In this paper we consider the k-link visibility polygon of an object inside a polygonal environment with a reflective edge called a mirror. The k-link visibility polygon of an object inside a polygon P is the set of all points in P , which are visible to some points of that object with at most k − 1 intermediate points, under the property that consecutive intermediate points are mutually visibl...

We consider the methods of construction simple polygons for a set S of n points and applying them for searching the minimal area polygon. In this paper we propose the approximate algorithm, which generates the simple polygonalizations of a fixed set of points and finds the minimal area polygon, in O (n) time and using O(n) memory. Keywords—simple polygon, approximate algorithm, minimal area pol...

The two fundamental problems in a pattern recognition system are feature extraction (shape measurement) and classification. The problem of extracting a vector of shape measurements from a digital image can be further decomposed into three subproblems. The first is the image segmentation problem, i.e., the separation of objects of interest from their background. The cluster analysis methods disc...

In this paper, we introduce a modified fence fill algorithm for filling a polygon. Fence fill algorithm is a modified edge fill algorithm. As opposed to the edge fill algorithm that fills pixels starting from the polygon edge to the maximum screen coordinates, the fence fill algorithm fills pixels bounded by the polygon edge and the fence. This involves large number of calculations to find the ...

This paper proposes a novel methodology for creating efficient polygon models for spatial datasets. A comprehensive analysis framework is proposed that takes a spatial cluster as an input and generates a polygon model for the cluster as an output. The framework creates a visually appealing, simple, and smooth polygon for the cluster by minimizing a fitness function. We propose a novel polygon f...

Polygon-based classification was performed on multi-scale images of SPOT4 XS, SPOT5 XS, IKONOS XS, QuickBird XS and QuickBird Pansharpaned (PS) covering an agricultural area located in Karacabey, Turkey. The objective of the study was to assess the classification accuracies of different spatial resolution images on an agricultural land using the polygon-based classification techniques. The exis...

We present two new versions of the chromatic art gallery problem that can improve upper bound of the required colors pretty well. In our version, we employ restricted angle guards so that these modern guards can visit α-degree of their surroundings. If α is between 0 and 180 degree, we demonstrate that the strong chromatic guarding number is constant. Then we use orthogonal 90-degree guards for...

The paper presents a parallel algorithm for polygon approximation targeted at reconfigurable multi-ring hardware. The proposed algorithm grows the edges of polygon approximation that is based on principle of merging. The edge/s are grown simultaneously at point/s where the minimum merging error is produced. The merging process is made faster by carrying it out in two stages: i) During first sta...

Let Fq be a finite field of cardinality q and characteristic p. Let P (x) be any one-variable Laurent polynomial over Fq of degree (d1, d2) respectively and p d1d2. For any fixed s ≥ 1 coprime to p, we prove that the q-adic Newton polygon of the L-functions of exponential sums of P (xs) has a tight lower bound which we call HodgeStickelberger polygon, depending only on the d1, d2, s and the res...