ГЕОМЕТРИЧНЕ МОДЕЛЮВАННЯ СКЛАДНИХ ОБ’ЄКТІВ НА ОСНОВІ ПОЛІТОЧКОВИХ ВІДОБРАЖЕНЬ ВІДРІЗКІВ ПРЯМИХ

The convex hull of a planer set of points can be defined as the set of vertices of the smallest convex polygon containing all the points. If S is a planer set of points then convex layers of S can be derived by iteratively computing the convex hull of S and then removing it from S. Computation of the convex layers has widely been studied in the static environment where the set of points is fixed. The theoretical lower bound of computing the convex layers of a fixed set of points is O (n log n). The static convex layers algorithms with the optimal time complexity have already been proposed in the literature. A set of points where the points can be inserted or deleted is called a dynamic set of points. The set of convex layers should be reconstructed from the scratch at each insertion or deletion if a static convex layers algorithm was used to handle a dynamic set of points. Therefore, it takes O (n log n) time to handle an insertion or a deletion even for an optimal static convex layers algorithm. A dynamic convex layers algorithm has been proposed recently that can perform an insertion or a deletion by doing a slight modification to the existing set of convex layers. It takes O (n) time for an insertion or a deletion. It assumes that the set of points does not contain collinear points and that assumption is not valid in practical applications. Furthermore, the notion of tangent used in that approach restricts the extension of the algorithm into higher dimensions. This paper proposes a novel dynamic convex layers algorithm to eliminate the drawbacks in the existing algorithm. Salient feature of this algorithm is that it represents each layer as a set of line segments. The layers are modified upon an insertion or a deletion of a point by adding some new line segments and deleting some existing line segments. The proposed algorithm takes O (n 3 /k 2 ) time for an insertion or a deletion where k is the number of convex layers. A computer implementation is also presented. The proposed algorithm can work with set of points with collinear points and coincident points. The notion used in the algorithm can easily be extended to higher dimensions. Suppose the set of convex layers have already been found for a given set of points. Further, suppose that the layers are close to each other and new points are expected to fall within the region bounded by the outermost layer. This kind of situations widely occurs in practice and then the proposed algorithm takes O (n) time for an inclusion or a deletion.

This paper presents a new method based on the application of the Hough Transform for solving the robot motion problem and their intermediate steps: geometric modelling and collision detection. In terms of modelling, given a set of points, which is the representation of a given object, the maximum inner and the minimum outer spherically-extended polytopes (s-tope) are automatically generated. Collision detection is based on the computation of the translational penetration distance. Such a distance also allows to compute an intermediate point when collision avoidance is required. The set of intermediate points describes a solution to the path-planning problem. This new approach introduces an important decrease in the computational time required for robot motion planning.

A systematic approach to the modeling of deformable rodlike objects is presented. Various rodlike objects such as cords and wires are manipulated in many manufacturing processes. In such processes, it is important for successful manipulation to evaluate their shapes on a computer in advance because their shapes can be changed easily and their deformation often shows hysteresis properties. In this paper, we develop an analytical method to model the shape of deformable rodlike objects including hysteresis properties. First, we investigate the mechanism of hysteresis. Second, the potential energy of a rodlike object and the geometric constraints imposed on it are formulated. The shape of the object can be derived by minimizing the potential energy under the geometric constraints. Thirdly, a procedure to compute the shape of a deformed rodlike object is developed by applying a non-linear programming technique. Finally, we show some numerical examples with hysteresis using our proposed method.

Several formulations based on Random Fields (RFs) have been proposed for joint categorization and segmentation (JCaS) of objects in images. The RF's sites correspond to pixels or superpixels of an image and one defines potential functions (typically over local neighborhoods) which define costs for the different possible assignments of labels to several different sites. Since the segmentation is unknown a priori, one cannot define potential functions over arbitrarily large neighborhoods as that may cross object boundaries. Categorization algorithms extract a set of interest points from the entire image and solve the categorization problem by optimizing cost functions that depend on the feature descriptors extracted from these interest points. There is some disconnect between segmentation algorithms which consider local neighborhoods and categorization algorithms which consider non-local neighborhoods. In this work, we propose to bridge this gap by introducing a novel formulation which uses models of objects with deformable parts, classically used for object categorization, to solve the JCaS problem. We use these models to introduce two new classes of potential functions for JCaS; (a) the first class of potential functions encodes the model score for detecting an object as a function of its visible parts only, and (b) the second class of potential functions encodes shape priors for each visible part and is used to bias the segmentation of the pixels in the support region of the part, towards the foreground object label. We show that most existing deformable parts formulations can be used to define these potential functions and that the resulting potential functions can be optimized exactly using min-cut. As a result, these new potential functions can be integrated with most existing RF-based formulations for JCaS.

In this study, we present a new calibration method for the cooperation of wide-angle and pan-tilt-zoom (PTZ) cameras. A wide-angle camera enables the surveillance of a large area. However, it may be difficult to perceive the detail of an object. On the other hand, a PTZ camera enables the surveillance of the object detail. However, its view is limited when the camera zooms on a specific object. Therefore, the cooperation can complement the disadvantage of two types of cameras. For an object appears in the image of wide-angle camera, the desired pan and tilt angles of a PTZ camera for focusing on the object can be computed from its image coordinate. Previous methods can be classified into three categories: 3D world coordinate system, scene-dependent, or special technique. They are not simple and instinctive enough. The proposed method is simply based on the 2D image plane of wide-angle camera. A set of calibration points are selected directly on the image. Every point is a pair of pan/tilt angles (p, t) and 2D coordinate (x, y). Then, the calibration parameters are calculated from the set of points. An experiment was designed to evaluate the accuracy of the proposed method at fixed points. The results show that the proposed method is accurate enough for the cooperation of dual cameras. In advance, a prototype system for capturing close-up images of moving objects in an open area was implemented to demonstrate the feasibility of the proposed method.

We present a multi-level partition of unity algebraic set surfaces (MPU-APSS) for surface reconstruction which can be represented by either a projection or in an implicit form. An algebraic point set surface (APSS) defines a smooth surface from a set of unorganized points using local moving least-squares (MLS) fitting of algebraic spheres. However, due to the local nature, APSS does not work well for geometry editing and modeling. Instead, our method builds an implicit approximation function for the scattered point set based on the partition of unity approach. By using an octree subdivision strategy, we first adaptively construct local algebraic spheres for the point set, and then apply weighting functions to blend together these local shape functions. Finally, we compute an error-controlled approximation of the signed distance function from the surface. In addition, we present an efficient projection operator which makes our representation suitable for point set filtering and dynamic point resampling. We demonstrate the effectiveness of our unified approach for both surface reconstruction and geometry modeling such as surface completion.

A novel entropy-based mapping method for determining the protein-protein interactions in viral genomes by using coevolution analysis

This paper presents an overview of our efforts in modeling-from-realty to create virtual reality models through observation of real objects. These efforts span three aspects: how to create geometric models of virtual objects; how to create photometric models of virtual objects; and how to integrate such virtual objects with real scenes. For geometric model creation, we have developed a two-step method: simultaneous alignment and volumetric view merging. For photometric model creation, we have developed two methods, model-based and eigen-texture rendering methods, both of which automatically create models by observing the real objects. For the integration of virtual objects with real scenes, we have developed a method that renders virtual objects based on real illumination distribution. We have successfully tested the proposed methods by using real images to demonstrate their effectiveness.

This paper addresses the problem of segmenting an unstructured set of 3D points sampled from a physical model. Given such a set of points the first problem is that of creating a polyhedral approximation of the model. For that we introduce an algorithm which extends Boissonnat's work and generates a triangular surface approximation. The proposed method allows the reconstruction of objects with arbitrary genus and proposes an automatic termination procedure. The next step in the process concerns the segmentation of the data points into regions for which each may be fitted by a single surface. Here we summarize our experiences with a region growing technique based on angle between normals criteria. Using just first order derivative estimations it is shown that the method is able to classify segments into predefined second order surface classes.

The paper describes an approach to solid modeling of geometric objects in the form of an organized three-parameter set of points in three-dimensional space. The relevance of the research topic is due to the widespread use of solid-state models in various branches of science and technology, mechanical engineering, construction and medicine. Solid-state computer models are currently one of the basic computer graphics tools and an integral part of computer- aided design and calculation systems. It is widely used as one of the control elements of CNC machines and 3D printing, the development of information systems in the design and construction of buildings and structures, finite element calculations of deformed states in aircraft and mechanical engineering, their manufacture in medicine, etc. The choice of point calculus as a mathematical apparatus for the analytical description of solid models of geometric objects is substantiated. Examples of modeling sets of elliptical bodies and toroidal bodies in a simplex of three-dimensional space are given.

Textured surface models of three-dimensional objects are gaining importance in computer graphics applications. These models often have to be merged from several overlapping partial models which have to be registered (i.e. the relative transformation between the partial models has to be determined) prior to the merging process. In this paper a method is presented that makes use of both camera-based depth information (e.g. from stereo) and the luminance image. The luminance information is exploited to determine corresponding point sets on the partial surfaces using an optical flow approach. Quaternions are then employed to determine the transformation between the partial models which minimizes the sum of the 3-D Euclidian distances between the corresponding point sets. In order to find corresponding points on the partial surfaces luminance information is linearized. The procedure is iterated until convergence is reached. In contrast to only using depth information, employing luminance speeds up convergence and reduces remaining degrees of freedom (e.g. when registering sphere-like shapes).

In this paper, a pattern search (PS)-based solution is proposed for nonconvex multiband cooperative sensing (NCMCS) problem in cognitive radio systems. This problem consists of maximizing cumulative throughput subject to constraints on cumulative interference, probability of detection, and probability of false alarm. Initially in existing literature, this problem was solved under constraints that make it convex. However, removing the conditions for convexity and solving the NCMCS problem have been shown to improve performance. A two-step PS-based solution is presented: The first step uses uniformly distributed random sets of input points to find a solution. The set of points that gives the maximum throughput is chosen as input to the PS algorithm. Numerical examples show the improvement of the proposed method over existing genetic-algorithm-based solution, as well as PS-algorithm-based solution that uses a single set of random points as inputs. The proposed two-step solution gives higher cumulative throughput and is not sensitive to the choice of input, unlike the PS-based solution using a single set of random points as input.

The process of building mathematical models of static objects and systems, which includes the solution of two problems: structural and parametric identification, is considered. At the same time, the task of identifying the structure of the model is more difficult and primary. The problem of structural identification of interval models of the characteristic of a static object is the problem of multiple solving of problems of parametric identification of this model, and therefore, from a computational point of view, it is NP complex. The procedure for finding the optimal structure of the model is considered as a directed selection of a defined set of structures in such a way as to minimize the number of iterations of the formation of interval systems of nonlinear algebraic equations. The article formulates the problem of structural identification of interval models of static objects, as a problem of repeatedly searching for solutions of interval systems of nonlinear algebraic equations, in the form of optimization problems with a nonlinear objective function and nonlinear constraints. For the first time, a method of structural identification of interval models of the characteristics of static objects based on the analysis of interval data is proposed and substantiated, which, unlike the existing ones, is based on self-organization and self-adaptation procedures of computing procedures by analogy with artificial bee colony (АBC), which gives the ability to implement model structure identification procedures with lower computational complexity and obtain interval models with simpler structures compared to known methods. The proposed method was tested on the example of building an interval model of the characteristics of a small hydroelectric plant for the purpose of research and ensuring the maximum efficiency of the use of hydropower resources, which demonstrated the effectiveness of using computational procedures based on the artificial bee colony. Accordingly, the proposed method makes it possible to obtain simple, from the point of view of complexity, interval models of complex static objects with a given guaranteed accuracy and with a lower computational complexity of identifying these models. Such features of the method ensure the effective development of the mathematical apparatus, which is used both in decision-making processes and in the processes of preparing decisions in intellectualized data-oriented systems.

This article proposes a SLAM algorithm referred to as RGBD-Sphere SLAM. The key innovation of this work is the prototypical system that demonstrates how formal models of 3D geometric shape and appearance can be transformed into generative classification models that detect and recognize these shapes. Object models are specified as shape programs in PSML; a custom-built procedural language for 3D object modeling. Classifiers for each PSML shape are created by simulating how instances of each shape manifest in real-world sensor data, e.g., color images and range images. The proposed RGBD-Sphere SLAM algorithm demonstrates a prototypical example of the system. Here, the PSML program specifies spherical 3D objects having diffuse surface albedos and distinct color appearances. A recognizer uses PSML models of each object's geometry and appearance to detect instances of these objects within streaming RGBD sensor data. The detected model parameters are then integrated into an RGBD SLAM algorithm; hence the name RGBD-Sphere SLAM. This article describes the PSML programs, the spherical detection and recognition algorithms used, and describes the impact this approach has for improving the performance of RGBD SLAM approaches by incorporating detected objects as landmarks. This is the first example of a prototypical system that externalizes the geometric and appearance modeling to a programming language from which a recognizer is created, and marks an important step towards enabling users to “program” their problem space and allow computers to transform the formal object models, as expressed in PSML, into customized classifiers suited for specific sensor suites, e.g., color imagery and depth imagery.

Presented is a computational method for physical modeling of mechanical objects of constrained movement. In a physical modeling environment, an object’s behavior is modeled as it is implied by its geometry and substance, and the appearing physical (mechanical, thermal, and other) phenomena. The developed software is able to describe various forms of movement of a rigid object, configure obstacles in the space, check for collisions of the moving object with the obstacles, and compute post-collision trajectories of the object. The motivation for the background research is an industrial problem, namely, spatial positioning of moving objects without using extra energy. The novelty of this work is in (a) the interactive definition of constituents of the modeling environment, (b) the integrated simulation of an arbitrary sequence of spatial movements and multiple collisions, and (c) the applicability to preliminary design of mechanical equipment. The process of physical modeling has been implemented in six phases: (a) geometric modeling and determination of the substantial attributes of the object, (b) computing of the pre-defined movements, (c) specification and positioning obstacles in the space, (d) checking for single and multiple collisions, (e) computing of post-collision movements, and (f) controlling of multiple and repeated events. Among others, the developed software is able to compute compound movements in the space and any sequence of eccentric collisions with four types of obstacles.