Optimal tiling of heterogeneous images

A novel information theoretical approach has been developed, implemented and tested to approximate large, heterogeneous images with maps of varying spatial resolution and predefinedcomplexity. The goal of the approximation is the derivation of units in the spatial domain rather than determining classes in the attribute (spectral) domain. The proposed procedure is a regular, hierarchical tiling. The value of each tile is the local mean and the parti tion leads to a map represented by a region quadtree with minimum Kullback-divergence from the original image. Kullback-divergence is a non-parametric measure of dissimilarity of two spatial distributions and is applied here because of several advantageous properties. This tiling procedure can be also viewed as data compression, and it optimizes information loss under constraint on the spatial arrangement and number of tiles. The methodology is illustrated by the sampling design of an environmental soil mapping project of the salt-affected rangeland in Hortobagy, north-east Hungary.     

Penrose tiling

In a previous paper I discussed the topic of aperiodic tiling for the plane (Glassner, 1998). This technique helps us create patterns with lots of theme and variation, like the leaves on a tree. I continue discussing the subject. The basic approach is to take a bunch of 2D shapes and impose rules on how they can connect, like the pieces of a jigsaw puzzle     

On tiling under tomographic constraints

Given a tiling of a 2D grid with several types of tiles, we can count for every row and column how many tiles of each type it intersects. These numbers are called the projections. We are interested in the problem of reconstructing a tiling which has given projections. Some simple variants of this problem, involving tiles that are 1×1 or 1×2 rectangles, have been studied in the past, and were proved to be either solvable in polynomial time or -complete. In this note, we make progress toward a comprehensive classification of various tiling reconstruction problems, by proving -completeness results for several sets of tiles.     

面向异构多核处理器的的循环分块

将OpenACC编程模型用于异构多核处理器时,由于异构多核处理器加速设备内存有限,操作大量数据的代码不能获得很好的加速。针对这一问题,在OpenACC中引入循环分块子句,对循环进行分块处理,使每个循环块使用的数据能够存储在设备内存中;提出面向异构多核处理器的循环分块子句生成算法,并在基于Open64的"源-源"自动并行化系统Auto-ACC中进行实现。测试结果表明,在异构多核处理器上,扩展的循环分块子句及所提生成算法能够对程序进行明显的加速。     

Aperiodic tiling [computer graphics]

One of the most interesting ways of assembling small units is along one of the lattices that make up crystals. In this column I live entirely in a 2D world, so the crystals are nothing but collections of polygons in the plane. It is well known that there are only three regular polygons that can tile the plane. Here the verb tile means to cover the infinite plane with a set of polygons so that no gaps or overlaps exist among the polygons. Each polygon is called a tile and the composite pattern is called a tiling     

A cost-effective implementation of multilevel tiling

This paper presents a new cost-effective algorithm to compute exact loop bounds when multilevel tiling is applied to a loop nest having affine functions as bounds (nonrectangular loop nest). Traditionally, exact loop bounds computation has not been performed because its complexity is doubly exponential on the number of loops in the multilevel tiled code and, therefore, for certain classes of loops (i.e., nonrectangular loop nests), can be extremely time consuming. Although computation of exact loop bounds is not very important when tiling only for cache levels, it is critical when tiling includes the register level. This paper presents an efficient implementation of multilevel tiling that computes exact loop bounds and has a much lower complexity than conventional techniques. To achieve this lower complexity, our technique deals simultaneously with all levels to be tiled, rather than applying tiling level by level as is usually done. For loop nests having very simple affine functions as bounds, results show that our method is between 15 and 28 times faster than conventional techniques. For loop nests caving not so simple bounds, we have measured speedups as high as 2,300. Additionally, our technique allows eliminating redundant bounds efficiently. Results show that eliminating redundant bounds in our method is between 22 and 11 times faster than in conventional techniques for typical linear algebra programs.     

Width-bounded geodesic strips for surface tiling

We present an algorithm for computing families of geodesic curves over an open mesh patch to partition the patch into strip-like segments. Specifically, the segments can be well approximated using strips obtained by trimming long, rectangular pieces of material having a prescribed width δ. We call this the width-bounded geodesic strip tiling of a curved surface, a problem with practical applications such as the surfacing of curved roofs. The strips are said to be straight since they are constrained to fit within rectangles of width δ, in contrast to arbitrary, possible highly curved, strip segments. The straightness criterion, as well as a bound on strip widths, distinguishes our problem from ones previously studied for developable surface decomposition.     

Penrose tiling for visual secret sharing

Multimedia Tools and Applications - Visual secret sharing (VSS) has the advantage that the decryption is based on our human visual system without participation of any computational devices....     

A parallel algorithm for tiling problems

A parallel algorithm for tiling with polyominoes is presented. The tiling problem is to pack polyominoes in a finite checkerboard. The algorithm using lxmxn processing elements requires O(1) time, where l is the number of different kinds of polyominoes on an mxn checkerboard. The algorithm can be used for placement of components or cells in a very large-scale integrated circuit (VLSI) chip, designing and compacting printed circuit boards, and solving a variety of two- or three-dimensional packing problems.     

A neural network approach to tiling problems

The family of tiling problems comprises combinatorial optimization problems involving a grid and a number of shapes. Appropriate placements of the shapes on the grid are sought such that specific constraints concerning shape overlap and grid coverage are satisfied. The family of tiling problems has links with graph theory and is, thus, interesting from a theoretical point of view. Being related to VLSI circuit design, tiling problems are also of practical importance. In this piece of research, parallel implementations of representative tiling problems are proposed by employing three distinct harmony theory‐based artificial neural networks. Optimal solutions are always produced for appropriately selected values of the network parameters. Problem complexity has been found to affect the computational complexity of the solution. © 2001 John Wiley & Sons, Inc.     

A computational model for tiling recognizable two-dimensional languages

Tiling systems are a well accepted model to define recognizable two-dimensional languages but they are not an effective device for recognition unless a scanning strategy for the pictures is fixed. We define a tiling automaton as a tiling system equipped with a scanning strategy and a suitable data structure. The class of languages accepted by tiling automata coincides with the REC family. In this framework it is possible to define determinism, non-determinism and unambiguity. Then (deterministic) tiling automata are compared with the other known (deterministic) automata models for two-dimensional languages.     

Design and development of a reconfigurable tiling robot

Intelligent Service Robotics - This paper presents a novel polyromb-based self-reconfigurable domestic floor cleaning robot called “hRhombo” that consists of four rhombus-shaped modules...     

Cache tiling for high performance morphological image processing

Morphological image analysis is a technique of processing images through shape characteristics (Jain 1989). Because images are regular data structures, morphology algorithm's memory access patterns are predictable. By using read and write patterns, we derive a model of processing to examine inefficiencies in cache processing. We then develop a cache architecture for windowed processing that reduces cache thrashing. Our caching technique, cache tiling, improves efficiency dramatically for small caches independent of compiler optimizations. Programs are not affected, providing a transparent solution to improve caching. A system code, compilers, or profiling programs can determine the blocking necessary for the best performance. An analytical model for morphological processing's memory characteristics is presented that provides for exact cache analysis and prediction. The analytical model is compared to address traces to validate the model. Other algorithms such as inner product, matrix multiplication, and convolution also benefit from the architecture presented herein.     

The 4-way deterministic tiling problem is undecidable

It is shown that the (infinite) tiling problem by Wang tiles is undecidable even if the given tile set is deterministic by all four corners, i.e. a tile is uniquely determined by the colors of any two adjacent edges. The reduction is done from the Turing machine halting problem and uses the aperiodic tile set of Kari and Papasoglu.     

Optimizing convolution operations on GPUs using adaptive tiling

The research domain of Multimedia Content Analysis (MMCA) considers all aspects of the automated extraction of knowledge from multimedia data. High-performance computing techniques are necessary to satisfy the ever increasing computational demands of MMCA applications. The introduction of Graphics Processing Units (GPUs) in modern cluster systems presents application developers with a challenge. While GPUs are well known to be capable of providing significant performance improvements, the programming complexity vastly increases. To this end, we have extended a user transparent parallel programming model for MMCA, named Parallel-Horus, to allow the execution of compute intensive operations on the GPUs present in the cluster. The most important class of operations in the MMCA domain are convolutions, which are typically responsible for a large fraction of the execution time. Existing optimization approaches for CUDA kernels in general as well as those specific to convolution operations are too limited in both performance and flexibility. In this paper, we present a new optimization approach, called adaptive tiling, to implement a highly efficient, yet flexible, library-based convolution operation for modern GPUs. To the best of our knowledge, our implementation is the most optimized and best performing implementation of 2D convolution in the spatial domain available to date.     

基于循环分块的流水粒度优化算法

当计算划分层迭代数目较大,或是循环体单次迭代工作量较大,但可用的并行线程数目较小时,传统的基于循环分块的流水粒度优化方法无法进行处理。为此,提出一种基于循环分块减小流水粒度的方法,并根据流水并行循环的代价模型实现最优流水粒度的求解,设计实现了一个流水计算粒度的优化算法。对有限差分松弛法(FDR)的波前循环和时域有限差分法(FDTD)中典型循环的测试表明,与传统的流水粒度选择方法相比,所提算法能够得到更优的循环分块大小。     

Complexity analysis of propositional concurrent programs using domino tiling

The complexities of the possible rendezvous and the lockout problems for propositional concurrent programs are investigated in detail. We develop a unified strategy, based on domino tiling, to show that the above two problems with respect to a variety of propositional concurrent programs are complete for a broad spectrum of complexity classes, ranging from NLOGSPACE, PTIME, NP, PSPACE to EXPTIME. Our technique is novel in the sense that it demonstrates how two seemingly unrelated models, namely, propositional concurrent programs and dominoes, can be linked together in a natural and elegant fashion.     

利用相关性的快速块拼贴纹理合成

通过总结已有的纹理合成算法,采用基于样图的纹理合成方式提出了一种快速块拼贴纹理合成算法。该算法基于纹理的相关性,在搜索最佳目标纹理块时,通过相关位置偏移技术在样图中映射出已合成块的地址,适时加入螺旋搜索方法,利用块边界匹配算法将搜索到的地址块进行匹配,直到找到符合误差阈值的纹理块然后进行输出合成。通过实验发现,算法在处理随机性纹理和结构性纹理时都能取得比原先算法更好的合成效果,合成时间也大大加快。     

大屏幕无缝拼接系统的应用软件平台开发

在开放源码的三维绘制引擎OpenSceneGraph和Windows视频显示平台Direct Show的基础上,结合大屏幕投影的应用特点,利用一个通过网络连接的PC集群机组,开发了无缝拼接的三维渲染和视频播放大屏幕投影系统的软件平台,使之既可以用来观看各种格式的大屏幕电影,也可以交互浏览各种格式的三维虚拟场景。设计了主机/从机系统架构思想,利用OSG技术加载几何场景和视频,并提出在保留和立即两种模式下的同步控制技术——时间同步和帧同步。实践证明该方法效果理想,投入成本低,易于操作。