Hierarchical Space Decomposition Research Articles

Parallel Monte Carlo Search for Hough Transform

We investigate the problem of line detection in digital image processing and in special how state of the art algorithms behave in the presence of noise and whether CPU efficiency can be improved by the combination of a Monte Carlo Tree Search, hierarchical space decomposition, and parallel computing.The starting point of the investigation is the method introduced in 1962 by Paul Hough for detecting lines in binary images. Extended in the 1970s to the detection of space forms, what came to be known as Hough Transform (HT) has been proposed, for example, in the context of track fitting in the LHC ATLAS and CMS projects. The Hough Transform transfers the problem of line detection, for example, into one of optimization of the peak in a vote counting process for cells which contain the possible points of candidate lines. The detection algorithm can be computationally expensive both in the demands made upon the processor and on memory. Additionally, it can have a reduced effectiveness in detection in the presence of noise.Our first contribution consists in an evaluation of the use of a variation of the Radon Transform as a form of improving theeffectiveness of line detection in the presence of noise. Then, parallel algorithms for variations of the Hough Transform and the Radon Transform for line detection are introduced. An algorithm for Parallel Monte Carlo Search applied to line detection is also introduced. Their algorithmic complexities are discussed. Finally, implementations on multi-GPU and multicore architectures are discussed.

Verified distance computation between non-convex superquadrics using hierarchical space decomposition structures

Verified distance computation is an important task in various application domains. In some domains a proof of correctness is crucial. In this paper, we show how we can apply the methods provided by our uniform framework for verified geometric computations to derive verified bounds on the distance between non-convex objects. The framework features a layered structure enabling the algorithm to run independently whether the objects are described by implicit functions or parametric ones or by polyhedrons. The approach is based on the use of adaptively constructed hierarchical decompositions of the models. As a practical example we use various scenarios occurring in automatic surgery assistance systems for total hip replacement (THR). To ensure that an implant selected by the system fits into the patient's femoral shaft, we have to derive verified bounds on the distance between them. In this case, the models are either superquadrics or polyhedrons, both of which can be non-convex We first show how to increase the enclosure quality of implicit objects by incorporating interval contractors into the hierarchical space decomposition. Next, we describe the construction of a decomposition structure for parametric objects. After that, we present an improvement of the case selector for computing the distance between interval tree nodes, yielding tighter results. We also show how to integrate surface normals into the algorithm if first-order information is available and how to accelerate the solving process by incorporating information gained by non-verified floating-point solvers. Finally, we provide numerical results for all distance query types occurring during the THR procedure and examine whether it is advisable to perform the computation on the implicit model or on the parametric one if both are available. Further numerical results are presented for test cases involving contractors in the decomposition structures.

Engineering analysis in imprecise geometric models

Holes, gaps, dangling boundaries and other imperfections of the geometric models preclude direct application of traditional engineering analysis tools. In such cases geometric inaccuracies have to be removed using a geometry “healing” (repair) procedure which results in a valid solid model. Repair procedure applied to the geometric model is computationally expensive and often requires human intervention and supervision. On the other hand, the repair procedure applied to the surface meshes derived from the boundaries of a geometric model may negatively affect the quality of the Finite Element mesh whose construction follows the repair procedure.In this paper we describe a novel numerical technique that enables engineering analysis in imprecise geometric models without reconstructing a valid solid model. At the heart of the proposed method lies a modified geometrically adaptive integration technique. It uses a hybrid geometric model, that consists of a hierarchical space decomposition, boundary representation (B-rep) and distance fields. Hierarchical space decomposition helps to resolve the geometric imperfections, while the original geometric model is used to allocate the integration points in the boundary (geometry) cells. The proposed method uses solution structures that combine together the distance fields to the geometric boundaries, boundary conditions and basis functions to enforce the prescribed boundary conditions.Our approach has been verified on several numerical examples. Our numerical experiments confirm high reliability of the proposed engineering analysis approach for a wide range of geometric imperfections. Despite that the paper presents 2D examples the proposed approach can be generalized in 3D.

Real-time approximation of molecular interaction interfaces based on hierarchical space decomposition

The interaction interface between two molecules can be represented as a bisector surface equidistant from the two sets of spheres of varying radii representing atoms. We recursively divide a box containing both sphere-sets into uniform pairs of sub-boxes. The distance from each new box to each sphere-set is conservatively approximated by an interval, and the number of sphere-box computations is greatly reduced by pre-partitioning each sphere-set using a k d-tree. The subdivision terminates at a specified resolution, creating a box partition (BP) tree. A piecewise linear approximation of the bisector surface is then obtained by traversing the leaves of the BP tree and connecting points equidistant from the sphere-sets. In 124 experiments with up to 16,728 spheres, a bisector surface with a resolution of 1/2 4 of the original bounding box was obtained in 28.8 ms on average.

Non-contact 3D acquisition system based on stereo vision and laser triangulation

This paper proposes a novel contact 3D acquisition system based on stereo vision and laser triangulation. The system is composed by several software modules for data acquisition purposes, data calibration, data processing and data reconstruction of 3D scenes. Different 3D image techniques, such as, polynomial determination, cubic spline interpolation and hierarchical space decomposition were used. To validate this method, a simple laboratory prototype machine was built for the purpose of road profile acquisition, road macro and mega texture characterization. In this paper, only the results and discussion of road profile acquisition are presented.

Multithread implementation for calculating room impulse responses.

Modern simulation programs are committed to calculate full impulse responses instead of doing simple mapping presentations. The main problem here is how to obtain such IRs quickly but accurately. The usual algorithm simulates sound propagation by tracing a statistical ensemble of acoustic rays. In this contribution, we deal with a new ray‐triangle intersection algorithm, based on a three‐dimensional grid scheme, that provides significant performance improvement for ray tracing. We report about the introduction of a uniform grid ray‐tracing algorithm, which is optimized for acoustic models and can be up to five times faster (standard Pentium 4) than hierarchical space decomposition. Furthermore, the algorithm has been parallelized, taking advantage of the inherently independent propagation of distinct rays. On multicore processors, the computation employs a variable number of thread tracing groups of rays in parallel. The speed increase is almost linear with the number of cores. An overview is given to explain this approach. To support this fast calculation, an additional algorithm derives a suggested particle number and length from the mean free path properties of the room and the desired detection rate at the receiver. So time‐consuming guesses about the selecting particle numbers will be avoided.

A solid model-based off-line adaptive controller for feed rate scheduling for milling process

Most CAM packages available today provide NC simulation systems that generally use inexact solid representation as they are computationally intensive. Popular inexact volumetric NC simulation packages use either a voxel based 2.5D approach (particularly Image-space modeling) or Polyhedral approximations of 3D objects. The former does not degenerate with time but has limited resolution whereas the latter has a selectable resolution but degenerates rapidly with time. As against these, the authors’ use octree solid representation in their volumetric NC simulation system. This hierarchical space decomposition (HSD) technique combines the benefits of both the earlier approaches, i.e., it has a selectable resolution and does not degenerate with time. The basic input to the octree-based NC simulation system is the NC cutter path either in cutter location (CL) format or G/ M-code format. After the CL data are interpreted, the swept volume of the cutter is intersected with the blank at every small sampling interval along the tool path and the intersection is considered as the undeformed chip. The chip parameters necessary for predicting the milling force are extracted and using the material removal rate (MRR) model and cutting force is predicted. According to the simulation result the feed rate is adjusted based on force calculation to generate optimized CL File. The improvement can be seen from the experimental results presented. Such a simulation system will be useful, in addition to the visual check, for automatic verification of safety of machining and conformance of the produced part to design specifications as well as for the optimization of the feed rate and spindle speed.

A Uniform Approach for Utilizing Synergy between Inspection Technologies and Computational Methods

Emerging scanning technologies currently capture diverse data that includes geometrical and physical properties (i.e. normals, material and color). Yet, existing inspection computational methods do not satisfy industry demands. This paper proposes a new approach for inherently handling diverse data and utilizing the synergy between inspection technologies and digital processing methods. Two methods were developed: a Hierarchical Space Decomposition Model (HSDM), which sorts the sampled data, and a 3D Geometrical Bilateral Filter (3D GBF) that utilizes the diverse data. These methods provide efficient data reduction while preserving sharp features. The feasibility of this approach is demonstrated on the diverse data.

Surface Reconstruction of Freeform Objects Based on Multiresolution Volumetric Method

Recently developed 3D scanning devices are capable of capturing point clouds, as well as additional information, such as normals and texture. This paper describes a new and fast reverse engineering method for creating a 3D computerized model from data captured by such contemporary 3D scanning devices. The proposed method aggregates large-scale 3D scanned data into an extended Hierarchical Space Decomposition Model (HSDM) based on Octree data structure. This model can represent both an object’s boundary surface and its interior volume. The HSDM enables data reduction, while preserving sharp geometrical features and object topology. As a result the execution time of the reconstruction process is significantly reduced. Moreover, the proposed model naturally allows multiresolution surface reconstruction, represented by a mesh with regular properties. Based on the proposed volumetric model, the surface reconstruction process becomes more robust and stable with respect to sampling noise.

SURFACE RECONSTRUCTION OF FREEFORM OBJECTS BASED ON HIERARCHICAL SPACE DECOMPOSITION

This paper describes a new and fast method for reconstructing a 3D computerized model from a cloud of points sampled from the object's surface. The proposed method aggregates very large scale 3D scanning data into a Hierarchical Space Decomposition Model (HSDM), realized by the Octree data structure. This model can represent both the boundary surface and the interior volume of an object. Based on the proposed volumetric model, the boundary reconstruction process becomes more robust and stable with respect to sampling noise. The hierarchical structure of the proposed volumetric model enables data reduction, while preserving critical geometrical features and object topology. As a result of data reduction, the execution time of the reconstruction process is significantly reduced. Moreover, the proposed model naturally allows multiresolution boundary extraction, represented by a mesh with regular properties. The proposed surface reconstruction approach is based on Connectivity Graph extraction from HSDM, and facet reconstruction. This method's feasibility will be presented on a number of complex objects.

Efficient surface reconstruction method for distributed CAD

This paper describes a new fast Reverse Engineering (RE) method for creating a 3D computerized model from an unorganized cloud of points. The proposed method is derived directly from the problems and difficulties currently associated with remote design over the Internet, such as accuracy, transmission time and representation at different levels of abstraction. With the proposed method, 3D models suitable for distributed design systems can be reconstructed in real time. The mesh reconstruction approach is based on aggregating very large scale 3D scanned data into a Hierarchical Space Decomposition Model (HSDM), realized by the Octree data structure. Then, a Connectivity Graph (CG) is extracted and filled with facets. The HSDM can represent both the boundary surface and the interior volume of an object. Based on the proposed volumetric model, the surface reconstruction process becomes robust and stable with respect to sampling noise. Moreover, the data received from different surface/volume sampling devices can be handled naturally. The hierarchical structure of the proposed volumetric model enables data reduction, while preserving significant geometrical features and object topology. As a result, reconstruction and transmission over the network are efficient. Furthermore, the hierarchical representation provides a capability for extracting models at desired levels of detail, thus enabling designers to collaborate at any product development stage: draft or detailed design.