Regular patterns

Dancers and choreographers employ symmetric patterns of bodies on stage fluidly and in fleeting ways. Ballet, folk, and contemporary dances often arrange dancers in two categories: men and women, two colors of costumes, antagonistic groups, etc. This paper investigates danced two-colored or dichromatic symmetry patterns, and continues an earlier investigation on how such danced symmetry patterns may be seamlessly morphed from one symmetry type to another, in a manner similar to visual parquet deformations. It also looks briefly at how they are employed in a variety of dance forms. These explorations may make for engaging activities for math classes or

Large parts of the tidal estuary of river Elbe (Germany) are characterized by regular patterns of sand dunes. They are presumed to evolve due to complex sand transport mechanisms and show multi-faceted migration patterns. Direction and magnitude of their migration are influenced by hydrodynamic boundary conditions such as river runoff and tides. Dune Migration can lead to residual sand transport rates, depending on its direction and magnitude and the dune’s characteristics. The understanding of dune migration patterns and associated sand transport is the basis of an effective sediment management as well as an important requirement for planning offshore structures. This study focuses on methods for computing migration and sand transport rates in automated ways. In a comparison and validation of different approaches, a cross-correlation technique was found to produce best results. From a unique data set of up to six annual bathymetrical multi-beam soundings between 1995 and 2010, dune...

Affine transformations are of vital importance in many tasks pertaining to motion design and animation. Interpolation of affine transformations is non-trivial. Typically, the given affine transformation is decomposed into simpler components which are easier to interpolate. This may lead to unintuitive results, while in some cases, such solutions may not work. In this work, we propose an interpolation framework which is based on a Lie group representation of the affine transformation. The Lie group representation decomposes the given transformation into simpler and meaningful components, on which computational tools like the exponential and logarithm maps are available in closed form. Interpolation exists for all affine transformations while preserving a few characteristics of the original transformation. A detailed analysis and several experiments of the proposed framework are included.

Planar ornaments, a.k.a. wallpapers, are regular repetitive patterns which exhibit translational symmetry in two independent directions. There are exactly 17 distinct planar symmetry groups. We present a fully automatic method for complete analysis of planar ornaments in 13 of these groups, specifically, the groups called p6m, p6, p4g, p4m, p4, p31m, p3m, p3, cmm, pgg, pg, p2 and p1. Given the image of an ornament fragment, we present a method to simultaneously classify the input into one of the 13 groups and extract the so called fundamental domain (FD), the minimum region that is sufficient to reconstruct the entire ornament. A nice feature of our method is that even when the given ornament image is a small portion such that it does not contain multiple translational units, the symmetry group as well as the fundamental domain can still be defined. This is because, in contrast to common approach, we do not attempt to first identify a global translational repetition lattice. Though the presented constructions work for quite a wide range of ornament patterns, a key assumption we make is that the perceivable motifs (shapes that repeat) alone do not provide clues for the underlying symmetries of the ornament. In this sense, our main target is the planar arrangements of asymmetric interlocking shapes, as in the symmetry art of Escher.

Self organizing templates used as etch masks and growth seeds enable efficient mass fabrication of nanoscale device layers. In this work we introduce a new way to direct self-organisation of nanoscale pore formation during anodisation of metal layers of direct relevance to nanofabrication process flows. We demonstrate and quantitatively characterize how proximal surface oxidation frustrates and redirects random pore ordering in the film. Our results show a strict correlation between pore formation and oxide thickness on the aluminum surface providing important information on pore nucleation and growth in substrate-supported thin films and confirming the predictions of several existing theoretical models on pore growth. We find a line ar relation between applied voltage and intrinsic self organizing interpore distance for supported thin films (from 80 to 150 nm) over a wide potential window between 40 and 120 V, mirroring behavior of thicker unsupported foils but with a different coefficient of proportionality. Using this technique, we are able to produce arbitrary and highly regular patterns of pores while manipulating pore pitch up to 20% from the natural spacing. This work demonstrates for the first time how local oxidation can direct self organisation.

We propose to measure the quality of an affine motion by its steadiness, which we formulate as the inverse of its Average Relative Acceleration (ARA). Steady affine motions, for which ARA=0, include translations, rotations, screws, and the golden spiral. To facilitate the design of pleasing in-betweening motions that interpolate between an initial and a final pose (affine transformation), B and C , we propose the Steady Affine Morph (SAM), defined as A t ∘ B with A = C ∘ B -1 . A SAM is affine-invariant and reversible. It preserves isometries (i.e., rigidity), similarities, and volume. Its velocity field is stationary both in the global and the local (moving) frames. Given a copy count, n , the series of uniformly sampled poses, A i/n ∘ B , of a SAM form a regular pattern which may be easily controlled by changing B , C , or n , and where consecutive poses are related by the same affinity A 1/n . Although a real matrix A t does not always exist, we show that it does for a convex and...

Traditional image analysis methods are mostly pixel-based and use the spectral differences of landscape elements at the Earth surface to classify these elements or to extract element properties from the Earth Observation image. Geographic object-based image analysis (GEOBIA) has received considerable attention over the past 15 years for analyzing and interpreting remote sensing imagery. In contrast to traditional image analysis, GEOBIA works more like the human eye-brain combination does. The latter uses the object's color (spectral information), size, texture, shape and occurrence to other image objects to interpret and analyze what we see. GEOBIA starts by segmenting the image grouping together pixels into objects and next uses a wide range of object properties to classify the objects or to extract object's properties from the image. Significant advances and improvements in image analysis and interpretation are made thanks to GEOBIA. In June 2010 the third conference on GEOBIA took place at the Ghent University after successful previous meetings in Calgary (2008) and Salzburg (2006). This special issue presents a selection of the 2010 conference papers that are worked out as full research papers for JAG. The papers cover GEOBIA applications as well as innovative methods and techniques. The topics range from vegetation mapping, forest parameter estimation, tree crown identification, urban mapping, land cover change, feature selection methods and the effects of image compression on segmentation. From the original 94 conference papers, 26 full research manuscripts were submitted; nine papers were selected and are presented in this special issue. Selection was done on the basis of quality and topic of the studies. The next GEOBIA conference will take place in Rio de Janeiro from 7 to 9 May 2012 where we hope to welcome even more scientists working in the field of GEOBIA.

We propose to measure the quality of an affine motion by its steadiness, which we formulate as the inverse of its Average Relative Acceleration (ARA). Steady affine motions, for which ARA=0, include translations, rotations, screws, and the golden spiral. To facilitate the design of pleasing in-betweening motions that interpolate between an initial and a final pose (affine transformation), B and C , we propose the Steady Affine Morph (SAM), defined as A t ∘ B with A = C ∘ B -1 . A SAM is affine-invariant and reversible. It preserves isometries (i.e., rigidity), similarities, and volume. Its velocity field is stationary both in the global and the local (moving) frames. Given a copy count, n , the series of uniformly sampled poses, A i/n ∘ B , of a SAM form a regular pattern which may be easily controlled by changing B , C , or n , and where consecutive poses are related by the same affinity A 1/n . Although a real matrix A t does not always exist, we show that it does for a convex and...

Large parts of the tidal estuary of river Elbe (Germany) are characterized by regular patterns of sand dunes. They are presumed to evolve due to complex sand transport mechanisms and show multi-faceted migration patterns. Direction and magnitude of their migration are influenced by hydrodynamic boundary conditions such as river runoff and tides. Dune Migration can lead to residual sand transport rates, depending on its direction and magnitude and the dune’s characteristics. The understanding of dune migration patterns and associated sand transport is the basis of an effective sediment management as well as an important requirement for planning offshore structures. This study focuses on methods for computing migration and sand transport rates in automated ways. In a comparison and validation of different approaches, a cross-correlation technique was found to produce best results. From a unique data set of up to six annual bathymetrical multi-beam soundings between 1995 and 2010, dune...

Rare itemset mining is a relatively recent topic of study in data mining. In certain application domains, such as online banking transaction analysis, sensor data analysis, and stock market analysis, rare patterns are patterns with low support and high confidence that are extremely interesting when compared to frequent patterns. Numerous applications generate large amounts of continuous data streams. We require efficient algorithms capable of processing data streams in order to analyze them and find unique patterns. The strategies developed for static databases cannot be used to data streams. As a result, we require algorithms created expressly for data stream processing in order to extract critical unique patterns. Rare pattern mining is still in its infancy, with only a few ways available. To address this is developed the Dynamic Support Range-based Hybrid-Eclat Algorithm (DSRHEA), an Eclatbased technique for mining unique patterns from a data stream using bit-set vertical mining with two item-based optimizations. The detected patterns are kept in a prefix-based rare pattern tree that uses double hashing to maintain the unusual pattern in the data stream. Testing showed that the proposed method did well in terms of how long it took to run, how many rare patterns it made and accuracy.

– Web Utility mining has recently been an emerging topic in the field of data mining and so is the web mining, an important research topic in database technologies. Thus, the web utility mining is effective in not only discovering the frequent temporal web transactions & generating high utility itemsets, but also identifying the profit of webpages. For enhancing the web utility mining, this study proposes a mixed approach to the techniques of web mining, temporal high utility itemsets & On-shelf utility mining algorithms, to provide web designers and decision makers more useful and meaningful web information. In the two Phases of the algorithm, we came out with the more efficient and modern techniques of web & utility mining inorder to yield excellent results on web transactional databases.

Mining frequent patterns over data streams is an interesting problem due to its wide application area. In this study, a novel method for sliding window frequent patterns mining over data streams is proposed. This method utilizes a compressed and memory efficient tree data structure to store and to maintain sliding window transactions. The method dynamically reconstructs and compresses tree data structure to control the amount of memory usage. Moreover, the mining task is efficiently performed using the data structure when a user issues a mining request. The mining process reuses the tree structure to extract frequent patterns and does not need additional memory requirement. Experimental evaluations on real datasets show that our proposed method outperforms recently proposed sliding window based algorithms.

Data mining and knowledge discovery is an active research work and getting popular by the day because it can be applied in different type of data like web click streams, sensor networks, stock exchange data and time-series data and so on. Data streams are not devoid of research problems. This is attributed to non-stop data arrival in numerous, swift, varying with time, erratic and unrestricted data field. It is highly important to find the regular prototype in single pass data stream or minor number of passes when making use of limited space of memory. In this survey the review on the final progress in the study of regular model mining in data streams. Mining algorithms are talked about at length and further research directions have been suggested.

Since mining frequent patterns from transactional databases involves an exponential mining space and generates a huge number of patterns, efficient discovery of user-interest-based frequent pattern set becomes the first priority for a mining algorithm. In many real-world scenarios it is often sufficient to mine a small interesting representative subset of frequent patterns. Temporal periodicity of pattern appearance can be regarded as an important criterion for measuring the interestingness of frequent patterns in several applications. A frequent pattern can be said periodic-frequent if it appears at a regular interval given by the user in the database. In this paper, we introduce a novel concept of mining periodic-frequent patterns from transactional databases. We use an efficient tree-based data structure, called Periodic-frequent pattern tree (PF-tree in short), that captures the database contents in a highly compact manner and enables a pattern growth mining technique to generate the complete set of periodic-frequent patterns in a database for user-given periodicity and support thresholds. The performance study shows that mining periodic-frequent patterns with PF-tree is time and memory efficient and highly scalable as well.

This paper proposes a prefix-tree structure, called CPS-tree (Compact Pattern Stream tree) that efficiently discovers the exact set of recent frequent patterns from high-speed data stream. The CPS-tree introduces the concept of dynamic tree restructuring technique in handling stream data that allows it to achieve highly compact frequency-descending tree structure at runtime and facilitates an efficient FP-growth-based [1] mining technique.

Mining regular patterns in data streams is an emerging research area and also a challenging problem in present days because in Data streams new data comes continuously with varying rates. Closed item set mining gained lot of implication in data mining research from conventional mining methods. So in this paper we propose a narrative approach called CRPDS (Closed Regular Patterns in Data Streams) with vertical data format using sliding window model. To our knowledge no method has been proposed to mine closed regular patterns in data streams. As the stream flows our CRPDS-method mines closed regular itemsets based on regularity threshold and user given support count. The experimental results show that the proposed method is efficient and scalable in terms of memory and time.

More and more applications such as traffic modeling, military sensing and tracking, online data processing etc., generate a large amount of data streams every day. Efficient knowledge discovery of such data streams is an emerging active research area in data mining with broad applications. Different from data in traditional static databases, data streams typically arrive continuously in high speed with huge amount and changing data distribution. This raises new issues that need to be considered when developing association rule mining techniques for stream data. Due to the unique features of data stream, traditional data mining techniques which require multiple scans of the entire data sets can not be applied directly to mine stream data, which usually allows only one scan and demands fast response time.