Efficient algorithms for computation of the loss curve of video sources

The loss curve of a video source characterizes the loss rate of the video stream generated by the source as a function of the allocated buffer size for a given transmission rate. The loss curve is useful in the optimal allocation of resources when the video stream is transmitted over a packet network, so that the desired tradeoff can be reached among the loss rate, bandwidth and the buffer space to be allocated in the network. We present an algorithm for computation of the entire loss curve of an elementary video stream. In contrast to earlier algorithms which employ statistical approaches, our algorithm is deterministic and computes the exact loss curve of the video stream. The algorithm exploits the piecewise linearity of the loss curve and computes only the points at which the slope of the loss curve changes. We also present an extension of the algorithm to MPEG-2 transport streams. The efficiency of the algorithm is demonstrated by results from several example video streams. For example, the algorithm was able to compute the entire loss curve of a 2-h elementary video stream in approximately 11 s on a Sun Ultra-2 workstation.     

Controlled linear perturbation

We present an algorithmic solution to the robustness problem in computational geometry, called controlled linear perturbation, and demonstrate it on Minkowski sums of polyhedra. The robustness problem is how to implement real RAM algorithms accurately and efficiently using computer arithmetic. Approximate computation in floating point arithmetic is efficient but can assign incorrect signs to geometric predicates, which can cause combinatorial errors in the algorithm output. We make approximate computation accurate by performing small input perturbations, which we compute using differential calculus. This strategy supports fast, accurate Minkowski sum computation. The only prior robust implementation uses a less efficient algorithm, requires exact algebraic computation, and is far slower based on our extensive testing.     

Approximation of 3D surface-to-surface intersection curves

This paper addresses the problem of approximating a surface-to-surface intersection curve. Accurate computation of an intersection curve is not practical due to the degree explosion problem, when function decomposition is used, and fundamentally is not possible because of some computational reasons. Therefore, in practical applications, an approximate intersection curve with a low degree is extensively used. However, the approximation of an intersection curve needs to consider the topological and numerical aspects together to produce the approximate curve to be as close to the exact one as possible, since approximation inevitably involves both numerical and topological errors. In this paper, algorithms to compute an approximate intersection curve, which are topologically consistent and numerically accurate with the exact intersection curve, are presented. A set of sufficient conditions for an approximate curve to be topologically consistent with the exact one are provided, and the use of a validated ordinary differential equation solver is discussed. The approximate curve is then refined to reduce the error against the exact curve through optimization. The proposed method is demonstrated with examples.     

Approximating the Medial Axis from the Voronoi Diagram with a Convergence Guarantee

The medial axis of a surface in 3D is the closure of all points that have two or more closest points on the surface. It is an essential geometric structure in a number of applications involving 3D geometric shapes. Since exact computation of the medial axis is difficult in general, efforts continue to improve their approximations. Voronoi diagrams turn out to be useful for this approximation. Although it is known that Voronoi vertices for a sample of points from a curve in 2D approximate its medial axis, a similar result does not hold in 3D. Recently, it has been discovered that only a subset of Voronoi vertices converge to the medial axis as sample density approaches infinity. However, most applications need a nondiscrete approximation as opposed to a discrete one. To date no known algorithm can compute this approximation straight from the Voronoi diagram with a guarantee of convergence. We present such an algorithm and its convergence analysis in this paper. One salient feature of the algorithm is that it is scale and density independent. Experimental results corroborate our theoretical claims.     

Bus and Buffer Usage in In-Home Digital Networks: Applying the Dantzig–Wolfe Decomposition

In an in-home digital network several data streams (audio, video) may run simultaneously over a shared communication device, e.g. a bus. The burstiness of a data stream can be reduced by buffering data at the sending and receiving side, thereby allowing a lower bus share allocation for the stream. In this paper we present an algorithm that determines how much of the bus capacity and buffer space should be allocated to each stream, in order to have a feasible transmission schedule for each stream. Furthermore, the algorithm determines a transmission schedule for each stream, indicating how much data is transmitted over time. We model the problem as a linear program and apply a Dantzig–Wolfe decomposition such that the multiple-stream problem can be solved by repeatedly solving single-stream problems. For these single-stream problems we briefly describe efficient algorithms to solve them.     

Approximating the Medial Axis from the Voronoi Diagram with a Convergence Guarantee

The medial axis of a surface in 3D is the closure of all points that have two or more closest points on the surface. It is an essential geometric structure in a number of applications involving 3D geometric shapes. Since exact computation of the medial axis is difficult in general, efforts continue to improve their approximations. Voronoi diagrams turn out to be useful for this approximation. Although it is known that Voronoi vertices for a sample of points from a curve in 2D approximate its medial axis, a similar result does not hold in 3D. Recently, it has been discovered that only a subset of Voronoi vertices converge to the medial axis as sample density approaches infinity. However, most applications need a nondiscrete approximation as opposed to a discrete one. To date no known algorithm can compute this approximation straight from the Voronoi diagram with a guarantee of convergence. We present such an algorithm and its convergence analysis in this paper. One salient feature of the algorithm is that it is scale and density independent. Experimental results corroborate our theoretical claims.     

Performance evaluation of smoothing algorithms for transmittingprerecorded variable-bit-rate video

The transfer of prerecorded, compressed variable-bit-rate video requires multimedia services to support large fluctuations in bandwidth requirements on multiple time scales. Bandwidth smoothing techniques can reduce the burstiness of a variable-bit-rate stream by transmitting data at a series of fixed rates, simplifying the allocation of resources in video servers and the communication network. This paper compares the transmission schedules generated by the various smoothing algorithms, based on a collection of metrics that relate directly to the server, network, and client resources necessary for the transmission, transport, and playback of prerecorded video. Using MPEG-1 and MJPEG video data and a range of client buffer sizes, we investigate the interplay between the performance metrics and the smoothing algorithms. The results highlight the unique strengths and weaknesses of each bandwidth smoothing algorithm, as well as the characteristics of a diverse set of video clips     

Twin-float arithmetic

We present a heuristically certified form of floating-point arithmetic and its implementation in CoCoALib. This arithmetic is intended to act as a fast alternative to exact rational arithmetic, and is developed from the idea of paired floats expounded by Traverso and Zanoni (2002). As prerequisites we need a source of (pseudo-)random numbers, and an underlying floating-point arithmetic system where the user can set the precision. Twin-float arithmetic can be used only where the input data are exact, or can be obtained at high enough precision. Our arithmetic includes a total cancellation heuristic for sums and differences, and so can be used in classical algebraic algorithms such as Buchberger’s algorithm. We also present a (new) algorithm for recovering an exact rational value from a twin-float, so in some cases an exact answer can be obtained from an approximate computation.     

Approximate medial axis as a Voronoi subcomplex

Medial axis as a compact representation of shapes has evolved as an essential geometric structure in a number of applications involving 3D geometric shapes. Since exact computation of the medial axis is difficult in general, efforts continue to approximate them. One line of research considers the point cloud representation of the boundary surface of a solid and then attempts to compute an approximate medial axis from this point sample. It is known that the Voronoi vertices converge to the medial axis for a curve in 2D as the sample density approaches infinity. Unfortunately, the same is not true in 3D. Recently, it is discovered that a subset of Voronoi vertices called poles converge to the medial axis in 3D. However, in practice, a continuous approximation as opposed to a discrete one is sought.Recently few algorithms have been proposed which use the Voronoi diagram and its derivatives to compute this continuous approximation. These algorithms are scale or density dependent. Most of them do not have convergence guarantees, and one of them computes it indirectly from the power diagram of the poles. Recently, we proposed a new algorithm that approximates the medial axis straight from the Voronoi diagram in a scale and density independent manner with convergence guarantees. In this paper, we present several experimental results with this algorithm that support our theoretical claims and also show its effectiveness on practical data sets.     

An Approximate Gradient Algorithm for Constrained Distributed Convex Optimization

In this paper, we propose an approximate gradient algorithm for the multi-agent convex optimization problem with constraints. The agents cooperatively compute the minimum of the sum of the local objective functions which are subject to a global inequality constraint and a global constraint set. Instead of each agent can get exact gradient, as discussed in the literature, we only use approximate gradient with some computation or measurement errors. The gradient accuracy conditions are presented to ensure the convergence of the approximate gradient algorithm. Finally, simulation results demonstrate good performance of the approximate algorithm.      

Enhancing wireless video streaming using lightweight approximate authentication

In this paper, we propose a novel lightweight approximate authentication algorithm that provides efficient protection for wireless video streaming where attacks on the stream are possible, but classical integrity protection algorithms are impractical because bit errors occur naturally. The benefits of the proposed algorithm over other algorithms are fast execution and small message authentication code size. Moreover, the approximate authentication supports error resilient video decoding by dropping seriously damaged packets, thus improving the perceived quality of the video stream. The performance of the algorithm is demonstrated via numerical analysis, simulations and measurements over modeled and real wireless channels.     

GPU-based offset surface computation using point samples

We present an efficient algorithm to perform approximate offsetting operations on geometric models using GPUs. Our approach approximates the boundary of an object with point samples and computes the offset by merging the balls centered at these points. The underlying approach uses Layered Depth Images (LDI) to organize the samples into structured points and performs parallel computations using multiple cores. We use spatial hashing to accelerate intersection queries and balance the workload among various cores. Furthermore, the problem of offsetting with a large distance is decomposed into successive offsetting using smaller distances. We derive bounds on the accuracy of offset computation as a function of the sampling rate of LDI and offset distance. In practice, our GPU-based algorithm can accurately compute offsets of models represented using hundreds of thousands of points in a few seconds on a GeForce GTX 580 GPU. We observe more than 100 times speedup over prior serial CPU-based approximate offset computation algorithms.     

FOS: A Funnel-Based Approach for Optimal Online Traffic Smoothing of Live Video

Traffic smoothing is an efficient means to reduce the bandwidth requirement for transmitting a variable-bit-rate video stream. Several traffic-smoothing algorithms have been presented to offline compute the transmission schedule for a prerecorded video. For live video applications, Sen present a sliding-window algorithm, referred to as$SLWIN(k)$, to online compute the transmission schedule on the fly.$SLWIN(k)$looks ahead$W$video frames to compute the transmission schedule for the next$k$frametimes, where$kleq w$. Note that$W$is upper bounded by the initial delay of the transmission. The time complexity of$SLWIN(k)$is$O(Wast N/k)$for an$N$frame live video. In this paper, we present an$O(N)$online traffic-smoothing algorithm and two variants, denoted as$FOS$,$FOS1$and$FOS2$, respectively. Note that$O(N)$is a trivial lower bound of the time complexity of the traffic-smoothing problem. Thus, the proposed algorithm is optimal. We compare the performance of our algorithms with$SLWIN(k)$based on several benchmark video clips. Experiment results show that$FOS2$, which adopts the aggressive workahead heuristic, further reduces the bandwidth requirement and better utilizes the client buffer for real-time interactive applications in which the initial delays are small.     

Sliding window top-k dominating query processing over distributed data streams

Preference query processing is important for a wide range of applications involving distributed databases, such as network monitoring, web-based systems, and market analysis. In such applications, data objects are generated frequently and massively, which presents an important and challenging problem of continuous query processing over distributed data stream environments. A top-k dominating query, which has been receiving much research attention recently, returns the k data objects that dominate the highest number of data objects in a given dataset, and due to its dominance-based ranking function, we can easily obtain superior data objects. An emerging requirement in distributed stream environments is an efficient technique for continuously monitoring top-k dominating data objects. Despite of this fact, no study has addressed this problem. In this paper, therefore, we address the problem of continuous top-k dominating query processing over distributed data stream environments. We present two algorithms that monitor the exact top-k dominating data and efficiently eliminate unqualified data objects for the result, which reduces both communication and computation costs. In addition to these algorithms, we present an approximate algorithm that further reduces both communication and computation costs. Extensive experiments on both synthetic and real data have demonstrated the efficiency and scalability of our algorithms.     

Fast exact nearest patch matching for patch-based image editing and processing

This paper presents an efficient exact nearest patch matching algorithm which can accurately find the most similar patch-pairs between source and target image. Traditional match matching algorithms treat each pixel/patch as an independent sample and build a hierarchical data structure, such as kd-tree, to accelerate nearest patch finding. However, most of these approaches can only find approximate nearest patch and do not explore the sequential overlap between patches. Hence, they are neither accurate in quality nor optimal in speed. By eliminating redundant similarity computation of sequential overlap between patches, our method finds the exact nearest patch in brute-force style but reduces its running time complexity to be linear on the patch size. Furthermore, relying on recent multicore graphics hardware, our method can be further accelerated by at least an order of magnitude (≥10×). This greatly improves performance and ensures that our method can be efficiently applied in an interactive editing framework for moderate-sized image even video. To our knowledge, this approach is the fastest exact nearest patch matching method for high-dimensional patch and also its extra memory requirement is minimal. Comparisons with the popular nearest patch matching methods in the experimental results demonstrate the merits of our algorithm.     

Fast polygonal approximation of digital curves using relaxed straightness properties

Several existing DSS (digital straight line segment) recognition algorithms can be used to determine the digital straightness of a given one-pixel-thick digital curve. Because of the inherent geometric constraints of digital straightness, these algorithms often produce a large number of segments to cover a given digital curve representing a real-life object=image. Thus, a curve segment, which is not exactly digitally straight, but appears to be visually straight, is fragmented into multiple DSS when these algorithms are run. In this paper, a new concept of approximate straightness is introduced by relaxing certain conditions of DSS, and an algorithm is described to extract those segments from a digital curve. The number of such segments required to cover the curve is found to be significantly fewer than that of the exact DSS-cover. As a result, the data set required for representing a curve also reduces to a large extent. The extracted set of segments can further be combined to determine a compact polygonal approximation of a digital curve based on certain approximation criteria and a specified error tolerance. The proposed algorithm involves only primitive integer operations and thus runs very fast compared to those based on exact DSS. The overall time complexity becomes linear in the number of points present in the representative set. Experimental results on several digital curves demonstrate the speed, elegance and efficacy of the proposed method.     

Partitioning Trimmed Spline Surfaces into NonSelf-Occluding Regions for Visibility Computation

Computing the visible portions of curved surfaces from a given viewpoint is of great interest in many applications. It is closely related to the hidden surface removal problem in computer graphics, and machining applications in manufacturing. Most of the early work has focused on discrete methods based on polygonization or ray-tracing and hidden curve removal. In this paper we present an algorithm for decomposing a given surface into regions so that each region is either completely visible or hidden from a given viewpoint. Initially, it decomposes the domain of each surface based on silhouettes and boundary curves. To compute the exact visibility, we introduce a notion of visibility curves obtained by projection of silhouette and boundary curves and decomposition of the surface into nonoverlapping regions. These curves are computed using marching methods and we present techniques to compute all the components. The nonoverlapping and visible portions of the surface are represented as trimmed surfaces and we present a representation based on polygon trapezoidation algorithms. The algorithms presented use some recently developed algorithms from computational geometry like triangulation of simple polygons and point location. Given the nonoverlapping regions, we use an existing randomized algorithm for visibility computation. We also present results from a preliminary implementation of our algorithm.     

Approximate General Sweep Boundary of a 2D Curved Object

This paper presents an algorithm to compute an approximation to the general sweep boundary of a 2D curved moving object which changes its shape dynamically while traversing a trajectory. In effect, we make polygonal approximations to the trajectory and to the object shape at every appropriate instance along the trajectory so that the approximated polygonal sweep boundary is within a given error bound ϵ > 0 from the exact sweep boundary. The algorithm interpolates intermediate polygonal shapes between any two consecutive instances, and constructs polygons which approximate the sweep boundary of the object. Previous algorithms on sweep boundary computation have been mainly concerned about moving objects with fixed shapes; nevertheless, they have involved a fair amount of symbolic and/or numerical computations that have limited their practical uses in graphics modeling systems as well as in many other applications which require fast sweep boundary computation. Although the algorithm presented here does not generate the exact sweep boundaries of objects, it does yield quite reasonable polygonal approximations to them, and our experimental results show that its computation is reasonably fast to be of a practical use.     

利用半点计算椭圆曲线双标量乘法算法

实现椭圆曲线密码体制最主要的运算是椭圆曲线点群上的标量乘法(或点乘)运算。一些基于椭圆曲线的密码协议比如ECDSA签名验证,就需要计算双标量乘法kP+lQ,其中P、Q为椭圆曲线点群上的任意两点。一个高效计算kP+lQ的方法就是同步计算两个标量乘法,而不是分别计算每个标量乘法再相加。通过对域F2m上的椭圆曲线双标量乘法算法进行研究,将半点公式应用于椭圆曲线的双标量乘法中,提出了一种新的同步计算双标量乘法算法,分析了效率,并与传统的基于倍点运算的双标量乘法算法进行了详细的比较,其效率更优。     

The computation of elementary functions in radix 2 p

Many hardware-oriented algorithms computing the usual elementary functions (sine, cosine, exponential, logarithm, ...) only use shifts and additions. In this paper, we present new algorithms using shifts, adds and “small multiplications” (i. e. multiplications by few-digit-numbers). These CORDIC-like algorithms compute the elementary functions in radix 2 ^p (instead of the standard radix 2) and use table look-ups. The number of the required steps to compute functions with a given accuracy is reduced and since we use a quick “small multiplier”, the computation time is reduced.