We reinterpret an inequality, due originally to Sidorenko, for linear extensions of posets in terms convex subsets the symmetric group \(\mathfrak{S}_n\). conjecture that analogous inequalities hold arbitrary (not-necessarily-finite) Coxeter groups \(W\), and prove this hyperoctahedral \(B_n\) all right-angled groups. Our proof (and new \(\mathfrak{S}_n\)) use a combinatorial insertion map clos...

Changes in the chemical composition and antioxidant activity of flaxseed hull during maturation were investigated. P129 hull variety was studied at four maturation stages (St1, St2, St3, and St4). Significant variation in proximate composition and flaxseed hull oil characteristics were observed. A significant increase in the carbohydrates content of the hull was observed during development. The...

A convex hull is a polygon which encloses all given set of points.Euler number or Euler characteristic of an image has proven to be an important feature in many image analyses and visual inspection applications. This paper presents an algorithm for fast computing the convex hull of a planar scattered point set, which pre-strike an initial convex hull boundary, remove internal points in the boun...

In this paper, convex hull based features are used for recognition of isolated Roman numerals using a Multi Layer Perceptron (MLP) based classifier. Experiments of convex hull based features for handwritten character recognition are few in numbers. Convex hull of a pattern and the centroid of the convex hull both are affine invariant attributes. In this work, 25 features are extracted based on ...

We introduce order-k α-hulls and αshapes — generalizations of α-hulls and α-shapes. Being also a generalization of k-hull (known in statistics as “k-depth contour”), order-k α-hull provides a link between shape reconstruction and statistical depth. As a generalization of α-hull, order-k α-hull gives a robust shape estimation by ignoring locally up to k outliers in a point set. Order-k α-shape p...

In this paper, artificial bee colony (ABC) algorithms are introduced to optimize ship hull forms for reduced drag. Two versions of ABC algorithm are used: one is the basic ABC algorithm, and the other is an improved artificial bee colony (IABC) algorithm. A recently developed fast flow solver based on the Neumann-Michell theory is used to evaluate the drag of the ship in the optimization proces...

We present structural properties of the farthest line-segment Voronoi diagram in the piecewise linear L∞ and L1 metrics, which are computationally simpler than the standard Euclidean distance and very well suited for VLSI applications. We introduce the farthest line-segment hull, a closed polygonal curve that characterizes the regions of the farthest line-segment Voronoi diagram, and is related...

The marching cubes algorithm has been widely adopted for extracting a surface mesh from a volumetric description of the visual hull reconstructed from silhouettes. However, typical volumetric descriptions, such as an octree, provide only a binary description about the visual hull. The lack of interpolation information along each voxel edge, which is required by the marching cubes algorithm, usu...

Imprecision is a long-standing problem in CAD design and high accuracy image-based reconstruction applications. The visual hull which is the closed silhouette equivalent shape of the objects of interest is an important concept in image-based reconstruction. We extend the domain-theoretic framework, which is a robust and imprecision capturing geometric model, to analyze the imprecision in the ou...