Applications of topology in computer algorithms

The aim of this paper is to discuss some applications of general topology in computer algorithms including modeling and simulation, and also in computer graphics and image processing. While the progress in these areas heavily depends on advances in computing hardware, the major intellectual achievements are the algorithms. The applications of general topology in other branches of mathematics are not discussed, since they are not applications of mathematics outside of mathematics.Comment: This paper is based on the invited lecture at International Conference on Topology and Applications held in August 23--27, 1999, at Kanagawa University in Yokohama, Japa

Edge Detection Technology using Image processing in Matlab

An edge may be defined as a set of connected pixels that forms a boundary between two disarrange regions. Edge detection is a method of segmenting an image into regions of conclusion. Edge detection plays an very important role in digital image processing and practical aspects of our life. In this report, we studied various edge detection techniques as Robert, Sobel and Canny operators. On comparing them we can see that canny edge detector performs better than all other edge detectors on various aspects such as it is flexible in nature, doing better for noisy imageand gives sharp edges , low probability of detecting false edges etc DOI: 10.17762/ijritcc2321-8169.150520

Differential Elimination and Biological Modelling

International audienceThis paper describes applications of a computer algebra method, differential elimination, to applied mathematics problems mostly borrowed from biology. The two considered applications are related to the parameters estimation and the model reduction problems. In both cases, differential elimination can be viewed as a preparation to numerical treatments. Together with the applications, the paper introduces two implementations of the differential elimination algorithms: the diffalg package and the BLAD libraries

Mapping polygons to the grid with small Hausdorff and Fréchet distance

We show how to represent a simple polygon P by a (pixel-based) grid polygon Q that is simple and whose Hausdorff or Fréchet distance to P is small. For any simple polygon P, a grid polygon exists with constant Hausdorff distance between their boundaries and their interiors. Moreover, we show that with a realistic input assumption we can also realize constant Fréchet distance between the boundaries. We present algorithms accompanying these constructions, heuristics to improve their output while keeping the distance bounds, and experiments to assess the output