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Showing papers on "Filter (video) published in 2007"


Journal ArticleDOI
TL;DR: A survey of modern nonlinear filtering methods for attitude estimation based on the Gaussian assumption that the probability density function is adequately specified by its mean and covariance is provided.
Abstract: This paper provides a survey of modern nonlinear filtering methods for attitude estimation. Early applications relied mostly on the extended Kalman filter for attitude estimation. Since these applications, several new approaches have been developed that have proven to be superior to the extended Kalman filter. Several of these approaches maintain the basic structure of the extended Kalman filter, but employ various modifications in order to provide better convergence or improve other performance characteristics. Examples of such approaches include: filter QUEST, extended QUEST and the backwards-smoothing extended Kalman filter. Filters that propagate and update a discrete set of sigma points rather than using linearized equations for the mean and covariance are also reviewed. A twostep approach is discussed with a first-step state that linearizes the measurement model and an iterative second step to recover the desired attitude states. These approaches are all based on the Gaussian assumption that the probability density function is adequately specified by its mean and covariance. Other approaches that do not require this assumption are reviewed, Associate Professor, Department of Mechanical & Aerospace Engineering. Email: johnc@eng.buffalo.edu. Associate Fellow AIAA. Aerospace Engineer, Guidance, Navigation and Control Systems Engineering Branch. Email: Landis.Markley@nasa.gov. Fellow AIAA. Postdoctoral Research Fellow, Department of Mechanical & Aerospace Engineering. Email: cheng3@eng.buffalo.edu. Member AIAA.

1,116 citations


Journal ArticleDOI
TL;DR: In this article, a closed-form cardinalized probability hypothesis density (CPHD) filter is proposed, which propagates not only the PHD but also the entire probability distribution on target number.
Abstract: The multitarget recursive Bayes nonlinear filter is the theoretically optimal approach to multisensor-multitarget detection, tracking, and identification. For applications in which this filter is appropriate, it is likely to be tractable for only a small number of targets. In earlier papers we derived closed-form equations for an approximation of this filter based on propagation of a first-order multitarget moment called the probability hypothesis density (PHD). In a recent paper, Erdinc, Willett, and Bar-Shalom argued for the need for a PHD-type filter which remains first-order in the states of individual targets, but which is higher-order in target number. In this paper we show that this is indeed possible. We derive a closed-form cardinalized PHD (CPHD) filter, which propagates not only the PHD but also the entire probability distribution on target number.

830 citations


Journal ArticleDOI
TL;DR: A recursive filter, optimal in the minimum-variance unbiased sense, is developed where the estimation of the state and the input are interconnected and the state estimation problem is transformed into a standard Kalman filtering problem.

526 citations


Journal ArticleDOI
TL;DR: This work presents ClassBench, a suite of tools for benchmarking packet classification algorithms and devices and seeks to eliminate the significant access barriers to realistic test vectors for researchers and initiate a broader discussion to guide the refinement of the tools and codification of a formal benchmarking methodology.
Abstract: Packet classification is an enabling technology for next generation network services and often a performance bottleneck in high-performance routers. The performance and capacity of many classification algorithms and devices, including TCAMs, depend upon properties of filter sets and query patterns. Despite the pressing need, no standard performance evaluation tools or filter sets are publicly available. In response to this problem, we present ClassBench, a suite of tools for benchmarking packet classification algorithms and devices. ClassBench includes a filter set generator that produces synthetic filter sets that accurately model the characteristics of real filter sets. Along with varying the size of the filter sets, we provide high-level control over the composition of the filters in the resulting filter set. The tool suite also includes a trace generator that produces a sequence of packet headers to exercise packet classification algorithms with respect to a given filter set. Along with specifying the relative size of the trace, we provide a simple mechanism for controlling locality of reference. While we have already found ClassBench to be very useful in our own research, we seek to eliminate the significant access barriers to realistic test vectors for researchers and initiate a broader discussion to guide the refinement of the tools and codification of a formal benchmarking methodology. (The ClassBench tools are publicly available at the following site: http://www.arl.wustl.edu/~det3/ClassBench/.)

478 citations


Journal ArticleDOI
TL;DR: Using linear minimum-variance unbiased estimation, a recursive filter is derived where the estimation of the state and the input are interconnected, based on the assumption that no prior knowledge about the dynamical evolution of the unknown input is available.

452 citations


Journal ArticleDOI
01 Feb 2007
TL;DR: This correspondence presents a novel hybrid wrapper and filter feature selection algorithm for a classification problem using a memetic framework that incorporates a filter ranking method in the traditional genetic algorithm to improve classification performance and accelerate the search in identifying the core feature subsets.
Abstract: This correspondence presents a novel hybrid wrapper and filter feature selection algorithm for a classification problem using a memetic framework. It incorporates a filter ranking method in the traditional genetic algorithm to improve classification performance and accelerate the search in identifying the core feature subsets. Particularly, the method adds or deletes a feature from a candidate feature subset based on the univariate feature ranking information. This empirical study on commonly used data sets from the University of California, Irvine repository and microarray data sets shows that the proposed method outperforms existing methods in terms of classification accuracy, number of selected features, and computational efficiency. Furthermore, we investigate several major issues of memetic algorithm (MA) to identify a good balance between local search and genetic search so as to maximize search quality and efficiency in the hybrid filter and wrapper MA

426 citations


Patent
09 May 2007
TL;DR: In this paper, the authors present a method of organizing and processing data in a distributed computing system, which is also implemented as a computer program on a computer medium and as a distributed computer system.
Abstract: The present invention is a method of organizing and processing data in a distributed computing system. The invention is also implemented as a computer program on a computer medium and as a distributed computer system. Software modules can be configured as hardware. The method and system organizes select content which is important to an enterprise operating said distributed computing system. The select content is represented by one or more predetermined words, characters, images, data elements or data objects. The computing system has a plurality of select content data stores for respective ones of a plurality of enterprise designated categorical filters which include content-based filters, contextual filters and taxonomic classification filters, all operatively coupled over a communications network. A data input is processed through at least one activated categorical filter to obtain select content, and contextually associated select content and taxonomically associated select content as aggregated select content. The aggregated select content is stored in the corresponding select content data store. A data process from the group of data processes including a copy process, a data extract process, a data archive process, a data distribution process and a data destruction process is associated with the activated categorical filter and the method and system applies the associated data process to a further data input based upon a result of that further data being processed by the activated categorical filter utilizing the aggregated select content data.

378 citations


Journal ArticleDOI
TL;DR: The matched filter response to the detection of blood vessels is increased by proposing better filter parameters found by using an optimization procedure on 20 retina images of the DRIVE database.

319 citations


Patent
30 Jan 2007
TL;DR: In this paper, a temporary filter is described for use in percutaneous intravascular procedures for the treatment of diseased blood vessels, such as angioplasty or stent placement procedures.
Abstract: A temporary filter is described for use in percutaneous intravascular procedures for the treatment of diseased blood vessels, such as angioplasty or stent placement procedures. The guide wire which is used to direct a catheter (such as a balloon catheter) to a treatment site contains a deployable filter. The guide wire is moveable independently of the catheter and can be used to position the filter at a desired location downstream of the treatment site. The guide wire includes parts moveable with respect to each other and the filter is connected to these parts in such a way that it can be deployed and collapsed by relative movement of the parts.

313 citations


Journal ArticleDOI
TL;DR: In this paper, a robust fault detection for networked control systems with large transfer delays, in which it is impossible to totally decouple the fault effects from unknown inputs (including model uncertainties and external plant disturbances), is presented.
Abstract: This paper deals with the design of robust fault detection for networked control systems with large transfer delays, in which it is impossible to totally decouple the fault effects from unknown inputs (including model uncertainties and external plant disturbances). First, we employ the multirate sampling method together with the augmented state matrix method to model the long random delay networked control systems as Markovian jump systems. Then, a Hinfin fault detection filter is designed based on the model developed. Through the appropriate choice of the filter gain, the filter is convergent if there is no disturbance in the system, meanwhile the effect of disturbances on the residual will satisfy a prescribed Hinfin performance. The problem of achieving satisfactory sensitivity of the residual to fault is formulated and its solution is given. Finally, a numerical example is presented to illustrate the effectiveness of the proposed techniques.

202 citations


Book ChapterDOI
30 May 2007
TL;DR: In this paper, the performance of the non-local means filter was improved by introducing adaptive local dictionaries and a new statistical distance measure to compare patches, and the new Bayesian NL-means filter is better parametrized.
Abstract: Partial Differential equations (PDE), wavelets-based methods and neighborhood filters were proposed as locally adaptive machines for noise removal Recently, Buades, Coll and Morel proposed the Non-Local (NL-) means filter for image denoising This method replaces a noisy pixel by the weighted average of other image pixels with weights reflecting the similarity between local neighborhoods of the pixel being processed and the other pixels The NL-means filter was proposed as an intuitive neighborhood filter but theoretical connections to diffusion and non-parametric estimation approaches are also given by the authors In this paper we propose another bridge, and show that the NL-means filter also emerges from the Bayesian approach with new arguments Based on this observation, we show how the performance of this filter can be significantly improved by introducing adaptive local dictionaries and a new statistical distance measure to compare patches The new Bayesian NL-means filter is better parametrized and the amount of smoothing is directly determined by the noise variance (estimated from image data) given the patch size Experimental results are given for real images with artificial Gaussian noise added, and for images with real image-dependent noise

Journal ArticleDOI
TL;DR: In this paper, a novel balanced coupled-line bandpass filters, using suitable balanced coupled line sections and quarter-wavelength resonators, are proposed to achieve the desired differential-mode response and the level of common-mode noise.
Abstract: Novel balanced coupled-line bandpass filters, using suitable balanced coupled-line sections and quarter-wavelength resonators, are proposed. For design purposes, the differential- and common-mode equivalent half-circuits are established. Based on these circuits, a better balanced filter structure is implemented so that the desired differential-mode response may be realized and the level of common-mode noise may be minimized simultaneously. Besides, a suitable capacitive or inductive cross-coupled effect is introduced so as to create two transmission zeros for improving the filter selectivity; however, it also enhances the signal imbalance and degrades the common-mode rejection. In this study, various second- and fourth-order balanced filters are implemented to discuss the associated differential-mode responses and the signal-imbalance phenomena resulted from the cross-coupled effect. Specifically, the fourth-order filter with a common-mode rejection ratio of 40 dB within the passband is demonstrated and examined

Journal ArticleDOI
TL;DR: A noise removal algorithm that combines a total variational filter (ROF filter) with a fourth-order PDE filter (LLT filter) and takes the advantage of both filters since it is able to preserve edges while avoiding the staircase effect in smooth regions.

Journal ArticleDOI
TL;DR: Some ways to mix approximate filter dimensioning and optimization (based on network synthesis) and optimization, allowing a fast and accurate design of microwave filters are explored.
Abstract: In this article, a process that might be described as "synthesis and approximation" was outlined. Starting from an exact prototype, the desired physical configuration using equivalent circuits and corrections to the resonators due to the influence of the coupling networks was approximated. A process that might be described as "approximation and optimization" was also outlined. Starting from an approximate filter network, optimization can be used to find an exact equal ripple solution. The starting point can be generated using synthesis or narrow-band approximations when appropriate. Applying optimization in an intelligent way allows the designer to circumvent some of the limitations of the classic ladder synthesis method. This article explores some ways to mix approximate filter dimensioning (based on network synthesis) and optimization (based on EM modeling), allowing a fast and accurate design of microwave filters

Patent
15 Mar 2007
TL;DR: In this paper, a latent semantic mapping (LSM) filter is used to classify multimedia content into two categories based on the one or more parameters of the multimedia content and then the tag is input into the LSM filter.
Abstract: Methods and apparatuses to filter multimedia content are described. The multimedia content in one embodiment is analyzed for one or more parameters. The multimedia content in one embodiment is filtered based on the one or more parameters using a latent semantic mapping (“LSM”) filter. In one embodiment, the one or more parameters include information about a structure of the multimedia content. A tag that encapsulates the one or more parameters may be generated. Then, the tag is input into the latent semantic mapping filter. In one embodiment, the LSM filter is trained to recognize the multimedia content based on the one or more parameters. In one embodiment, more than two categories are provided for a multimedia content. The multimedia content is classified in more than two categories using the LSM filter. The multimedia content may be blocked based on the classifying.

Journal ArticleDOI
TL;DR: A variant of a least squares ensemble (Kalman) filter that is suitable for implementation on parallel architectures and produces results that are identical to those from sequential algorithms when forward observation operators that relate the model state vector to the expected value of observations are linear.
Abstract: A variant of a least squares ensemble (Kalman) filter that is suitable for implementation on parallel architectures is presented. This parallel ensemble filter produces results that are identical to those from sequential algorithms already described in the literature when forward observation operators that relate the model state vector to the expected value of observations are linear (although actual results may differ due to floating point arithmetic round-off error). For nonlinear forward observation operators, the sequential and parallel algorithms solve different linear approximations to the full problem but produce qualitatively similar results. The parallel algorithm can be implemented to produce identical answers with the state variable prior ensembles arbitrarily partitioned onto a set of processors for the assimilation step (no caveat on round-off is needed for this result). Example implementations of the parallel algorithm are described for environments with low (high) communication lat...


Patent
04 Oct 2007
TL;DR: In this article, the authors present a video surveillance, storage, and alerting system having surveillance cameras, video analytics devices, audio sensory devices, other sensory devices and a plurality of data storage devices.
Abstract: The present invention is a video surveillance, storage, and alerting system having surveillance cameras, video analytics devices, audio sensory devices, other sensory devices, and a plurality of data storage devices. A network management module monitors network status of all subsystems including cameras, servers, storage devices, etc. and shows actively monitored areas on a physical map. A vehicle information module retrieves information from a law enforcement database about vehicles detected in the video data based on the vehicle's license plate, including information about stolen vehicles, as well as warrant, wanted person, and mug shot information for registered drivers of the vehicles. Video tips are received and processed from anonymous and non-anonymous sources. A correlation engine correlates primitive events and compound events from each of the subsystems, weighted by attributes of the events, across both space and time, and an alerting engine generates alerts and performs actions based on the correlation. A hierarchical storage manager manages storage of the vast amounts of data, including video data, based on importance of the data calculated from attributes of the data. A privacy filter ensures no private data is detected, correlated, or stored.

Journal ArticleDOI
TL;DR: The results show that FILA substantially outperforms the existing TAG-based approach and range caching approach in terms of both network lifetime and energy consumption under various network configurations.
Abstract: Top-k monitoring is important to many wireless sensor applications. This paper exploits the semantics of top-k query and proposes an energy-efficient monitoring approach called FILA. The basic idea is to install a filter at each sensor node to suppress unnecessary sensor updates. Filter setting and query reevaluation upon updates are two fundamental issues to the correctness and efficiency of the FILA approach. We develop a query reevaluation algorithm that is capable of handling concurrent sensor updates. In particular, we present optimization techniques to reduce the probing cost. We design a skewed filter setting scheme, which aims to balance energy consumption and prolong network lifetime. Moreover, two filter update strategies, namely, eager and lazy, are proposed to favor different application scenarios. We also extend the algorithms to several variants of top-k query, that is, order-insensitive, approximate, and value monitoring. The performance of the proposed FILA approach is extensively evaluated using real data traces. The results show that FILA substantially outperforms the existing TAG-based approach and range caching approach in terms of both network lifetime and energy consumption under various network configurations.

Journal ArticleDOI
TL;DR: This paper presents a hybrid valued sequential state estimation algorithm, and its particle filter-based implementation, that extends the standard color particle filter in two ways: first, target detection and deletion are embedded in the particle filter without relying on an external track initialization and cancellation algorithm.

Journal ArticleDOI
TL;DR: A high Q-factor photonic microwave filter showing tuning and reshaping capabilities and based on stimulated Brillouin scattering is demonstrated, demonstrating the wide tuning range of the filter, its reshaping capability, and Q factor of 670.
Abstract: A high Q-factor photonic microwave filter showing tuning and reshaping capabilities and based on stimulated Brillouin scattering is demonstrated. The filter bandpass can be continuously tuned, changing the microwave oscillator used to generate the pump power, and the filter shape can be modified by modulating the microwave tone. A single bandpass over the microwave spectrum can be obtained by using single-sideband suppressed carrier modulation. Experimental results demonstrate the wide tuning range of the filter, its reshaping capability, and Q factor of 670.

Journal ArticleDOI
TL;DR: In this paper, a simplified method for evaluating the power-handling capability inside an RF filter has been introduced based on the general cross-coupled prototype network theory, modern EM modeling techniques, and well-established breakdown threshold analysis.
Abstract: A simplified method for evaluating the power-handling capability inside an RF filter has been introduced based on the general cross-coupled prototype network theory, modern EM modeling techniques, and well-established breakdown threshold analysis. The electrical field strength and voltages evaluated using either the single-cavity resonator (eigen mode) model or simply the prototype model have been presented and compared against the direct EM computation of the complete filter structure. Close agreement has been found between the full EM modeling and the scaling of a single resonator or even prototype network analysis only. This procedure is expected to simplify the multipaction and ionization breakdown analysis of filters and filter-based diplexers and multiplexers. The method presented is general and is applicable to all filter types that can be described in a circuit model. Practical issues such as the multicarrier operation, sharp edge condition, design margin, and prevention techniques are also covered.

Proceedings ArticleDOI
01 Oct 2007
TL;DR: In this paper, the analysis, design and optimization of a LCL filter topology to connect a 7MW NPC inverter to the grid is presented. And the simulation results were evaluated in order to access the performance of the proposed filter and the quality of the current injected into the grid.
Abstract: This paper deals with the analysis, design and optimization of a LCL filter topology to connect a 7MW NPC inverter to the grid. Following the requirements based on the IEEE 519-1992 recommendation and the German Guideline VDEW, simulation results were evaluated in order to access the performance of the proposed filter and the quality of the current injected into the grid.

Patent
19 Jul 2007
TL;DR: In this article, a method of operating an audio system that provides audio radiation to a plurality of listening positions includes providing at least one source of audio signals at each listening position, at each array of speaker elements is provided.
Abstract: A method of operating an audio system that provides audio radiation to a plurality of listening positions includes providing at least one source of audio signals. At each listening position, at least one array of speaker elements is provided. A filter is provided between the at least one source and at least one of the speaker elements at a first listening position. The filter is optimized so that the filter reduces acoustic energy radiated from the first array to at least one other listening position of the plurality of listening positions, compared to acoustic energy radiated from the first array to the first listening position.

Patent
31 Oct 2007
TL;DR: In this paper, a TANK filter is provided for a lead wire of an active medical device (AMD), which includes a capacitor in parallel with an inductor, where values of capacitance and inductance are selected such that the filter is resonant at a selected frequency.
Abstract: A TANK filter is provided for a lead wire of an active medical device (AMD). The TANK filter includes a capacitor in parallel with an inductor. The parallel capacitor and inductor are placed in series with the lead wire of the AMD, wherein values of capacitance and inductance are selected such that the TANK filter is resonant at a selected frequency. In a preferred form, the TANK filter reduces or even eliminates the use of ferro-magnetic materials, and instead uses non-ferromagnetic materials so as to reduce or eliminate MRI image artifacts or the force or torque otherwise associated during an MRI image scan.

Journal ArticleDOI
TL;DR: It is proposed that the neural implementation of this Kalman filter involves recurrent basis function networks with attractor dynamics, a kind of architecture that can be readily mapped onto cortical circuits.
Abstract: Several behavioral experiments suggest that the nervous system uses an internal model of the dynamics of the body to implement a close approximation to a Kalman filter. This filter can be used to perform a variety of tasks nearly optimally, such as predicting the sensory consequence of motor action, integrating sensory and body posture signals, and computing motor commands. We propose that the neural implementation of this Kalman filter involves recurrent basis function networks with attractor dynamics, a kind of architecture that can be readily mapped onto cortical circuits. In such networks, the tuning curves to variables such as arm velocity are remarkably noninvariant in the sense that the amplitude and width of the tuning curves of a given neuron can vary greatly depending on other variables such as the position of the arm or the reliability of the sensory feedback. This property could explain some puzzling properties of tuning curves in the motor and premotor cortex, and it leads to several new predictions.

Journal ArticleDOI
TL;DR: A mixed-signal front-end processor for multichannel neuronal recording and special interface system incorporating an embedded CPU core in a programmable logic device accompanied by real-time software has been developed to allow connectivity to a computer host.
Abstract: A mixed-signal front-end processor for multichannel neuronal recording is described. It receives 12 differential-input channels of implanted recording electrodes. A programmable cutoff High Pass Filter (HPF) blocks dc and low-frequency input drift at about 1 Hz. The signals are band-split at about 200 Hz to low-frequency Local Field Potential (LFP) and high-frequency spike data (SPK), which is band limited by a programmable-cutoff LPF, in a range of 8-13 kHz. Amplifier offsets are compensated by 5-bit calibration digital-to-analog converters (DACs). The SPK and LFP channels provide variable amplification rates of up to 5000 and 500, respectively. The analog signals are converted into 10-bit digital form, and streamed out over a serial digital bus at up to 8 Mbps. A threshold filter suppresses inactive portions of the signal and emits only spike segments of programmable length. A prototype has been fabricated on a 0.35-mum CMOS process and tested successfully, demonstrating a 3-muV noise level. Special interface system incorporating an embedded CPU core in a programmable logic device accompanied by real-time software has been developed to allow connectivity to a computer host

Journal ArticleDOI
TL;DR: This paper presents both the theory and the experimental results of a method allowing simultaneous robot localization and odometry error estimation (both systematic and non-systematic) during the navigation.
Abstract: This paper presents both the theory and the experimental results of a method allowing simultaneous robot localization and odometry error estimation (both systematic and non-systematic) during the navigation. The estimation of the systematic components is carried out through an augmented Kalman filter, which estimates a state containing the robot configuration and the parameters characterizing the systematic component of the odometry error. It uses encoder readings as inputs and the readings from a laser range finder as observations. In this first filter, the non-systematic error is defined as constant and it is overestimated. Then, the estimation of the real non-systematic component is carried out through another Kalman filter, where the observations are obtained by two subsequent robot configurations provided by the previous augmented Kalman filter. There, the systematic parameters in the model are regularly updated with the values estimated by the first filter. The approach is theoretically developed for both the synchronous and the differential drive. A first validation is performed through very accurate simulations where both the drive systems are considered. Then, a series of experiments are carried out in an indoor environment by using a mobile platform with a differential drive.

01 Jan 2007
TL;DR: The results show that the optimized NL-means filter outperforms the classical implementation of the NL- means filter, as well as two other classical denoising methods (Anisotropic Diffusion and Total Variation minimization process) in terms of accuracy with low computation time.
Abstract: A critical issue in image restoration is the problem of noise removal while keeping the integrity of relevant image information. Denoising is a crucial step to increase image quality and to improve the performance of all the tasks needed for quantitative imaging analysis. The method proposed in this paper is based on a 3D optimized blockwise version of the Non Local (NL) means filter [1]. The NL-means filter uses the redundancy of information in the image under study to remove the noise. The performance of the NL-means filter has been already demonstrated for 2D images, but reducing the computational burden is a critical aspect to extend the method to 3D images. To overcome this problem, we propose improvements to reduce the computational complexity. These different improvements allow to drastically divide the computational time while preserving the performances of the NL-means filter. A fully-automated and optimized version of the NL-means filter is then presented. Our contributions to the NL-means filter are: (a) an automatic tuning of the smoothing parameter, (b) a selection of the most relevant voxels, (c) a blockwise implementation and (d) a parallelized computation. Quantitative validation was carried out on synthetic datasets generated with BrainWeb [2]. The results show that our optimized NL-means filter outperforms the classical implementation of the NL-means filter, as well as two other classical denoising methods (Anisotropic Diffusion [3] and Total Variation minimization process [4]) in terms of accuracy (measured by the Peak Signal to Noise Ratio) with low computation time. Finally, qualitative results on real data are presented.

Proceedings ArticleDOI
11 Jun 2007
TL;DR: It is shown that as filter costs increase, the best adaptive strategy is superior to any fixed strategy, despite the overhead of adaptivity, and a precomputation technique is given that can reduce the execution overhead of adaptive strategies.
Abstract: We consider the problem of optimizing and executing multiple continuous queries, where each query is a conjunction of filters and each filter may occur in multiple queries. When filters are expensive, significant performance gains are achieved by sharing filter evaluations across queries. A shared execution strategy in our scenario can either be fixed, in which filters are evaluated in the same predetermined order for all input, or adaptive, in which the next filter to be evaluated is chosen at runtime based on the results of the filters evaluated so far. We show that as filter costs increase, the best adaptive strategy is superior to any fixed strategy, despite the overhead of adaptivity. We show that itis NP-hard to find the optimal adaptive strategy, even if we are willing to approximate within any factor smaller than m where m is the number of queries. We then present a greedy adaptive execution strategy and show that it approximates the best adaptive strategy to within a factor O(log2m log n) where n is the number of distinct filters. We also give a precomputation technique that can reduce the execution overhead of adaptive strategies.