Computing a rectilinear shortest path amid splinegons in plane

We reduce the problem of computing a rectilinear shortest path between two given points s and t in the splinegonal domain \calS to the problem of computing a rectilinear shortest path between two points in the polygonal domain. As part of this, we define a polygonal domain \calP from \calS and transform a rectilinear shortest path computed in \calP to a path between s and t amid splinegon obstacles in \calS. When \calS comprises of h pairwise disjoint splinegons with a total of n vertices, excluding the time to compute a rectilinear shortest path amid polygons in \calP, our reduction algorithm takes O(n + h \lg{n}) time. For the special case of \calS comprising of concave-in splinegons, we have devised another algorithm in which the reduction procedure does not rely on the structures used in the algorithm to compute a rectilinear shortest path in polygonal domain. As part of these, we have characterized few of the properties of rectilinear shortest paths amid splinegons which could be of independent interest

Subclass Discriminant Analysis of Morphological and Textural Features for HEp-2 Staining Pattern Classification

Classifying HEp-2 fluorescence patterns in Indirect Immunofluorescence (IIF) HEp-2 cell imaging is important for the differential diagnosis of autoimmune diseases. The current technique, based on human visual inspection, is time-consuming, subjective and dependent on the operator's experience. Automating this process may be a solution to these limitations, making IIF faster and more reliable. This work proposes a classification approach based on Subclass Discriminant Analysis (SDA), a dimensionality reduction technique that provides an effective representation of the cells in the feature space, suitably coping with the high within-class variance typical of HEp-2 cell patterns. In order to generate an adequate characterization of the fluorescence patterns, we investigate the individual and combined contributions of several image attributes, showing that the integration of morphological, global and local textural features is the most suited for this purpose. The proposed approach provides an accuracy of the staining pattern classification of about 90%

Mobile vs. point guards

We study the problem of guarding orthogonal art galleries with horizontal mobile guards (alternatively, vertical) and point guards, using "rectangular vision". We prove a sharp bound on the minimum number of point guards required to cover the gallery in terms of the minimum number of vertical mobile guards and the minimum number of horizontal mobile guards required to cover the gallery. Furthermore, we show that the latter two numbers can be calculated in linear time.Comment: This version covers a previously missing case in both Phase 2 &

Approximate Euclidean shortest paths in polygonal domains

Given a set $\mathcal{P}$ of $h$ pairwise disjoint simple polygonal obstacles in $\mathbb{R}^2$ defined with $n$ vertices, we compute a sketch $\Omega$ of $\mathcal{P}$ whose size is independent of $n$, depending only on $h$ and the input parameter $\epsilon$. We utilize $\Omega$ to compute a $(1+\epsilon)$-approximate geodesic shortest path between the two given points in $O(n + h((\lg{n}) + (\lg{h})^{1+\delta} + (\frac{1}{\epsilon}\lg{\frac{h}{\epsilon}})))$ time. Here, $\epsilon$ is a user parameter, and $\delta$ is a small positive constant (resulting from the time for triangulating the free space of $\cal P$ using the algorithm in \cite{journals/ijcga/Bar-YehudaC94}). Moreover, we devise a $(2+\epsilon)$-approximation algorithm to answer two-point Euclidean distance queries for the case of convex polygonal obstacles.Comment: a few updates; accepted to ISAAC 201

Most vital segment barriers

We study continuous analogues of "vitality" for discrete network flows/paths, and consider problems related to placing segment barriers that have highest impact on a flow/path in a polygonal domain. This extends the graph-theoretic notion of "most vital arcs" for flows/paths to geometric environments. We give hardness results and efficient algorithms for various versions of the problem, (almost) completely separating hard and polynomially-solvable cases

Query-points visibility constraint minimum link paths in simple polygons

We study the query version of constrained minimum link paths between two points inside a simple polygon $P$ with $n$ vertices such that there is at least one point on the path, visible from a query point. The method is based on partitioning $P$ into a number of faces of equal link distance from a point, called a link-based shortest path map (SPM). Initially, we solve this problem for two given points $s$, $t$ and a query point $q$. Then, the proposed solution is extended to a general case for three arbitrary query points $s$, $t$ and $q$. In the former, we propose an algorithm with $O(n)$ preprocessing time. Extending this approach for the latter case, we develop an algorithm with $O(n^3)$ preprocessing time. The link distance of a $q$-$visible$ path between $s$, $t$ as well as the path are provided in time $O(\log n)$ and $O(m+\log n)$, respectively, for the above two cases, where $m$ is the number of links