Cuckoo Search with Lévy Flights for Weighted Bayesian Energy Functional Optimization in Global-Support Curve Data Fitting

ABSTRACT. The problem of data fitting is very important in many theoretical and applied fields. In this paper, we consider the problem of optimizing a weighted Bayesian energy functional for data fitting by using global-support approximating curves. By global-support curves we mean curves expressed as a linear combination of basis functions whose support is the whole domain of the problem, as opposed to other common approaches in CAD/CAM and computer graphics driven by piecewise functions (such as B-splines and NURBS) that provide local control of the shape of the curve. Our method applies a powerful nature-inspired metaheuristic algorithm called cuckoo search, introduced recently to solve optimization problems. A major advantage of this method is its simplicity: cuckoo search requires only two parameters, many fewer than other metaheuristic approaches, so the parameter tuning becomes a very simple task.The paper shows that this new approach can be successfully used to solve our optimization problem. To check the performance of our approach, it has been applied to five illustrative examples of different types, including open and closed 2D and 3D curves that exhibit challenging features, such as cusps and self-intersections. Our results show that the method performs pretty well, being able to solve our minimization problem in an astonishingly straightforward way.This research has been kindly supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project Ref. no. TIN2012-30768, Toho University (Funabashi, Japan), and the University of Cantabria (Santander, Spain)

Toward Controllable and Robust Surface Reconstruction from Spatial Curves

Reconstructing surface from a set of spatial curves is a fundamental problem in computer graphics and computational geometry. It often arises in many applications across various disciplines, such as industrial prototyping, artistic design and biomedical imaging. While the problem has been widely studied for years, challenges remain for handling different type of curve inputs while satisfying various constraints. We study studied three related computational tasks in this thesis. First, we propose an algorithm for reconstructing multi-labeled material interfaces from cross-sectional curves that allows for explicit topology control. Second, we addressed the consistency restoration, a critical but overlooked problem in applying algorithms of surface reconstruction to real-world cross-sections data. Lastly, we propose the Variational Implicit Point Set Surface which allows us to robustly handle noisy, sparse and non-uniform inputs, such as samples from spatial curves

Cuckoo Search with Lévy Flights for Weighted Bayesian Energy Functional Optimization in Global-Support Curve Data Fitting

The problem of data fitting is very important in many theoretical and applied fields. In this paper, we consider the problem of optimizing a weighted Bayesian energy functional for data fitting by using global-support approximating curves. By global-support curves we mean curves expressed as a linear combination of basis functions whose support is the whole domain of the problem, as opposed to other common approaches in CAD/CAM and computer graphics driven by piecewise functions (such as B-splines and NURBS) that provide local control of the shape of the curve. Our method applies a powerful nature-inspired metaheuristic algorithm called cuckoo search, introduced recently to solve optimization problems. A major advantage of this method is its simplicity: cuckoo search requires only two parameters, many fewer than other metaheuristic approaches, so the parameter tuning becomes a very simple task. The paper shows that this new approach can be successfully used to solve our optimization problem. To check the performance of our approach, it has been applied to five illustrative examples of different types, including open and closed 2D and 3D curves that exhibit challenging features, such as cusps and self-intersections. Our results show that the method performs pretty well, being able to solve our minimization problem in an astonishingly straightforward way

A Survey of Surface Reconstruction from Point Clouds

International audienceThe area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contains a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece-wise smooth representation of the original shape, recent work has taken on more specialized priors to address significantly challenging data imperfections, where the reconstruction can take on different representations – not necessarily the explicit geometry. We survey the field of surface reconstruction, and provide a categorization with respect to priors, data imperfections, and reconstruction output. By considering a holistic view of surface reconstruction, we show a detailed characterization of the field, highlight similarities between diverse reconstruction techniques, and provide directions for future work in surface reconstruction

Surface Reconstruction from Unorganized Point Cloud Data via Progressive Local Mesh Matching

This thesis presents an integrated triangle mesh processing framework for surface reconstruction based on Delaunay triangulation. It features an innovative multi-level inheritance priority queuing mechanism for seeking and updating the optimum local manifold mesh at each data point. The proposed algorithms aim at generating a watertight triangle mesh interpolating all the input points data when all the fully matched local manifold meshes (umbrellas) are found. Compared to existing reconstruction algorithms, the proposed algorithms can automatically reconstruct watertight interpolation triangle mesh without additional hole-filling or manifold post-processing. The resulting surface can effectively recover the sharp features in the scanned physical object and capture their correct topology and geometric shapes reliably. The main Umbrella Facet Matching (UFM) algorithm and its two extended algorithms are documented in detail in the thesis. The UFM algorithm accomplishes and implements the core surface reconstruction framework based on a multi-level inheritance priority queuing mechanism according to the progressive matching results of local meshes. The first extended algorithm presents a new normal vector combinatorial estimation method for point cloud data depending on local mesh matching results, which is benefit to sharp features reconstruction. The second extended algorithm addresses the sharp-feature preservation issue in surface reconstruction by the proposed normal vector cone (NVC) filtering. The effectiveness of these algorithms has been demonstrated using both simulated and real-world point cloud data sets. For each algorithm, multiple case studies are performed and analyzed to validate its performance

Optical measurement and signal evaluation relating to particulate properties during purification of biological suspensions

The variable nature of conditions in downstream processing operations in biotechnological and other areas necessitates the on-line monitoring of process variables for rapid analysis and possibly subsequent control to optimise yield in a multi-stage purification process. Optical measurement of such parameters offers a fast and non-invasive method to interrogate the process with the added advantage of the possibility to construct a robust, miniaturised measurement system using modern optical components. The problems encountered are turbulent and turbid conditions which are usually unsuitable for light scattering measurements. Also access to the process stream is often not simple and a method of automatic sampling must be employed. This thesis describes the application of dynamic light scattering to downstream processing operations and particularly to the measurement of virus-like particles and separation from their yeast host. The construction of a miniaturised dynamic light scattering system is also described. Several data analysis methods are assessed with a view to using them in a rapid analysis configuration. Most of the methods require moderate processing power but consideration is given to extensions to the standard techniques to apply them in a parallel processing environment which today is on the increase. The improvement of the convergence of such routines is discussed with the addition of prior information. A particular area of interest is the rapid sample preparation required before analysis by light scattering to improve the data quality. Large particulate material is usually not tolerated well in this method of measurement and should be removed. A technique is described and tested which facilitates rapid in-situ sample preparation and optical analysis. Otherwise sample preparation is carried out prior to analysis. As well as a dynamic light scattering study, an overview of optical measurement by other means in yeast-based systems is discussed with a view to optimising the system configuration

Enforcing Temporal Consistency in Physically Constrained Flow Field Reconstruction with FlowFit by Use of Virtual Tracer Particles

Processing techniques for particle based optical flow measurement data such as 3D Particle Tracking Velocimetry (PTV) or the novel dense Lagrangian Particle Tracking method Shake-The-Box (STB) can provide time-series of velocity and acceleration information scattered in space. The following post-processing is key to the quality of space-filling velocity and pressure field reconstruction from the scattered particle data. In this work we describe a straight-forward extension of the recently developed data assimilation scheme FlowFit, which applies physical constraints from the Navier-Stokes equations in order to simultaneously determine velocity and pressure fields as solutions to an inverse problem. We propose the use of additional artificial Lagrangian tracers (virtual particles), which are advected between the flow fields at single time instants to achieve meaningful temporal coupling. This is the most natural way of a temporal constraint in the Lagrangian data framework. Not FlowFit's core method is altered in the current work, but its input in form of Lagrangian tracks. This work shows that the introduction of such particle memory to the reconstruction process significantly improves the resulting flow fields. The method is validated in virtual experiments with two independent DNS test cases. Several contributions are revised to explain the improvements, including correlations of velocity and acceleration errors in the reconstructions and the flow field regularization within the inverse problem