Locally adaptable mathematical morphology using distance transformations

We investigate how common binary mathematical morphology operators can be adapted so that the size of the structuring element can vary across the image pixels. We show that when the structuring elements are balls of a metric, locally adaptable erosion and dilation can be efficiently implemented as a variant of distance transformation algorithms. Opening and closing are obtained by a local threshold of a distance transformation, followed by the adaptable dilation.     

Parallel and sequential transformations on digital images

In this paper, the relation between parallel and sequential algorithms is discussed. We regard algorithms as definitions of transformations and investigated the relation between the sets of transformations defined by parallel and sequential algorithms. Three problems are treated mainly. The problems and the results for the problems may be summarized as follows. (1) Characterization of transformations which are both parallel and sequential—A necessary and sufficient condition for a transformation to be both parallel and sequential has been established. (2) Equivalence problems—The equivalence problem for two algorithms, one of which is parallel, is decidable, hence, the equivalence problem for two sequential algorithms is undecidable, i.e. an algorithm for deciding whether or not two given algorithms, one of which is parallel, define the same transformation has been presented. However, we have shown there is no algorithm for deciding whether or not two given sequential algorithms define the same transformation. (3) Translation problems—An algorithm for translating a parallel (sequential) algorithm into an equivalent sequential (parallel) algorithm has been presented.     

Computing with graphs and graph transformations

Many software applications require the construction and manipulation of graphs. In standard programming languages, this is accomplished using low‐level mechanisms such as pointer manipulation or array indexing. In contrast, graph productions are a convenient high‐level visual notation for coding graph modifications. A graph production replaces one subgraph by another subgraph. Graph productions can define a graph grammar and graph language, or can directly transform an input graph into an output graph. Graph transformation has been applied in many areas, including the definition of visual languages and their tools, the construction of software development environments, the definition of constraint programming algorithms, the modeling of distributed systems, and the construction of neural networks. One application is presented in detail: the interpretation of mathematical notation in scanned document images. The graph models the set of mathematical symbols, and their spatial and logical relationships. This graph is transformed by productions written in the PROGRES language. Copyright © 1999 John Wiley & Sons, Ltd.     

Separable algorithms for distance transformations on irregular grids

In this article, we propose to investigate two extensions of the E²DT (squared Euclidean Distance Transformation) on irregular isothetic grids (or I-grids), such as quadtree/octree or run-length encoded d-dimensional images. We enumerate the advantages and drawbacks of the I-CDT, based on the cell centres, and the ones of the I-BDT, which uses the cell borders. One of the main problem we mention is that no efficient algorithm has been designed to compute both transforms in arbitrary dimensions. To tackle this problem, we describe in this paper two algorithms, separable in dimension, to compute these distance transformations in the two-dimensional case, and we show that they can be easily extended to higher dimensions.     

An efficient classification and rendering method using tagged distance maps

Several high-speed volume rendering methods generate spatial data structures for speedup. Although they are useful for improving rendering speed, much time may be required to regenerate them. We propose an efficient classification and rendering method that supports fast classification. While original space-leaping needs to perform distance transformations for all voxels, our method modifies the values of some parts of the entire map by assigning predefined tag values when a voxels transparency is changed. The rendering algorithm is an extension of the space-leaping method and it determines the next sampling position by interpreting the values of those tagged voxels. This allows us to reclassify the volume quickly and to render datasets without loss of image quality.     

Parallel distance transforms on a linear array architecture

Distance transformation (DT) has been widely used for image matching and shape analysis. In this paper, a parallel algorithm for computing distance transformation is presented. First, it is shown that the algorithm has an execution time of 6N−4 cycles, for an N×N image using a parallel architecture that requires ⌈N/2⌉ parallel processors. By doing so, the real time requirement is fulfilled and its execution time is independent of the image contents. In addition, a partition method is developed to process an image when the parallel architecture has a fixed number of processing elements (PEs); say two or more. The total execution time for an N×N image by employing a fixed number of PEs is 2[N²/M+2(M−1)], when M is the fixed number of PEs.     

Three-dimensional Euclidean distance transformation and its application to shortest path planning

In this paper, we present a novel method to obtain the three-dimensional Euclidean distance transformation (EDT) in two scans of the image. The shortest path can be extracted based on the distance maps using the minimum value tracing. The EDT is obtained correctly and efficiently in a constant time for arbitrary types of images, including the existence of obstacles. By adopting the new dynamically rotational mathematical morphology, we not only guarantee the collision-free in the shortest path, but also reduce the time complexity dramatically.     

Computing simple-path convex hulls in hypergraphs

In a connected hypergraph a vertex set X is simple-path convex (sp-convex, for short) if either |X|?1 or X contains every vertex on every simple path between two vertices in X (Faber and Jamison, 1986 [7]), and the sp-convex hull of a vertex set X is the minimal superset of X that is sp-convex. In this paper, we give a polynomial algorithm to compute sp-convex hulls in an arbitrary hypergraph.     

Fuzzy Weirstrass theorem and convex fuzzy mappings

The convexity and continuity of fuzzy mappings are defined through a linear ordering and a metric on the set of fuzzy numbers. The local-global minimum property of real-valued convex functions is extended to convex fuzzy mappings. It is proved that a strict local minimizer of a quasiconvex fuzzy mapping is also a strict global minimizer. Characterizations for convex fuzzy mappings and quasiconvex fuzzy mappings are given. In addition, the Weirstrass theorem is extended from real-valued functions to fuzzy mappings.     

General intensity transformations and differential invariants

We consider the group of invertible image gray-value transformations and propose a generating equation for a complete set of differential gray-value invariants up to any order. Such invariants describe the image's geometrical structure independent of how its gray-values are mapped (contrast or brightness adjustments).This work has been carried out as part of the national priority research program 3D Computer Vision, supported by the Netherlands Ministries of Economic Affairs and Education and Science through a SPIN grant. The support from the participating industrial companies is gratefully acknowledged.     

Learner attending auto-monitor in distance learning using image recognition and Bayesian Networks

Distance learning is one of the common education methods. Its advantage lies in that the student can learn at anytime or anyplace. However, such a learning mode relies highly on the dependence of the student. Under different environments and conditions, not all the students can be attentive. In this research, an auto-detection system has been designed, using image processing and recognition technique, for defining the facial expressions and behavior easily found when a learner is inattentive or in bad mentality under distance learning environment. From the learner’s facial expressions and behavior features, the attentiveness of the student during distance learning can be determined by Bayesian Networks Model.After implementing the system of this research, and performing practical test, it is found that the accuracy of identifying the features of bad mentality and inattentive behavior is high. From Bayesian Networks assessment and inference, the learning attentiveness of the student can be determined precisely to have the teacher control the learning condition of the student explicitly.     

Computer mediated communication in distance education

Abstract  This paper describes experiences with computer mediated communication (CMC) in a postgraduate information systems module over two successive years. CMC was introduced primarily for pedagogical reasons, although a further aim was to carry out an exploratory investigation into factors affecting its successful adoption and the benefits to students. Students participated in a case study discussion through a bulletin board. Student participation, though not compulsory, was high at 82%. Over 80% of students surveyed thought their experience with electronic mail assisted learning, that the case study discussion was more useful than a conventional assignment, that the instructor seemed more accessible and that further use of electronic mail in their studies was desirable. Problems encountered included difficulties in learning to use the communications software and inadequacies in documentation. Social interaction amongst students and between students and the instructor was relatively low. Recommendations are that future work should concentrate on the quality of documentation and technical support, the ease of use of software chosen and the integration of technology across the organization.     

Decision-making with distance measures and induced aggregation operators

In this paper, we present a new decision-making approach that uses distance measures and induced aggregation operators. We introduce the induced ordered weighted averaging distance (IOWAD) operator. IOWAD is a new aggregation operator that extends the OWA operator by using distance measures and a reordering of arguments that depends on order-inducing variables. The main advantage of IOWAD is that it provides a parameterized family of distance aggregation operators between the maximum and the minimum distance based on a complex reordering process that reflects the complex attitudinal character of the decision-maker. We studied some of IOWAD’s main properties and different particular cases and further generalized IOWAD by using Choquet integrals. We developed an application in a multi-person decision-making problem regarding the selection of investments. We found that the main advantage of this approach is that it is able to provide a more complete picture of the decision-making process, enabling the decision-maker to select the alternative that it is more in accordance with his interests.     

Convex rear view mirrors compromise distance and time-to-contact judgements

Convex rear view mirrors increasingly replace planar mirrors in automobiles. While increasing the field of view, convex mirrors are also taken to increase distance estimates and thereby reduce safety margins. However, this study failed to replicate systematic distance estimation errors in a real world setting. Whereas distance estimates were accurate on average, convex mirrors lead to significantly more variance in distance and spacing estimations. A second experiment explored the effect of mirrors on time-to-contact estimations, which had not been previously researched. Potential effects of display size were separated from effects caused by distortion in convex mirrors. Time-to-contact estimations without a mirror were most accurate. However, not distortion, but visual angle seemed to cause estimation biases. Evaluating advantages and disadvantages of convex mirrors is far more complex than expected so far.     

An upper bound for the distance between a zero and a critical point of a solution of a second order linear differential equation

This paper presents an upper bound for the distance between a zero and a critical point of a solution of the second order linear differential equation (p(x)y^′)^′+q(x)y(x)=0, with p(x),q(x)>0. It also compares it with previous results.     

Computer systems for distributed and distance learning

Abstract Network-based learning is now such an important area that it would seem timely to examine progress to date and to draw conclusions regarding the direction of further research. This paper is the result of a survey of computer systems for distributed and distance learning, focusing on projects that help to illustrate the evolution of this important field. An examination such as this is important in its own right as a resource for other researchers wishing to pursue the subject further, but the survey also helps to highlight some of the major trends of past projects and to suggest some of the ways in which progress may be made in the future.     

Increasing validity in the evaluation of new distance learning technologies

In the development of distance learning, advances in cognitive science merge with new technology to deliver instruction worldwide. However, one major difficulty in evaluating the efficacy of these tools is determining which elements of instruction truly lead to observed changes in student performance. The purpose of this paper is to briefly review current use of various research methods for evaluating instructional technologies, discuss previous solutions to balancing the conflicting demands of internal and external validity, and then to propose a new research design that achieves this goal in a manner compatible with many instructional technology applications. The design, called a Strand of Pearls design, leverages the practice of delivering instruction in sequential modules to generate robust findings for which claims of internal validity, external validity, and maximal generalizability can be made.