Color-spanning localized query

Imagine a wooden plate with a set of non-overlapping geometric objects painted on it. How many of them can a carpenter cut out using a panel saw making guillotine cuts, i.e., only moving forward through the material along a straight line until it is split into two pieces? Already fifteen years ago, Pach and Tardos investigated whether one can always cut out a constant fraction if all objects are axis-parallel rectangles. However, even for the case of axis-parallel squares this question is still open. In this paper, we answer the latter affirmatively. Our result is constructive and holds even in a more general setting where the squares have weights and the goal is to save as much weight as possible. We further show that when solving the more general question for rectangles affirmatively with only axis-parallel cuts, this would yield a combinatorial O(1)-approximation algorithm for the Maximum Independent Set of Rectangles problem, and would thus solve a long-standing open problem. In practical applications, like the mentioned carpentry and many other settings, we can usually place the items freely that we want to cut out, which gives rise to the two-dimensional guillotine knapsack problem: Given a collection of axis-parallel rectangles without presumed coordinates, our goal is to place as many of them as possible in a square-shaped knapsack respecting the constraint that the placed objects can be separated by a sequence of guillotine cuts. Our main result for this problem is a quasi-PTAS, assuming the input data to be quasi-polynomially bounded integers. This factor matches the best known (quasi-polynomial time) result for (non-guillotine) two-dimensional knapsack.

The Farthest Spatial Skyline Queries

In this paper we consider query versions of visibility testing and visibility counting. Let S be a set of n disjoint line segments in ℜ2 and let s be an element of S. Visibility testing is to preprocess S so that we can quickly determine if s is visible from a query point q. Visibility counting involves preprocessing S so that one can quickly estimate the number of segments in S visible from a query point q. We present several data structures for the two query problems. The structures build upon a result by O'Rourke and Suri (1984) who showed that the subset, VS(s), of ℜ2 that is weakly visible from a segment s can be represented as the union of a set, CS(s), of O(n2) triangles, even though the complexity of VS(s) can be Ω(n4). We define a variant of their covering, give efficient output-sensitive algorithms for computing it, and prove additional properties needed to obtain approximation bounds. Some of our bounds rely on a new combinatorial result that relates the number of segments of S visible from a point p to the number of triangles in ∪s∈S CS(s) that contain p.

We derive efficient algorithms for coarse approximation of complex algebraic hypersurfaces, useful for estimating the distance between an input polynomial zero set and a given query point. Our methods work best on sparse polynomials of high degree (in any number of variables) but are nevertheless completely general. The underlying ideas, which we take the time to describe without an excess of algebraic geometry terminology, come from tropical geometry. We then apply our methods to finding roots of n × n systems near a given query point, thereby reducing a hard algebraic problem to high-precision linear optimization. We prove new upper and lower complexity estimates along the way.

MSSQ: Manhattan Spatial Skyline Queries

The paper presents an efficient algorithm for solving the nearest- neighbor problem in the plane, based on generalized Voronoi diagram construction. The input for the problem is the set of circular sites S with varying radii, the query point p and the metric (Minkowski or power) according to which the site neighboring the query point, is to be reported. The IDG/NNM software was developed for an experimental study of the problem. The experimental results demonstrate that the Voronoi diagram method outperforms the k — d tree method for all tested input site configurations. The similarity between the nearest-neighbor relationship in the Minkowski and power metrics was also established.KeywordsVoronoi DiagramDelaunay TriangulationQuery PointVoronoi RegionNeighbor ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Let P be a set of n points in the plane. We present an efficient algorithm for preprocessing P, so that, for a given query point q, we can quickly report the largest disk that contains q but its interior is disjoint from P. The storage required by the data structure is O(n log n), the preprocessing cost is O(n log 2 n), and a query takes O( log 2 n) time. We also present an alternative solution with an improved query cost and with slightly worse storage and preprocessing requirements.

For the disadvantage in modeling at complex areas, advancing-frontal triangulation method was firstly applied in building numerical model of FLAC3D software. Suitable date structure and algorithm based on Fish program language was mainly studied. The position criterion of adjacent edges to current edge is brought in to improve the efficiency of algorithm; equilateral triangle or isosceles triangle mesh is generated to improve elements’ quality; element size is controlled by simple mathematics means so smooth graded triangular mesh is constructed. Through the research, the first independent FLAC3D pre-process is developed successfully, without relying on other modeling software. Application example shows the feasibility of the method.

In some special rescue scenarios, the needed goods should be transported by drones because of the landform. Therefore, in this study, we investigate a multi-objective vehicle routing problem with time window and drone transportation constraints. The vehicles are used to transport the goods and drones to customer locations, while the drones are used to transport goods vertically and timely to the customer. Three types of objectives are considered simultaneously, including minimization of the total energy consumption of the trucks, total energy consumption of the drones, and the total number of trucks. An improved artificial bee colony algorithm is designed to solve the problem. In the proposed algorithm, each solution is represented by a two-dimensional vector, and the initialization method based on the Push-Forward Insertion Heuristic is embedded. To enhance the exploitation abilities, an improved employed heuristic is developed to perform detailed local search. Meanwhile, a novel scout bee strategy is presented to improve the global search abilities of the proposed algorithm. Several instances extended from the Solomon instances are used to test the performance of the proposed improved artificial bee colony algorithm. Experimental comparisons with the other efficient algorithms in the literature verify the competitive performance of the proposed algorithm.

Moving objects database systems are specialized to store and process data with spatiotemporal attributes. A simple object type in this context is a moving point, which can represent the motion of a pedestrian, car or airplane. Another, more complex, type of object is a moving region, which is a region that changes position and shape over time. This thesis discusses various aspects for handling moving regions. One topic in this thesis is the region interpolation problem, where snapshots of regions are interpolated to moving regions. This procedure can be performed in several ways with varying results. The goal is to achieve a high quality result, which means primarily that the database model should match the corresponding real world objects as accurately as possible. Another chapter presents a new, polyhedra based, model for moving regions. This has two advantages compared to the prevailing unit based models: Complex moving regions, especially the results of binary set operations as, for instance, “union” can be represented in a much more compact way. Furthermore, operations on moving regions can be mapped into geometrical operations on polyhedra, for which robust and efficient algorithms are available. Based on this new model, operations for spatiotemporal coverage analysis of moving regions are developed. This is a set of operations to determine which regions are covered for which time intervals by a given moving region. In the light of large forest fires in the world, a method for creating moving regions from earth satellite scan data is discussed, that has several advantages over the prevailing methods. Another topic is the decomposition of moving regions into smaller and less complex entities, to improve their manageability in moving objects databases. Finally, an alternative data model for moving regions is introduced, which is optimized for rigid objects. The class of moving regions supported by that model is unable to change shape, but in return rotational movement is modeled accurately. For this new data type, useful operations like “moving point inside”, “traversed area” and more are introduced. As a part of this work, reference implementations for all these topics are distributed in form of freely available C++ libraries, which can be easily integrated into existing moving objects database systems, as, for example, the DBMS Secondo developed at the FernUniversitat in Hagen.

Template matching techniques are widely used in many computer vision tasks. Generally, a likelihood value is calculated from similarity measures, however the relation between these measures and the data likelihood is often incorrectly stated. It is clear that accurate likelihood estimation will improve the efficiency of the matching algorithms. This paper introduces a novel method for estimating the likelihood PDFS accurately based on the PDF Projection Theorem, which provides the correct relation between the feature likelihood and the data likelihood, permitting the use of different types of features for different types of objects and still estimating consistent likelihoods. The proposed method removes the normalization and bias problems that are usually associated with the likelihood calculations. We demonstrate that it significantly improves template matching in pose estimation problems. Qualitative and quantitative results are compared against traditional likelihood estimation schemes.

In this paper, we study the Obstructed Nearest Neighbor (ONN) problem: given a set of points and a set of polygonal obstacles in two dimensions, find the k nearest neighbors to a query point according to the length of the shortest obstacle-avoiding path between two points. ONN query is useful both as a stand-alone tool in geographical information systems and as a primitive for spatial data analysis such as clustering and classification in the presence of obstacles. We propose an efficient ONN algorithm that processes only the data points and obstacles relevant to the query in an incremental way and thus filters out a large number of points and obstacles. Experiments on spatial data sets show the algorithm scales well with respect to the input data size and the number of nearest neighbors requested.

In multiobjective optimization, the R2 indicator is widely used for designing the indicator-based algorithms, and the Tchebycheff approach is commonly employed in the decomposition-based algorithms. Despite their wide use, the connection between these two different paradigms is still not well understood, particularly in the field of multiobjective efficient global optimization (MOEGO). Considering that expected improvement (EI) is a cornerstone in efficient global optimization (EGO), this article first studies the relationship between R2-based EI and Tchebycheff-based EI. Then, we introduce a many-to-few (M2F) decomposition framework, offering a new perspective for linking the R2-based method and the Tchebycheff decomposition approach. By incorporating M2F decomposition into MOEGO, a new algorithm called R2/D-EGO is proposed. At each iteration, R2/D-EGO utilizes the Tchebycheff decomposition paradigm to generate a set of candidate solutions, each one corresponding to a different weight vector. Subsequently, a subset of query points is selected from the candidates based on the lower bound of R2-based EI. Empirical results indicate that the proposed R2/D-EGO is highly competitive in comparison with both the R2-based and decomposition-based MOEGO algorithms in the parallel (or batch) setting.

Motivated by the bus escape routing problem in printed circuit boards, we revisit the following problem: given a set of n axis-parallel rectangles inside a rectangular region \({\mathscr {R}}\), find the maximum number of rectangles that can be extended toward the boundary of \({\mathscr {R}}\), without overlapping each other. We provide an efficient algorithm for solving this problem in \(O(n^2 \log ^3 n \log \log n)\) time, improving over the current best \(O(n^3)\)-time algorithm available for the problem.

Tracking is regarded as one of the most fundamental tasks in computer vision. It is used in many computer vision applications in fields such as surveillance, robotic navigation and 3D reconstruction to name but a few. Despite decades of research, the goal of fully automatic tracking of arbitrary types of objects in real world conditions is still an open problem. In this paper, we take a step toward the goal of general real-world tracking, and demonstrate a unified generative model for Bayesian multifeature, adaptive target tracking, or AMFT for short (Adaptive Multiple Feature Tracker). We derive a unified generative model for multi-sensory adaptive tracking which cleanly integrates tracking and the modeling of appearance change across multiple features in the same framework. The unified multi-feature observation model ensures that if one feature is not confident, e.g., color after an object crosses into a region of shadow, it is automatically down-weighted in its contribution to the appearance model update. In this way, without pre-training of specific object models, we achieve an extensible tracker for general object types, robust to real-world problems of clutter, appearance/lighting change and target model drift. The standard modeling assumptions made by a non-adaptive generative model are illustrated by the probabilistic graphical model in Figure 1(a). The unknown target state (e.g., location, size, velocity) xt is assumed to change with time t according to some process parameterized by A. At every time t, we make some noisy observations zt of the target xt (e.g., raw image or color histograms). The target is then tracked online by computing the posterior, p(xt |z1:t) over the true target location recursively. In the case of the Kalman filter (KF), all the distributions involved are Gaussian. In the case of the particle filter (PF), all the distributions involved are represented non-parametrically by a set of samples [1]. The true target model, e.g., the appearance or color histogram to search for, is assumed to be part of the parameters H, i.e., it is known and fixed by an operator or initialized by some external process. In many cases however, the true appearance of the target H may change significantly in time, e.g., the appearance changes when a subject moves between shade and sunlight. This is the case for outdoor surveillance applications and is the motivation for this research. Adaptive trackers [2, 3, 4, 6] have been proposed to update the target appearance online in various heuristic ways. We can formalise this more general modeling assumption generatively, by the generalized dynamic Bayesian network illustrated in Figure 1(b). In contrast to Figure 1(a), the true target model which was previously included in the fixed parameters H, is now included as the the initial condition y0 of a dynamic latent variable yt , formalizing the modeling assumption that the target appearance can change over time. In addition to the target state xt , the target appearance yt will therefore be incrementally and recursively updated as part of the process of inferring the latent variables in this model p(xt ,yt |z1:t). The latent space is of course now greatly expanded, and poses a more challenging inference problem than that of Figure 1(a). In Section 2 of the paper, we detail the specific parametric form of the model and an efficient inference algorithm. We evaluate our method (AMFT) against three contemporary trackers: A standard single feature particle filter (PF), mean-shift (MS) [5] and incremental visual tracking (IVT) [4]. The PF and MS trackers are non-adaptive color-based trackers, while IVT aims for pose and illumination change robustness by performing online adaptation in a subspace appearance model. Note that the AMFT, PF and IVT trackers track object scale, but MS does not. We evaluated these methods on a series of challenging video clips exhibiting a wide variety of data and object types for tracking, including far-field indoor and outdoor pedestrians with and without carried objects, vehicle tracking, and near-field indoor face trackH 1 x2 x3