Geometric Spanners for Points Inside a Polygonal Domain

Let P be a set of n points inside a polygonal domain D. A polygonal domain with h holes (or obstacles) consists of h disjoint polygonal obstacles surrounded by a simple polygon which itself acts as an obstacle. We first study t-spanners for the set P with respect to the geodesic distance function d where for any two points p and q, d(p,q) is equal to the Euclidean length of the shortest path from p to q that avoids the obstacles interiors. For a case where the polygonal domain is a simple polygon (i.e., h=0), we construct a (sqrt(10)+eps)-spanner that has O(n log^2 n) edges where eps is the a given positive real number. For a case where there are h holes, our construction gives a (5+eps)-spanner with the size of O(sqrt(h) n log^2 n). Moreover, we study t-spanners for the visibility graph of P (VG(P), for short) with respect to a hole-free polygonal domain D. The graph VG(P) is not necessarily a complete graph or even connected. In this case, we propose an algorithm that constructs a (3+eps)-spanner of size almost O(n^{4/3}). In addition, we show that there is a set P of n points such that any (3-eps)-spanner of VG(P) must contain almost n^2 edges

An experimental study of a point set registration algorithm

We study the problem of point set registration in the plane to measure the similarity between point sets in the plane. This problem plays an important role in a variety of applications, from computer vision to molecular biology. Here, in this project, we study, implement, test, and evaluate FPPMA which is one of the fastest algorithmic approaches in this context. We then compare the results with another well-known technique in the computer vision community (GMMReg method). Finally, we generalize FPPMA to solve the groupwise point set registration problem

Geometric Spanners for Points Inside a Polygonal Domain

Let P be a set of n points inside a polygonal domain D. A polygonal domain with h holes (or obstacles) consists of h disjoint polygonal obstacles surrounded by a simple polygon which itself acts as an obstacle. We first study t-spanners for the set P with respect to the geodesic distance function π where for any two points p and q, π(p, q) is equal to the Euclidean length of the shortest path from p to q that avoids the obstacles interiors. For a case where the polygonal domain is a simple polygon (i.e., h = 0), we construct a ( √ 10 + )-spanner that has O(n log 2 n) edges. For a case where there are h holes, our construction gives a (5 + )-spanner with the size Moreover, we study t-spanners for the visibility graph of P (V G(P), for short) with respect to a hole-free polygonal domain D. The graph V G(P) is not necessarily a complete graph or even connected. In this case, we propose an algorithm that constructs a (3 + )-spanner of size O(n 4/3+δ ). In addition, we show that there is a set P of n points such that any (3 − ε)-spanner of V G(P) must contain Ω(n²) edges

Clinical and manometric evaluation of postoperative anorectal function in patients after trans-anal pull-through for Hirschsprung disease

Abstract Background Transanal endorectal pull-through (TEPT) surgery is a new trend in the treatment of Hirschsprung disease, and evaluating its functional outcome is difficult. The purpose of this study is to evaluate the defecation pattern after TEPT surgery in pediatrics. Material and methods In this cross-sectional survey, 40 patients with Hirschsprung disease were studied. They underwent a one-stage transanal pull-through procedure from May 2007 till April 2015 in Namazi hospital by the same surgeon. All the patients had the aganglionic segment in the rectosigmoid, confirmed by pre-operation barium enema and post-operation histopathology. The patients were 40 children with mean operation age of 36.6 months old. The success rate of surgery was evaluated by following the questionnaire form. Clinical evaluation with bowel function score and anorectomanometry were carried out. Result One hundred percent of them had a daily stool. Eighty-five percent of patients never experienced pain during defecation, 10% experienced occasional pain, and the rest felt pain with every defecation. Just one case (5%) reported using a laxative. Regarding improvements after the operation, 75% were completely okay, 20% felt much better, and 5% reported some improvements. The average National Health Service score was 8.375, which seems satisfactory. The mean average anal sphincter in the group with soiling was 39.67 and in the group without soiling was 34.83, which is in the normal range in both groups, and there was no significant difference between these groups (P > 0.05). Conclusion The defecation pattern after TEPT surgery were satisfactory in almost all cases, even in infancy. Most patients had satisfactory manometry and clinical result