geometry and machine instructions for various objectives. This report provides a classification of this huge state of the art, and elicits the relation between each single algorithm and a list of desirable objectives during Process Planning. The objectives themselves are listed and discussed, along with possible needs for tradeoffs. Additive Manufacturing technologies are broadly categorized to explicitly relate classes of devices and supported features. Finally, this report offers an analysis of the state of the art while discussing open and challenging problems from both an academic and an industrial perspective.Comment: European Union (EU); Horizon 2020; H2020-FoF-2015; RIA - Research and Innovation action; Grant agreement N. 68044

Shape Representation in Primate Visual Area 4 and Inferotemporal Cortex

The representation of contour shape is an essential component of object recognition, but the cortical mechanisms underlying it are incompletely understood, leaving it a fundamental open question in neuroscience. Such an understanding would be useful theoretically as well as in developing computer vision and Brain-Computer Interface applications. We ask two fundamental questions: “How is contour shape represented in cortex and how can neural models and computer vision algorithms more closely approximate this?” We begin by analyzing the statistics of contour curvature variation and develop a measure of salience based upon the arc length over which it remains within a constrained range. We create a population of V4-like cells – responsive to a particular local contour conformation located at a specific position on an object’s boundary – and demonstrate high recognition accuracies classifying handwritten digits in the MNIST database and objects in the MPEG-7 Shape Silhouette database. We compare the performance of the cells to the “shape-context” representation (Belongie et al., 2002) and achieve roughly comparable recognition accuracies using a small test set. We analyze the relative contributions of various feature sensitivities to recognition accuracy and robustness to noise. Local curvature appears to be the most informative for shape recognition. We create a population of IT-like cells, which integrate specific information about the 2-D boundary shapes of multiple contour fragments, and evaluate its performance on a set of real images as a function of the V4 cell inputs. We determine the sub-population of cells that are most effective at identifying a particular category. We classify based upon cell population response and obtain very good results. We use the Morris-Lecar neuronal model to more realistically illustrate the previously explored shape representation pathway in V4 – IT. We demonstrate recognition using spatiotemporal patterns within a winnerless competition network with FitzHugh-Nagumo model neurons. Finally, we use the Izhikevich neuronal model to produce an enhanced response in IT, correlated with recognition, via gamma synchronization in V4. Our results support the hypothesis that the response properties of V4 and IT cells, as well as our computer models of them, function as robust shape descriptors in the object recognition process

Shape representation and coding of visual objets in multimedia applications — An overview

Emerging multimedia applications have created the need for new functionalities in digital communications. Whereas existing compression standards only deal with the audio-visual scene at a frame level, it is now necessary to handle individual objects separately, thus allowing scalable transmission as well as interactive scene recomposition by the receiver. The future MPEG-4 standard aims at providing compression tools addressing these functionalities. Unlike existing frame-based standards, the corresponding coding schemes need to encode shape information explicitly. This paper reviews existing solutions to the problem of shape representation and coding. Region and contour coding techniques are presented and their performance is discussed, considering coding efficiency and rate-distortion control capability, as well as flexibility to application requirements such as progressive transmission, low-delay coding, and error robustnes