Object-space Algorithm Research Articles

A simple, efficient and versatile objective space algorithm for multiobjective integer programming

In the last years a multitude of algorithms have been proposed to solve multiobjective integer programming problems. However, only few authors offer open-source implementations. On the other hand, new methods are typically compared to code that is publicly available, even if this code is known to be outperformed. In this paper, we aim to overcome this problem by proposing a new state-of-the-art algorithm with an open-source implementation in C++. The underlying method falls into the class of objective space methods, i.e., it decomposes the overall problem into a series of scalarized subproblems that can be solved with efficient single-objective IP-solvers. It keeps the number of required subproblems small by avoiding redundancies, and it can be combined with different scalarizations that all lead to comparably simple subproblems. Our algorithm bases on previous results but combines them in a new way. Numerical experiments with up to ten objectives validate that the method is efficient and that it scales well to higher dimensional problems.

Multimodal visualization of complementary color-coded FA map and tensor glyphs for interactive tractography ROI seeding

Fiber tractography is still unique in providing detailed imaging of white matter fiber bundles and connectivity between different brain regions. For finding specific fiber bundles, the most applied technique is tracking fibers from the seeds in a region of interest (ROI) within a diffusion tensor imaging (DTI) volume, or the limitation of tracking results to the ROI. Color-encoded fractional anisotropy (FA) map derived from DTI data, neuroanatomical atlas, and anatomical T1-weighted magnetic resonance imaging (MRI) data have been proposed as complementary data to improve the placement of an ROI. Mental mapping of colors in color-encoded FA map to directions requires a cognitive process. This paper addresses the fusion of shape with color to make the ROI drawing more a perceptual rather than a cognitive task. We propose the rendering of diffusion tensors as superquadric glyphs (shape) superimposed over the standard practice consisting of a color-encoded FA map (color) co-registered to a T1-weighted MRI image (anatomical constraint). A novel object-space algorithm that can efficiently render diffusion tensor glyphs is presented. A strategy for distributing the GPU hardware workload was devised to maximize its occupancy and reduce its stall. Implementations with a compute shader, and a geometry shader are detailed comparatively. We show that our proposal outperforms other rendering solutions. Preliminary quantitative comparisons of the nerve fibers reconstructed by interactive seeding strategies with and without the glyphs suggest that the first approach is more accurate in conveying directional information.

A binary coded brain storm optimization for fault section diagnosis of power systems

Fault section diagnosis (FSD) of power systems plays an important role in power system operation. In order to quickly and accurately diagnose the fault section or sections after the occurrence of an event, a novel variant of brain storm optimization (BSO) in objective space algorithm, referred to as BCBSO (binary coded BSO), is proposed in this paper. The FSD problem is transformed into a 0–1 integer programming problem. The difference between the reported alarms and the expected states of protective relays and circuit breakers is used as the objective function. In BCBSO, each population individual is directly encoded as a binary vector and thereby the transcoding process can be avoided when solving the 0–1 integer programming problem. In addition, logical operations instead of floating operations are employed for binary strings, making the evolutionary process more convenient. In order to verify the performance of BCBSO, three test systems, i.e., the typical 4-substation power system, IEEE 118-bus system, and a practical power grid in Jilin province of China with different fault scenarios including single fault and multiple faults with failed and/or malfunctioned protective devices are employed. Six popular metaheuristic methods including ABC, BBO, DE, GA, PSO, and BSO are utilized to validate the effectiveness of BCBSO. The experimental results comprehensively demonstrate the superiority of BCBSO in terms of successful rate, diagnosis error, robustness, computation efficiency, convergence speed, and statistics. In addition, the effect of population size is investigated as well.

Locating Multiple Optima via Brain Storm Optimization Algorithms

Locating multiple optima/peaks in a single run and maintaining these found optima until the end of a run is the goal of multimodal optimization. Three variants of brain storm optimization (BSO) algorithms, which include original BSO algorithm, BSO in objective space algorithm with Gaussian random variable, and BSO in objective space algorithm with Cauchy random variable, were utilized to solve multimodal optimization problems in this paper. The experimental tests were conducted on eight benchmark problems and its applications in seven nonlinear equation system problems. The performance and effectiveness of various BSO algorithms on solving multimodal optimization problems were validated based on the experimental results. The conclusions could be made that the global search ability and solutions maintenance ability of an algorithm needs to be balanced simultaneously on solving multimodal optimization problems.

Primal and dual multi-objective linear programming algorithms for linear multiplicative programmes

Multiplicative programming problems (MPPs) are global optimization problems known to be NP-hard. In this paper, we employ algorithms developed to compute the entire set of nondominated points of multi-objective linear programmes (MOLPs) to solve linear MPPs. First, we improve our own objective space cut and bound algorithm for convex MPPs in the special case of linear MPPs by only solving one linear programme in each iteration, instead of two as the previous version indicates. We call this algorithm, which is based on Benson’s outer approximation algorithm for MOLPs, the primal objective space algorithm. Then, based on the dual variant of Benson’s algorithm, we propose a dual objective space algorithm for solving linear MPPs. The dual algorithm also requires solving only one linear programme in each iteration. We prove the correctness of the dual algorithm and use computational experiments comparing our algorithms to a recent global optimization algorithm for linear MPPs from the literature as well as two general global optimization solvers to demonstrate the superiority of the new algorithms in terms of computation time. Thus, we demonstrate that the use of multi-objective optimization techniques can be beneficial to solve difficult single objective global optimization problems.

An image-space algorithm for immersive views in 3-manifolds and orbifolds

We describe the first image-space ray-tracing algorithm to generate interior views of flat or hyperbolic 3-manifolds, orbifolds, and similar polyhedral complexes. The complexity of our algorithm is linear in the number of echoes for a given number of polygons, compared to exponential complexity for the object-space algorithm chosen as standard.

Visualizing Nonmanifold and Singular Implicit Surfaces with Point Clouds

We use octree spatial subdivision to generate point clouds on complex nonmanifold implicit surfaces in order to visualize them. The new spatial subdivision scheme only uses point sampling and an interval exclusion test. The algorithm includes a test for pruning the resulting plotting nodes so that only points in the closest nodes to the surface are used in rendering. This algorithm results in improved image quality compared to the naive use of intervals or affine arithmetic when rendering implicit surfaces, particularly in regions of high curvature. We discuss and compare CPU and GPU versions of the algorithm. We can now render nonmanifold features such as rays, ray-like tubes, cusps, ridges, thin sections that are at arbitrary angles to the octree node edges, and singular points located within plot nodes, all without artifacts. Our previous algorithm could not render these without severe aliasing. The algorithm can render the self-intersection curves of implicit surfaces by exploiting the fact that surfaces are singular where they self-intersect. It can also render the intersection curves of two implicit surfaces. We present new image space and object space algorithms for rendering these intersection curves as contours on one of the surfaces. These algorithms are better at rendering high curvature contours than our previous algorithms. To demonstrate the robustness of the node pruning algorithm we render a number of complex implicit surfaces such as high order polynomial surfaces and Gaussian curvature surfaces. We also compare the algorithm with ray casting interms of speed and image quality. For the surfaces presented here, the point clouds can be computed in seconds to minutes on atypical Intel based PC. Once this is done, the surfaces can be rendered at much higher frame rates to allow some degree of interactive visualization.

A visibility algorithm for hybrid geometry- and image-based modeling and rendering

Hybrid geometry- and image-based modeling and rendering systems use photographs taken of a real-world environment and mapped onto the surfaces of a 3D model to achieve photorealism and visual complexity in synthetic images rendered from arbitrary viewpoints. A primary challenge in these systems is to develop algorithms that map the pixels of each photograph efficiently onto the appropriate surfaces of a 3D model, a classical visible surface determination problem. This paper describes an object-space algorithm for computing a visibility map for a set of polygons for a given camera viewpoint. The algorithm traces pyramidal beams from each camera viewpoint through a spatial data structure representing a polyhedral convex decomposition of space containing cell, face, edge and vertex adjacencies. Beam intersections are computed only for the polygonal faces on the boundary of each traversed cell, and thus the algorithm is output-sensitive. The algorithm also supports efficient determination of silhouette edges, which allows an image-based modeling and rendering system to avoid mapping pixels along edges whose colors are the result of averaging over several disjoint surfaces. Results reported for several 3D models indicate the method is well suited for large, densely occluded virtual environments, such as building interiors.

Efficient visibility processing for projective texture mapping

Projective texture mapping is a powerful tool for image-based rendering. However, visibility information must be obtained in order to project correct textures onto the geometric sturcture. This paper presents a novel visibility algorithm for determining which polygons are visible from each camera position. It has object-space precision, but operates in both image-space and object-space to get better performance. It generates much less polygons than traditional object-space algorithms to help accelerate the speed of texture mapping. The techniques used to achieve these are conservative image-space occlusion testing and object-space shallow clipping. This algorithm has been successfully used to generate large-scale image-based rendering of a whole university campus, and image-based rendering of architectures under dynamic lighting.

SAR image simulation and analysis of alpine terrain

We describe the implementation of a so-called object-space algorithm to use a digital elevation model (DEM) and a sensor flight path as input for the production of simulated SAR images. The method aims to achieve a high geometric accuracy and employs a parametric mapping model based on SAR range and Doppler equations. Information about SAR layover and shadow areas is stored in a so-called ‘layover and shadow map’. We simulate ERS-1, X-SAR, and JERS-1 images of high-relief terrain, and compare them with corresponding real images. Manual measurements on the ERS-1 image show a simulation accuracy of better than 25 m, if sufficiently accurate sensor parameters are available. A cosine reflectance model delivers a good overall radiometric impression. However, this is being improved where ground truth exists, most notably on glaciers and areas covered with snow. As an application, we discuss the use of the simulated products for geometric rectification and radiometric calibration as a prerequisite for thematic analysis.

A combined constraint-space, objective-space approach for determining high-dimensional maximal efficient faces of multiple objective linear programs

Characterizations for efficient faces and certain maximal efficient faces of the objective set Y of a linear k-objective minimization problem are presented. These characterizations are used to develop an algorithm for etermining high-dimensional maximal efficient faces of Y. The algorithm requires as input an irredundant system of linear inequalities representing the efficiency equivalent polyhedron Y :=Y + R + k . A procedure for obtaining such a representation for Y has previously appeared in the literature and is included herein in order to make the paper self-contained. This latter procedure requires, in part, the generation of the efficient extreme points and efficient extreme rays of the constraint polyhedron. Hence, the overall method proposed herein can be viewed as a combined constraint-space, objective-space algorithm. The algorithm is complete for problems with 2 and 3 objectives. An illustrative numerical example is included.

A SURVEY OF OBJECT-SPACE HIDDEN SURFACE REMOVAL

We present a survey of the hidden surface removal literature, focusing on object-space algorithms. We give a brief definition and history of the problem, followed by a discussion of problems and algorithms associated with the priority ordering of faces. We go on to examine object-space algorithms in order of increasing object complexity: xy-parallel rectangles, ordered triangles, c-oriented faces, c-oriented polyhedra, polyhedral terrains, and general polyhedra. We also review recent work on merging visibility maps and moving viewpoints. Finally, we present a list of open problems.

Parallel depth-merge: A paradigm for hidden surface removal

Visualization is a key aspect in geometric modeling. Since the processing required for realistic display is often considerable, the design of parallel visualization algorithms is a trying taks. In this paper a new parallel approach to Hidden Surface Removal, called Parallel Depth-Merge (PDM), is proposed. PDM, intrinsically parallel, couples any already known HSR object-space algorithm with an image-space hierarchical merger. Resulting data are returned in a format well-suited both for plotting on vector devices and for use in shadow computations and shading algorithms. The proposed approach is designed for MIMD architectures, which use either shared or nonshared memory, and it does not require any special purpose hardware. The term paradigm is used to stress that the proposed approach is not based on the parallel redesigning of a known HSR algorithm. Conversely, it can be considered a general parallel solution to the problem, which allows different HSR object-space algorithms to be implemented uniformly on different MIMD architectures.