Efficient merging of multiple segments of B\'ezier curves

This paper deals with the merging problem of segments of a composite B\'ezier curve, with the endpoints continuity constraints. We present a novel method which is based on the idea of using constrained dual Bernstein polynomial basis (P. Wo\'zny, S. Lewanowicz, Comput. Aided Geom. Design 26 (2009), 566--579) to compute the control points of the merged curve. Thanks to using fast schemes of evaluation of certain connections involving Bernstein and dual Bernstein polynomials, the complexity of our algorithm is significantly less than complexity of other merging methods

A Solution Merging Heuristic for the Steiner Problem in Graphs Using Tree Decompositions

Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of treewidth sufficiently small to make these al- gorithms fast enough for practical use. Consequently, tree decomposition based algorithms have limited applicability to large scale optimization. However, by first reducing the input graph so that a small width tree decomposition can be found, we can harness the power of tree decomposi- tion based techniques in a heuristic algorithm, usable on graphs of much larger treewidth than would be tractable to solve exactly. We propose a solution merging heuristic to the Steiner Tree Problem that applies this idea. Standard local search heuristics provide a natural way to generate subgraphs with lower treewidth than the original instance, and subse- quently we extract an improved solution by solving the instance induced by this subgraph. As such the fixed parameter tractable algorithm be- comes an efficient tool for our solution merging heuristic. For a large class of sparse benchmark instances the algorithm is able to find small width tree decompositions on the union of generated solutions. Subsequently it can often improve on the generated solutions fast

Merging Galaxies in the SDSS EDR

We present a new catalog of merging galaxies obtained through an automated systematic search routine. The 1479 new pairs of merging galaxies were found in approximately 462 sq deg of the Sloan Digital Sky Survey Early Data Release (SDSS EDR; Stoughton et al. 2002) photometric data, and the pair catalog is complete for galaxies in the magnitude range 16.0 <= g* <= 20. The selection algorithm, implementing a variation on the original Karachentsev (1972) criteria, proved to be very efficient and fast. Merging galaxies were selected such that the inter-galaxy separations were less than the sum of the component galaxies' radii. We discuss the characteristics of the sample in terms of completeness, pair separation, and the Holmberg effect. We also present an online atlas of images for the SDSS EDR pairs obtained using the corrected frames from the SDSS EDR database. The atlas images also include the relevant data for each pair member. This catalog will be useful for conducting studies of the general characteristics of merging galaxies, their environments, and their component galaxies. The redshifts for a subset of the interacting and merging galaxies and the distribution of angular sizes for these systems indicate the SDSS provides a much deeper sample than almost any other wide-area catalog to date.Comment: 58 pages, which includes 15 figures and 6 tables. Figures 2, 8, 9, 10, 11, 13, and 14 are provided as JPEG files. For online atlas, see http://home.fnal.gov/~sallam/MergePair/ . Accepted for publication in A

Fast integer merging on the EREW PRAM

We investigate the complexity of merging sequences of small integers on the EREW PRAM. Our most surprising result is that two sorted sequences of $n$ bits each can be merged in $O(\log\log n)$ time. More generally, we describe an algorithm to merge two sorted sequences of $n$ integers drawn from the set $\{0,\ldots,m-1\}$ in $O(\log\log n+\log m)$ time using an optimal number of processors. No sublogarithmic merging algorithm for this model of computation was previously known. The algorithm not only produces the merged sequence, but also computes the rank of each input element in the merged sequence. On the other hand, we show a lower bound of $\Omega(\log\min\{n,m\})$ on the time needed to merge two sorted sequences of length $n$ each with elements in the set $\{0,\ldots,m-1\}$, implying that our merging algorithm is as fast as possible for $m=(\log n)^{\Omega(1)}$. If we impose an additional stability condition requiring the ranks of each input sequence to form an increasing sequence, then the time complexity of the problem becomes $\Theta(\log n)$, even for $m=2$. Stable merging is thus harder than nonstable merging

Restoration of images based on subspace optimization accelerating augmented Lagrangian approach

AbstractWe propose a new fast algorithm for solving a TV-based image restoration problem. Our approach is based on merging subspace optimization methods into an augmented Lagrangian method. The proposed algorithm can be seen as a variant of the ALM (Augmented Lagrangian Method), and the convergence properties are analyzed from a DRS (Douglas–Rachford splitting) viewpoint. Experiments on a set of image restoration benchmark problems show that the proposed algorithm is a strong contender for the current state of the art methods

An improved fast scanning algorithm based on distance measure and threshold function in region image segmentation

Segmentation is an essential and important process that separates an image into regions that have similar characteristics or features. This will transform the image for a better image analysis and evaluation. An important benefit of segmentation is the identification of region of interest in a particular image. Various algorithms have been proposed for image segmentation and this includes the Fast Scanning algorithm which has been employed on food, sport and medical image segmentation. The clustering process in Fast Scanning algorithm is performed by merging pixels with similar neighbor based on an identified threshold and the use of Euclidean Distance as distance measure. Such an approach leads to a weak reliability and shape matching of the produced segments. Hence, this study proposes an Improved Fast Scanning algorithm that is based on Sorensen distance measure and adaptive threshold function. The proposed adaptive threshold function is based on the grey value in an image’s pixels and variance. The proposed Improved Fast Scanning algorithm is realized on two datasets which contains images of cars and nature. Evaluation is made by calculating the Peak Signal to Noise Ratio (PSNR) for the Improved Fast Scanning and standard Fast Scanning algorithm. Experimental results showed that proposed algorithm produced higher PSNR compared to the standard Fast Scanning. Such a result indicate that the proposed Improved Fast Scanning algorithm is useful in image segmentation and later contribute in identifying region of interesting in pattern recognition