Quality metrics in high-dimensional data visualization: an overview and systematization

In this paper, we present a systematization of techniques that use quality metrics to help in the visual exploration of meaningful patterns in high-dimensional data. In a number of recent papers, different quality metrics are proposed to automate the demanding search through large spaces of alternative visualizations (e.g., alternative projections or ordering), allowing the user to concentrate on the most promising visualizations suggested by the quality metrics. Over the last decade, this approach has witnessed a remarkable development but few reflections exist on how these methods are related to each other and how the approach can be developed further. For this purpose, we provide an overview of approaches that use quality metrics in high-dimensional data visualization and propose a systematization based on a thorough literature review. We carefully analyze the papers and derive a set of factors for discriminating the quality metrics, visualization techniques, and the process itself. The process is described through a reworked version of the well-known information visualization pipeline. We demonstrate the usefulness of our model by applying it to several existing approaches that use quality metrics, and we provide reflections on implications of our model for future research.     

Oris: a tool for modeling, verification and evaluation of real-time systems

Oris is a tool for qualitative verification and quantitative evaluation of reactive timed systems, which supports modeling and analysis of various classes of timed extensions of Petri Nets. As most characterizing features, Oris implements symbolic state space analysis of preemptive Time Petri Nets, which enable schedulability analysis of real-time systems running under priority preemptive scheduling; and stochastic Time Petri Nets, which enable an integrated approach to qualitative verification and quantitative evaluation. In this paper, we present the current version of the tool and we illustrate its application to two different case studies in the areas of qualitative verification and quantitative evaluation, respectively.     

Look-ahead heuristics for the dynamic traveling purchaser problem

Given a set of products each with positive discrete demand, and a set of markets selling products at given prices, the traveling purchaser problem (TPP) looks for a tour visiting a subset of markets such that products demand is satisfied at minimum purchasing and traveling costs. In this paper we analyze a dynamic variant of the problem, where quantities may decrease as time goes on. Complete information is assumed on current state of the world, i.e. decision maker knows quantities available for each product in each market at present time and is informed about any consumption event when it occurs. Nevertheless, planner does not have any information on future events. Two groups of heuristics are described and compared. The first group consists of simplified approaches deciding which market to visit next on the basis of some greedy criteria considering only one of the two objective costs. The second one includes heuristics based on a look-ahead approach taking into account both traveling and purchasing costs and inserting some future prediction. Heuristics behavior has been tested on a large set of randomly generated instances under different levels of dynamism.     

Covering a line segment with variable radius discs

The paper addresses the problem of locating sensors with a circular field of view so that a given line segment is under full surveillance, which is termed as the disc covering problem on a line. The cost of each sensor includes a fixed component f, and a variable component that is a convex function of the diameter of the field-of-view area. When only one type of sensor or, in general, one type of disc, is available, then a simple polynomial algorithm solves the problem. When there are different types of sensors, the problem becomes hard. A branch-and-bound algorithm as well as an efficient heuristic are developed for the special case in which the variable cost component of each sensor is proportional to the square of the measure of the field-of-view area. The heuristic very often obtains the optimal solution as shown in extensive computational testing.     

A GPU framework for parallel segmentation of volumetric images using discrete deformable models

Despite the ability of current GPU processors to treat heavy parallel computation tasks, its use for solving medical image segmentation problems is still not fully exploited and remains challenging. A lot of difficulties may arise related to, for example, the different image modalities, noise and artifacts of source images, or the shape and appearance variability of the structures to segment. Motivated by practical problems of image segmentation in the medical field, we present in this paper a GPU framework based on explicit discrete deformable models, implemented over the NVidia CUDA architecture, aimed for the segmentation of volumetric images. The framework supports the segmentation in parallel of different volumetric structures as well as interaction during the segmentation process and real-time visualization of the intermediate results. Promising results in terms of accuracy and speed on a real segmentation experiment have demonstrated the usability of the system.     

Data structures for order-sensitive predicates in parallel nondeterministic systems

We study the problem of guaranteeing correct execution semantics in parallel implementations of logic programming languages in presence of built-in constructs that are sensitive to order of execution. The declarative semantics of logic programming languages permit execution of various goals in any arbitrary order (including in parallel). However, goals corresponding to extra-logical built-in constructs should respect the sequential order of execution to ensure correct semantics. Ensuring this correctness in presence of such built-in constructs, while efficiently exploiting maximum parallelism, is a difficult problem. In this paper, we propose a formalization of this problem in terms of operations on dynamic trees. This abstraction enables us to: (i) show that existing schemes to handle order-sensitive computations used in current parallel systems are sub-optimal; (ii) develop a novel, optimal scheme to handle order-sensitive goals that requires only a constant time overhead per operation. While we present our results in the context of logic programming, they will apply equally well to most parallel non-deterministic systems. Received: 20 April 1998 / 3 April 2000     

Efficient matching and indexing of graph models in content-basedretrieval

In retrieval from image databases, evaluation of similarity, based both on the appearance of spatial entities and on their mutual relationships, depends on content representation based on attributed relational graphs. This kind of modeling entails complex matching and indexing, which presently prevents its usage within comprehensive applications. In this paper, we provide a graph-theoretical formulation for the problem of retrieval based on the joint similarity of individual entities and of their mutual relationships and we expound its implications on indexing and matching. In particular, we propose the usage of metric indexing to organize large archives of graph models, and we propose an original look-ahead method which represents an efficient solution for the (sub)graph error correcting isomorphism problem needed to compute object distances. Analytic comparison and experimental results show that the proposed lookahead improves the state-of-the-art in state-space search methods and that the combined use of the proposed matching and indexing scheme permits for the management of the complexity of a typical application of retrieval by spatial arrangement     

Weighted walkthroughs between extended entities for retrieval by spatial arrangement

In the access to image databases, queries based on the appearing visual features of searched data reduce the gap between the user and the engineering representation. To support this access modality, image content can be modeled in terms of different types of features such as shape, texture, color, and spatial arrangement. An original framework is presented which supports quantitative nonsymbolic representation and comparison of the mutual positioning of extended nonrectangular spatial entities. Properties of the model are expounded to develop an efficient computation technique and to motivate and assess a metric of similarity for quantitative comparison of spatial relationships. Representation and comparison of binary relationships between entities is then embedded into a graph-theoretical framework supporting representation and comparison of the spatial arrangements of a picture. Two prototype applications are described.