TRAFFIC BEHAVIOR IN A TWO-LANE SYSTEM CONSISTING OF A MIXTURE OF BUSES AND CARS In this paper, we study a two-lane traffic system consisting of a mixture of cars and taxies. The taxies occasionally stop to pick up or drop off passengers. The empty taxi rate, getting on rate (defined as average number of passengers that get on taxi in unit time), fundamental diagram, passenger carry capability, and lane-changing frequency are investigated under different sets of parameters. Some insights are obtained and explained. For example, (i) the flow rate still decreases even if the taxies stop less frequently; (ii) getting on rate does not monotonically increase with the pick-up rate. The diagram of the maximum value of getting on rate is also presented, so that an optimum taxi number could be suggested. We expect our works could be useful for taxi administration and traffic management. Recently, traffic congestion has become a serious problem all over the world and has resulted in increases in economic expenses and environment pollutions. Therefore, it has been an urgent problem to understand complex traffic behavior and then to guide the traffic planning, designing, controlling and management. To simulate various complex behavior of traffic flow, several kinds of models have been proposed, such as hydrodynamic models, car-following models, cellular automaton (CA) models and gas-kinetic models (Chowdhury et al., 2000; Helbing, 2001; Hoogendoorn et al., 2005; Kerner, 2004; Maerivoet et al., 2005; Nagatani, 2002; Nagel et al., 2003) . Recently, CA models have been shown to be able to emulate much of the behavior of observed traffic flow, therefore, using CA has become a well-established method to model, analyze, understand, and even forecast the behavior of real road traffic. One of the most well-known CA model is NaSch model proposed in 1992 (Nagel et al., 1992) . Although it is very simple, it can reproduce some real traffic phenomena, such as spontaneous appearance of jams and start-stop waves. Because the roadway usually has two or more lanes in real traffic, the extension of the single lane traffic flow model to two-lane or multi-lane situations is very important and has been widely studied (Chowdhury et al., 1997; Knospe et al., 1999 Knospe et al., , 2002 Nagatani, 1996; Nagel et al., 1998; Rickert et al., 1996; Wagner et al., 1997) . On the other hand, taxies play an important role in city traffic. Nevertheless, to our knowledge, the two-lane traffic flow considering a mixture with taxies has not been studied. In this paper, we study a two-lane traffic system consisting of a mixture of cars and taxies. The taxies occasionally stop to pick up or drop off passengers. Extensive simulations have been carried out. Traffic behaviors including empty taxi rate, getting on rate (defined as average number of passengers that get on taxi in unit time), fundamental diagram, passenger carry capability, and lane-changing frequency are investigated under different sets of parameters. This paper is organized as follow. In the next section, the NaSch model and lane-changing rules are introduced. The simulation results are presented and discussed in Section III. The conclusion is given in section IV. In this paper, we have investigated a traffic system consisting of a mixture of cars and taxies. The taxies stop to pick up and drop off passengers on the right lane. The cars can change lane when hindered by preceding vehicles. We have studied empty taxi rate, getting on rate, fundamental diagram, carry capability, and lane changing frequency in the mixed traffic system. The dependence on pick up rate P on , the system density, the taxi number N taxi , taxi stop time T st and two travel distance parameters L 1 and L 2 is investigated. The diagram of the maximum value of getting on rate is also presented, so that an optimum taxi number could be suggested. Some unexpected results are reported. For example, (i) the flow rate still decreases even if the taxies stop less frequently; (ii) getting on rate does not monotonically increase with the pick-up rate. These results might be due to time interval between drop-off and pick-up process decreases with the increase of pick up rate. In our future work, some more realistic factors need to be considered. For example, (i) the taxies could also change lane; (ii) the inhomogeneous distribution of passengers. Furthermore, the study also needs to be extended to consider traffic network instead of a single road.

O O O O O O O O O B I I I I O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


An approach to generate test cases from use cases The system testing allows to verify the behaviour of the system under test and to guarantee the satisfaction of its requirements. This work describes a complete process to generate test cases from use cases for web applications. This process also resolves the lacks detected in existing approaches. The software systems need to improve their quality guarantee because of their growing complexity. A tool that assures the quality of software systems is the system testing. The system testing assures that the functionality of the system under test (SUT) satisfies its requirements. A system test case substitutes an actor and simulates its behaviour. This definition shows that the design of the system testing is based on the functional requirements of the system. Nowadays, it is usual to express the functional requirements of a web system through UML use case diagrams and text templates. Existing papers [3] , [6] , expose that use cases and text templates are adequate for web systems. Thus, use cases are an appropriate artefact to start the generation process of test cases for web systems.. We exposed how to apply existing works in the generation of test cases in a web application in a previous paper [5] . This paper introduces a new approach to generate test cases from requirements expressed by use cases.. Actually, we know two reports that analyse and compare approaches for generating system test cases from requirements. First report [2] analyzes 12 approaches. Second report [4] analyzes 13 approaches, 4 of them also included in Denger report. A list of references to all analyzed proposals may be found in [4] . Approaches analyzed in both reports have several common characteristics: approaches work with functional requirements, functional requirements are expressed with use cases, use cases are expressed in natural language and approaches are incomplete.. The goal of the generation process is to obtain several test cases to check that all the information included in the use cases have been successfully implemented in the web system under test. The generation of a test case involves the definition of, at least, three different elements: the test values, the interactions with the system under test and the expected result. The elements obtained at the end of the generation of test cases are a set of executable test cases (with test values, interactions and expected results). This paper has presented a new approach to generate test cases from use cases. We have shown how this process is applied in a web system using use cases. All the test information has been modelled with the UML Testing profile. This profile does not describe any notation for the modelling of test objectives. We have improved it using activities diagrams derived from the use cases. It is possible and valuable for web systems to generate test cases from use cases. It is possible to start the testing process as soon as the first requirements are available or stable. It avoids postponing all the testing process till the end of the software creation, when the accumulated delays impede a deep testing. The testing design in early phases also allows to detect errors, omissions and ambiguities in the requirements when it is still easy to correct them. A prototype tool has been built. It may be downloaded from www.lsi.us.es/~javierj/

O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Adaptive structure radial basis function network model for processes with operating region migration Adaptive structure radial basis function network model for processes with operating region migration http://researchonline.ljmu.ac.uk/2046/ Article LJMU has developed LJMU Research Online for users to access the research output of the University more effectively. Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Users may download and/or print one copy of any article(s) in LJMU Research Online to facilitate their private study or for non-commercial research. You may not engage in further distribution of the material or use it for any profit-making activities or any commercial gain.The version presented here may differ from the published version or from the version of the record. Please see the repository URL above for details on accessing the published version and note that access may require a subscription. Abstract: An adaptive structure radial basis function (RBF) network model is proposed in this paper to model nonlinear processes with operating region migration. The recursive orthogonal least squares algorithm is adopted to select new centers on-line, as well as to train the network weights. Based on the R matrix in the orthogonal decomposition, an initial center bank is formed and updated in each sample period. A new learning strategy is proposed to gain information from the new data for network structure adaptation. A center grouping algorithm is also developed to divide the centers into active and non-active groups, so that a structure with a smaller size is maintained in the final network model. The proposed RBF model is evaluated and compared to the two fixed-structure RBF networks by modeling a nonlinear time-varying numerical example. The results demonstrate that the proposed adaptive structure model is capable of adapting its structure to fit the operating region of the process effectively with a more compact structure and it significantly outperforms the two fixed structure RBF models. Abstract. An adaptive structure radial basis function (RBF) network model is proposed in this paper to model nonlinear processes with operating region migration. The recursive orthogonal least squares algorithm is adopted to select new centers on-line, as well as to train the network weights. Based on the R matrix in the orthogonal decomposition, an initial center bank is formed and updated in each sample period. A new learning strategy is proposed to gain information from the new data for network structure adaptation. A center grouping algorithm is also developed to divide the centers into active and non-active groups, so that a structure with a smaller size is maintained in the final network model. The proposed RBF model is evaluated and compared to the two fixed-structure RBF networks by modeling a nonlinear time-varying numerical example. The results demonstrate that the proposed adaptive structure model is capable of adapting its structure to fit the operating region of the process effectively with a more compact structure and it significantly outperforms the two fixed structure RBF models.

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Targeted Recruitment of Histone Modifications in Humans Predicted by Genomic Sequences Histone modifications are important epigenetic regulators and play a critical role in development. The targeting mechanism for histone modifications is complex and still incompletely understood. Here we applied a computational approach to predict genome-scale histone modification targets in humans by the genomic DNA sequences using a set of recent ChIPseq data. We found that a number of histone modification marks could be predicted with high accuracy. On the other hand, the impact of DNA sequences for each mark is intrinsically different dependent upon the target-and tissue-specificity. Diverse patterns are associated with different repetitive elements. Unexpectedly, we found that non-overlapping, functionally opposite histone modification marks could share similar sequence features. We propose that these marks may target a common set of loci but are mutually exclusive and that the competition may be important for developmental control. Taken together, we show that our computational approach has provided new insights into the targeting mechanism of histone modifications. T HE DISTRIBUTION OF HISTONE MODIFICATIONS is not uniform across the human genome. The active genes are often marked with histone acetylation and H3K4me3 (Barski et al., 2007; Bernstein et al., 2006; Liu et al., 2005; Wang et al., 2008) , whereas H3K27 trimethylation often marks developmental genes (Bernstein et al., 2006; Boyer et al., 2006; Lee et al., 2006) . H3K9 di-and tri-methylations are often associated with heterochromatin (Hall et al., 2002) . Certain marks preferentially target the 5 0 gene starts, whereas others are biased toward transcribed regions or gene deserts (Bernstein et al., 2006; Hall et al., 2002; Liu et al., 2005; Pokholok et al., 2005) . There are also distinct differences among differentially methylated marks within the same group. H3K4me3 punctually marks the transcription start sites (TSS) of most actively transcribed genes (Bernstein et al., 2006; Guenther et al., 2007; Liu et al., 2005; Pokholok et al., 2005) . Recently, it has been shown that H3K4me3 can also be recruited to genes that are poised for activation (Core and Lis, 2008; Guenther et al., 2007) . On the other hand, H3K4me2 and H3K4me1. Department of Biostatistics, Harvard School of Public Health, and Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, Cambridge, Massachusetts. We have developed a computational model to predict histone modification patterns in humans from genomic sequences. Our model is effective for the prediction of a number of histone marks, as evidenced by the ROC curves, regional predictions, and promoter and enhancer analysis. In addition, the computational method has also enabled us to explore the histone modification pattern at highly repetitive regions such as the centromere and pericentromere.. On the other hand, our model performs poorly for a number of repressive marks such as H4K20me3. Whereas new development of computational models and increased data quality are expected to further improve the prediction power, it is also likely that DNA sequences may not be important for some of these marks. We have identified two biological factors affecting the predictability of sequence-based models: target-specificity and tissue-specificity. Whereas data noise is also an important limiting factor, its impact can be removed in principle as technology advances.. We have detected similar sequence patterns between functionally opposite histone modifications exemplified by the H3K4me2 and H3K27me3 pair and hypothesized that these two marks are recruited toward common genomic loci and compete against each other for targeting. Direct interactions between the H3K4 and H3K27 methylation and demethylation machineries have been detected and they form a positive feedback loop. In particular, the H3K4 methyltransferase MLL can recruit the H3K27 demethylase UTX (Lee et al., 2007a) , whereas the H3K27 methyltransferase Ezh2 can recruit the H3K4 demethylase Rpb2 (Pasini et al., 2008) . Such feedback loops may be sufficient for establishing stable and heritable binary chromatin states (Dodd et al., 2007) . Our analysis suggests that there is an extra layer of cooperativity, that is, the epigenetic factors are recruited to common targets by the DNA sequences, thus facilitating interaction efficiency.. A major computational challenge for detection of sequence signals associated with epigenetic factors is that they are likely to involve the accumulation of many weak features (Sekinger et al., 2005; Straub and Becker, 2008) . Traditional methods for transcription factor binding motif discovery are not suitable for this task because they rely on the assumption that there exist distinct short sequence patterns. New approaches, such as those described in this paper, will undoubtedly provide new insights into the targeting mechanisms for epigenetic factors.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Learning Signaling Network Structures with Sparsely Distributed Data Flow cytometric measurement of signaling protein abundances has proved particularly useful for elucidation of signaling pathway structure. The single cell nature of the data ensures a very large dataset size, providing a statistically robust dataset for structure learning. Moreover, the approach is easily scaled to many conditions in high throughput. However, the technology suffers from a dimensionality constraint: at the cutting edge, only about 12 protein species can be measured per cell, far from sufficient for most signaling pathways. Because the structure learning algorithm (in practice) requires that all variables be measured together simultaneously, this restricts structure learning to the number of variables that constitute the flow cytometer's upper dimensionality limit. To address this problem, we present here an algorithm that enables structure learning for sparsely distributed data, allowing structure learning beyond the measurement technology's upper dimensionality limit for simultaneously measurable variables. The algorithm assesses pairwise (or n-wise) dependencies, constructs "Markov neighborhoods" for each variable based on these dependencies, measures each variable in the context of its neighborhood, and performs structure learning using a constrained search. In this paper, we describe an approximate, heuristic approach to apply Bayesian network structure inference to signaling pathways in a domain in which the entire variable set can not be observed simultaneously, resulting in sparsely distributed data. We learn the network structure using measurements of overlapping subsets of the variable set. Our approach seeks to minimize the number of experiments measured while maximizing the accuracy of model inference, by employing a set of biologically motivated assumptions. In our domain, we find that we are able to infer a model structure that contains the original structure inferred from a fully measured, 11-color dataset. MNA results contain higher confidence edges than those appearing in the original model, yielding nine additional edges for the same confidence cutoff. All the edges appear in the original model, as lower confidence edges. By ranking the edges based on their contribution to the model score, we are able to remove most of the additional edges, yielding a model that closely resembles the original model. We note that the ability to rank edges is useful for prioritizing model results, even if all edges map to causal connections.. One point for future work includes a more thorough theoretical treatment of the number of experiments required, given in terms of the size of the Markov neighborhoods, the number of variables, n, and the maximum measurable subset size, m. Or approach uses just 15 four-color experiments to accurately reproduce the results of an 11-color experiment (albeit with a shift in confidence). However, these results, particularly with regard to the number of measurements needed, are relevant for our particular domain, with its set of variables and treatment conditions. A different domain may have a very different correlation landscape, leading to very different requirement for experiments; furthermore, it may violate our assumptions to varying degrees, yielding poorer results. Our work has an additional caveat: because we simulate four-color data using an 11-color dataset, our data may be cleaner than data taken from actual independent experiments, which may contain more variability. We do not believe this will be a major source of variation, as the data is a moderately large sample drawn from the same distribution. Nevertheless, the results must be interpreted with caution, as they are not conclusive regarding the number of experiments needed or about the success of the modeling effort.. Although we present an example in which we scale up from a four-variable measurement capacity to an 11-variable model, our intent is to enable a larger measurement capability to scale to larger models, for instance, from 10 variables measured to models of 50-100. How would our approach differ for these larger scale models? We can expect to need a larger number of experiments in order to initially cover each pair of variables. On the other hand, the large scale models have the distinct advantage that, in contrast to the smaller scale models, they are less likely to encounter a neighborhood larger than their maximum measurable set size. This is because each signaling molecule has a finite, defined set of parents, so that a measurement capability of 10 molecules can more easily accommodate each variable and its likely parents than a four-color measurement capability. This fact also constrains the number of experiments that are necessary, because the combinatorial step of measuring subsets of size m from large neighborhoods is likely to be unnecessary. Although the details in terms of the number of experiments needed, and the success of the results will depend on various factors (prominently, the correlation landscape of the domain, and the particular dependencies among the variables, respectively), we anticipate that larger scale models will prove more amenable to this approach than smaller models. This work proffers an approach for approximate model inference in a pathway with a number of molecules exceeding our measurement capabilities. Although our results are specific to just one particular variable set, they nonetheless indicate the possibility that this approach is both feasible (in terms of the number of experiments required) and effective (in terms of the modeling results). It is our hope that this method can be used to infer increasingly large signaling pathway models. Particularly as measurement capabilities improve (for a cutting edge multivariate, single cell approach with high dimensionality, Tanner et al. [2007] ), it may be possible to build highly integrated models involving numerous canonical pathways, in order to discover points of cross talk, enrich our knowledge of various pathways, and enable a truly systems approach even in relatively uncharted domains. In this section, we demonstrate the utility of our algorithm with an example in which we build an eleven variable model, using subsets of size four. The data consists of measurements of signaling molecules important in T-cell signaling, measured under several activation and inhibition conditions as described in Sachs et al. (2005) . The variables modeled are the signaling molecules PKC, PKA, Raf, Mek, Erk, Akt, Plc , PIP2, PIP3, p38, and Jnk. For a full description of signaling molecules and employed conditions, see Sachs et al. (2005) . We have previously built the eleven variable model using the complete dataset. In this study, we sample from the full dataset to create subsets with a maximum measurement size of four. We take advantage of the full eleven color dataset to synthesize smaller data subsets, while still enabling a comparison of the results to the "ground truth" model, as determined by the model resulting from the full dataset.. Neighborhoods were assessed based on k-means clustering, using pairwise correlations as the dependence metric. For this variable set and data, a clear bimodality was found, such that the resulting clusters were convincingly legitimate, though they may be less clearcut in other domains. All neighborhoods found contained no more than four members, rendering pruning unnecessary. In cases where a "perturbation parent" lacked correlation with the target variable, its dataset was augmented with its value as described above.. Model results. The resulting model perfectly recapitulated all model edges from the original full data result. However, at the same confidence cutoff, it contained nine additional edges: Jnk ! p38, Mek ! Jnk, Mek ! Plc , Raf ! Akt, PKC ! Erk, PKC ! PIP3, PKA ! Plc , Mek ! Akt, and Mek ! Plc . Where do these additional edges come from? For a hint, we look at the results from the full data model. Our results are reported as averaged models as described in Sachs et al. (2005) , in which the confidence of each edge is determined by the weighted average of all high scoring models containing that edge. In the full data results, all nine of these edges appear, as lower confidence edges, specifically, these nine appear if the confidence cutoff is reduced from the original 0.85 to 0.76. Do these edges reflect accurate influence connections? In some cases they do, for instance, in the connection between Raf and Akt, an edge that is missed in the original model, due to its low confidence value. In other cases, they appear to reflect a correlation induced by a hidden coparent, as is likely the case in the edge between Jnk and p38, two MAPK's which may be influenced by the same MAPKK's or other upstream molecules. Still others require further investigation to determine their validity.. These edges did not make the confidence cutoff in the original model. Why did their confidence shift in these results? The answer most likely lies in the constrained search space-in the original model, a number of different edges may have helped to constrain the global model, explaining dependencies in the data about equally well. Because different model results contained different ones of these more minor edges, none of them sustained a high confidence level once the models were averaged. In this constrained search, many of the minor edges were not present in the search space (they did not appear in any neighborhood), greatly strengthening the minor edges that did remain.. This means that even at a very high confidence cutoff, our algorithm yields a dense graph (26 edges, compared to the 17 edges present in the original model). While these additional edges may reflect legitimate connections, it is crucial nevertheless to assess a relative confidence between them, particularly in the densely connected signaling space, where the conclusion that variables are not connected, or are less strongly connected is nearly as important as the detection of connectivity. In other words, a graph indicating that (nearly) all variables are connected to all other variables is not as informative as one indicating a relative ranking to emphasize stronger, higher confidence edges.. Ranking model edges. Because of the shift in confidence of model edges, we employ an additional approach to rank the confidence of the 26 edges present at confidence above 0.85 (in fact they mostly boasted a confidence of 0.99 or greater). We rank the edges based on the decrease in the model score when an edge is removed. Based on this criteria, of the seven weakest edges, six are edges that are also below the confidence cutoff in the original model. When these are removed, the model contains three edges that did not make the cutoff in the original model, and misses one edge (PKC ! Mek) that was strong in the original model but did not make the cutoff based on this ranking criteria. For simplicity, the unpruned dense model with 26 edges is not shown. The model with edges pruned as just described is shown in Figure 4 .. Number of employed experiments. As stated earlier, one goal of our algorithm assumptions is to minimize the number of needed measurements, to enable practical applications of this algorithm. Preliminary pairwise experiments, when performed in sets of 4, require just seven separate measurements per condition to account for all pairs of the eleven variables. When applicable, neighborhoods containing each other were collapsed, and neighborhoods represented (by chance) in the data of the preliminary experiments did not require further measurements. Consequently, in this study, only fifteen size-four subsets were needed for the Markov neighborhood algorithm. This represents a substantial savings when compared to the exhaustive subset count of 330 (see Introduction for details). Below, we present background useful for understanding the problem at hand and our proposed solution. We describe flow cytometry, introduce Bayesian networks, and provide an overview of our algorithm.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O


3D feature surface properties and their application in geovisualization New acquisition methods have increased the availability of surface property data that capture location-dependent data on feature surfaces. However, these data are not supported as fully in the geovisualization of the Digital City as established data categories such as feature attributes, 2D rasters, or geometry. Consequently, 3D surface properties are largely excluded from the information extraction and knowledge creation process of geovisualization despite their potential for being an effective tool in many such tasks. To overcome this situation, this paper examines the benefits of a better integration into geovisualization systems in terms of two examples and discusses technological foundations for surface property support. The main contribution is the identification of computer graphics techniques as a suitable basis for such support. This way, the processing of surface property data fits well into existing visualization systems. This finding is demonstrated through an interactive prototypic visualization system that extends an existing system with surface property support. While this prototype concentrates on technology and neglects user-related and task-related aspects, the paper includes a discussion on challenges for making surface properties accessible to a wider audience. Today's geovisualization systems enable users to work with data from various basic categories, such as feature attributes, 2D rasters, or multidimensional geometry. These categories fundamentally differ with respect to domain, usage, and technology. Each phenomenon can be represented in a Digital City using various data types depending upon performance, precision, the availability of algorithms or system support, or the availability of data or capabilities for its capture. Geovisualization systems provide users with category-specific means for transforming, correlating, and visualizing all data with the goal of extracting information and knowledge. Highly developed systems facilitate flexible visualization (Dykes, 2005) that encourages ideation in a non-predefined ways and enables exploratory data analysis (EDA).. Recently, an additional data category has received increasing attention: 3D surface properties. This category describes data attached to 3D feature surfaces; i.e., for each surface location, a data value of an arbitrary, but homogeneous, type can be stored. Surface properties are not limited to the Earth's surface but apply to any 3D feature, such as buildings or bridges. The simplest surface property is a constant value assigned to the feature's entire surface. Usually, surface properties provide location-dependent, varying values. Typically, such a property is sampled regularly and stored as a collection of 2D rasters along with one unique mapping function per surface patch (e.g., a polygon). A surface property covers the complete surface and maps a unique raster portion to each surface patch (Figure 1 ). Some surface properties can be described procedurally; i.e., there is a function that computes the property value given the surface location. This applies, for example, to surface-based simulations, even though the computational efforts for on-demand evaluation may be prohibitively high. Surface properties fit into the well-established coverages concept (Open Geospatial Consortium, 2000) . The difference between surface properties and existing coverage implementations, such as (massive) georeferenced 2D rasters, is the highly fragmented spatial domain.. New techniques enable the cost-effective acquisition of surface properties even for massive data sets. Examples are realistic and fully textured virtual 3D cities available in Google Earth or Bing Maps, such as Munich (Germany), Zurich (Switzerland), Manhattan (NY, USA), and others. There are various sources capable of producing data in this category:. • Remote sensing, e.g., facade textures from oblique imagery (Früh et al., 2D raster(s) Mapping functions 3D geometry 2004; Lorenz and Döllner, 2006) ,. • Physical simulation, e.g., photovoltaic potential (Šúri and Hofierka, 2004) or radio network coverage (Maciel et al., 1993) ,. • Spatial analysis, e.g., solar envelopes (Morello and Ratti, 2009 ), or architectural metrics such as vista quality, or building facade visibility.. Increasing data availability has been acknowledged with the inclusion of 3D surface properties in CityGML (Gröger et al., 2008) , the international standard of the Open Geospatial Consortium (OGC) for exchanging and storing virtual 3D city models. Naturally, surface properties should also be part of the information and knowledge extraction process (Gahegan, 2005) that drives geovisualization. Some potential benefits of integrating surface properties include the following:. • More precise phenomenon representation, e.g., finer granularity, or less abstraction of surface-related phenomena.. • Improved data access, e.g., the direct usage of surface properties generated by special-purpose software in geovisualization systems without the need for conversion to other data categories.. • Improved analysis techniques, e.g., access to more precise data, access to additional data, or incorporation of more complex analytical models. (2000)). Surface properties represent a generic, multi-functional data category for Digital City applications and systems. Whilst not novel in their own right, new acquisition methods such as automatic facade texture creation and generative methods such as 3D visual analysis and simulation have brought surface properties to the attention of a larger audience. This paper has demonstrated applications of surface properties for two scenarios, namely, photovoltaic potential analysis and residential quality assessment, which can be systematically designed and implemented based on surface property concepts. In general, surface properties have the potential for increasing expressiveness and detail in simulations and analyses as well as for capturing real-world phenomena using digital city models. To take advantage of their potential and to make effective use of them, surface property concepts can be flexibly adapted to given contexts and tasks.. To make effective use of surface properties in geovisualization and EDA, visualization systems and applications require efficient implementations of surface properties. This paper has focused on the implementation of operations as part of the visualization pipeline. The paper has presented ways in which computer graphics technology can be used as a basis for implementation, most of all for geovisualization, but also in the context of more general geoinformation systems. In particular, the successful integration of surface properties into applications and systems does not require major changes to the software architecture but the addition of orthogonal functional components. Starting from this basis, other aspects must be explored including operation access, implementation frameworks, and visualization aspects.. In the long term, surface properties should be supported in geovisualization and geoinformation systems in ways comparable to the current support available for attributes, 2D rasters, and geometry. Most likely, surface properties will become a core functionality of future Digital City systems, as they appear to be a system feature that relates to generic and multi-purpose functionality. Our prototypic visualization tool concentrates on the visual mapping of surface properties in virtual 3D city models that contains all data categories. It provides basic operations for the visual exploration of 3D city models, such as the loading of data sets or 3D navigation. It does not contain fixed surface property operations but provides direct access to the shader code for users to implement application-and task-specific operations. A major aspect is the merging of surface properties with other data categories. For this aspect, all available data are provided to the shader. The incorporation of surface properties into operations with respect to other data categories has not yet been implemented. Aggregation operations are also not implemented yet. Both are discussed in Section 4.. The tool uses Autodesk LandXplorer (Autodesk Inc., 2009), the Virtual Rendering System (VRS; Döllner and Hinrichs, 2002) , and OpenGL as graphics API. Shaders are written in GLSL (Rost, 2006) , the OpenGL Shading Language. A key functionality is providing all data contained in the virtual 3D city model to the shader. The different data categories are treated as follows:. Feature Attributes: Feature attributes of acceptable type are collected into arrays that are then copied to graphics memory. Acceptable types include integers, floating point numbers, booleans, and vectors. Strings currently cannot be processed in a straightforward manner in GLSL and are excluded.. 2D Rasters: 2D rasters are directly stored in textures if they do not exceed a hardware-dependent dimension limit. If they do, a texturing technique for massive texture data (Döllner and Baumann, 2000) is used.. 2D and 3D Geometry: Geometry is used for rendering and requires tessellation of surface patches into triangles. Each triangle is augmented with a patch ID and a feature ID that can be used to load respective attributes during shader execution. Additionally, mapping functions for each surface property and 2D raster are added.. Surface Properties: This prototype focuses on raster-based surface properties. They are considered textures and preprocessed for out-of-core rendering based on the massive texturing technology available in the LandXplorer library. During rendering, the out-of-core technique ensures the availability of required surface property data.. After loading all data, shader code is generated that provides easy access to all data such that the prototype can be quickly configured in real-time with operation code. Figure 5 shows the application architecture and data flow. Within the shader, additional properties such as local lighting or 3D location are made available. The specification of operations through shader code is demonstrated in the accompanying video (Figure 4) .. During rendering, the shader is executed for each pixel in which a surface is visible; i.e., operations are not applied to all cells available in a surface property but to all contributing pixels in the current view. This typically reduces the number of shader invocations and enables interactive frame rates. A disadvantage of this approach is aliasing, since surface property resolution(s) and pixel resolution do not match in most views. Advanced texture filtering capabilities and anti-aliasing through multi-sampling help reduce this problem. Both features are provided by the graphics hardware and have no effect on the shader code. Users may merely notice some slowdown during rendering.. The integration of surface properties does not require major changes to the original geovisualization system architecture. The most significant additions are the exposition of the shader to the user, which includes shader frame generation, and the provision of attribute data to the shader. The remaining architecture is taken directly from the Autodesk LandXplorer platform. Hence, our approach allows for surface properties to be added to existing geovisualization systems with minimal effort. Moreover, our system immediately benefits from technology for handling massive data sets and scales as well as the original visualization system. A less prototypic surface property support requires additional components for improved user interface and complex operations. We expect them to fit well into our architecture.. The performance of this architecture is mainly influenced by the dataloading rate. Rendering requires all necessary data to reside in graphics memory. Out-of-core algorithms hide load latencies by reverting to coarser resolutions (both for texture and geometry) until optimal data is available. This ensures interactive frame rates, even if data comes from a comparatively slow source such as a remote database. Typically, prefetching further reduces latencies. However, if large parts of the view change, e.g., due to rapid view point movements or dynamic texture data, latency hiding fails, and rendering must wait for data transfer from storage to graphics memory. Examples for dynamic texture data are time-varying sequences and simulation results with time-varying parameters. If no (or an insignificant amount of) data need to be transferred to graphics memory, rendering can fully utilize the GPU. In particular, dynamic processes such as distances to moving objects, which are computed on the GPU, have almost no influence on the frame rate.

O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O


Fast Gauss Bilateral Filtering Abstract The bilateral filter presents a natural combination of the Gaussian spatial and tonal filters. The bilateral filter was first proposed by [AW95] and then rediscovered in [SB97] within the so-called SUSAN approach and in [TM98] where its current name was coined. The bilateral filter can be also considered as a very powerful modification of the Yaroslavsky filter [Yar85] in which the spatial convolution with a box function is changed to the spatial convolution with a Gaussian.. Because of its edge-preserving ability and conceptual simplicity, the bilateral filter has become a popular and powerful image and shape processing tool. It has been extended and generalized in several ways [CT03] , [BCM05b, BCM05a] , [TSP07] and successively used for video enhancement [BM05, MS05] , mesh denoising [FDCO03] , high-dynamic-range (HDR) image compression [DD02] purposes, and many other image processing and computer graphics applications. See [PKTD07] for a nice overview of properties, extensions, and applications of the bilateral filtering approach.. Mathematically, the classical bilateral filter in its continuous setting is defined as a spatial-tonal normalized convolution I new (x) = g 1 (x − y)g 2 (I(x) − I(y))I(y)dy g 1 (x − y)g 2 (I(x) − I(y))dy , y ∈ R n , (. applied to an image I(x), x ∈ R n . Here g 1 (·) and g 2 (·) are Gaussian kernels used for spatial and tonal filtering, respectively. Often other types of decaying kernels are used in (1) instead of Gaussians.. Previous work on fast bilateral filtering. The nonlinear and nonlocal nature of (1) makes its straightforward implementation computationally expensive: a naive discrete implementation of (1) has O(N 2 ) computational complexity where N is a number of image elements (pixels/voxels). So various approaches have been proposed for accelerating the bilateral filter.. Noted that a separable convolution with a Gaussian is fast, Pham and Vliet [PvV05] suggested to apply a onedimensional bilateral filter subsequently to each spatial direction. The resulting filter scheme mimics (1) and is quiet fast. However it often generates undesired artifacts at image regions where image edges are aligned with coordinate axes.. Weiss [Wei06] introduced a 3D histogram based approach for accelerating the 2D bilateral filter with a square box spatial kernel. In a very recent paper [Por08] , Porikli has also employed a 3D histogram technique and achieved a remarkably low computational complexity when a box spatial kernel is used. Another achievement of the approach of [Por08] consists of a constant complexity algorithm for a modification of the Yaroslavsky filter with constant spatial kernel (i.e., g 1 = const in (1)).. Durand and Dorsey [DD02] proposed a fast approximation to the 2D bilateral filter by interpreting (1) as a Gaussian convolution with g 2 (η − I(y))I(y) where η is a parameter, computing the convolutions for a sparse set of values of η via 2D Fast Fourier Transforms (FFT), and then linearly interpolating the results. It turns out that the algorithm of [DD02] can be considered as a special case of a more general convolution-based scheme introduced by Paris and Durand in [PD06] where 3D FFT is combined with a downsampling strategy. In [PD09] Paris and Durand extended their approach to color images (bilateral filtering in 5D space). In their bilateral grid approach, Chen et al. [CPD07] combined the convolution-based representation of (1) [PD06] with a GPU parallelization scheme.. Of course, the above-mentioned approximations of the bilateral filter are not free of drawbacks. As noted in [PD09] , convolution and 3D grid based schemes may lead to memory overhead when dealing with multidimensional data. The histogram-based approaches of Weiss and Porikli [Wei06, Por08] are also sensitive to image dimensionality and, in addition, do not allow for controlling the approximation error.. Our approach. In this paper, we propose a fast and accurate approximation of the bilateral filter. The method is conceptually simple and combines the dimension elevation trick of [PD06] with Fast Gauss Transform (FGT), a technique for fast and error-controlled computation of a weighted sum of Gaussians. FGT belongs to the family of fast multipole methods which combine clustering and manipulations with truncated series expansions to achieve computationally efficient and accurate approximations of sums of radial basis functions. First we apply the dimension elevation trick of [PD06] and convert the discrete bilateral filter to a normalized weighted sum of Gaussians in a spatial-tonal domain. Then FGT is used for a fast and error-controlled numerical evaluation of the sum. To demonstrate the computational power of our approach we consider a number of applications including image denoisng and HDR image tone mapping. The contributions and benefits of our approach can be summarized as follows.. • It has linear computational complexity w.r.t image elements, such as pixels, voxels, etc.. • It allows the user to control speed/accuracy trade-off.. • It is applicable to non-uniformly sampled data.. • It leads to an extremely fast implementation of a version of the Yaroslavsky filter with a spatially constant kernel.. • It turns out to be very efficient for volumetric filtering and HDR image tone mapping tasks. In this paper, we have developed a FGT-based approach to a fast and accurate approximation of bilateral filtering with Gaussian kernels. Our FGT-based approximation has linear computational complexity and is precision guaranteed. It can be used to process high-dimensional and/or non-uniformlysampled image data. We have demonstrated that our method outperforms three recent state-of-the-art fast bilateral filtering schemes. We have also presented applications of our fast bilateral filter to real-time image and volume denoising and HDR image displaying problems. Our implementation of FGT is based on the original approach of Greengard and Strain [GS91, GS98] and, therefore, is especially efficient in dealing with low dimensional data. For high dimensional data, one should probably use the so-called IFGT, Improved Fast Gauss Transform, which has a number of benefits over FGT [YDGD03, MSR. * 08]. However our own experiments with IFGT were not very encouraging.. Given an image y = I(x), x ∈ R n , n = 2 or 3, let us recall that the Gaussian kernel in (3) is given by. 2 ) with vector of bandwidth pa- (7) it does not seem correct to use large epsilon values. However, as noted before, the FGT accuracy upper bound (7) represents the worst-case scenario and that scenario is not realized for typical images (e.g., for a typical image, its intensity distribution is not concentrated on a small set of points). In our numerical experiments, even setting ε = 10 3 leads to a reasonably good FGT-based approximation of the bilateral filter.. We will also need the standard deviation s d of 1D distribution of the intensity values {I(x)}.. Error metrics. Given an original image I(x), denote by I e (x) and I a (x) the images obtained after applying an exact filtering scheme (we consider the bilateral filter and its variations) and an approximation of the scheme (e.g., our FGTbased approximations), respectively. Let d j = I e j − I a j be the difference between the exact and approximated bilateral filtering results, where the subindex j = 1, 2, ..., N enumerates the image elements (pixels, voxels, etc.). In addition to the method noise d(x), the following error metrics are used for evaluating our fast bilateral filter:. where the abbreviations ARE, and MRE stand for average and maximum relative errors, respectively. We also employ PSNR, the peak signal-to-noise ratio (the larger, the better), used for similar purposes in [PD06, Por08] . Here. Timing and accuracy. The computation time is measured in seconds (s), minutes (m), and hours (h). All our numerical experiments reported in this paper were performed on a Core2 Extreme X9770 (3.2 GHz quad core, no parallelization was used) PC with 16GB RAM and 64 bit OS. We compare our FGT-based bilateral filter with the recent state-of-the-art CPU-based fast bilateral filtering schemes: the histogram-based approach of [Por08] , the FFT-based fast bilateral filter of [PD06] , and the separable bilateral filter of [PvV05] . We use the program codes available from the authors of [PD06] and from the web [Era08] for [Por08] . The Gaussian functions used in these codes are appropriately modified to coincide with G(x) defined in Section 3. We start our numerical experiments from the famous Lena image: Figure 1 presents the original image and an exact bilateral filtering result. Figure 2 delivers the visual, method noise, and PSNR comparisons of our FGT-based method with those developed in [PvV05] , [Por08] , and [PD06] . We set the number of bins equal to 256 in our evaluation of the approach of [Por08] and, as a ground truth benchmark, use exact bilateral filtering of the Lena image with a constant spatial kernel (it takes 9.8s to compute) instead of the right image of Figure 1 . Following notations adopted in [PD06, PD09] , we use ss and rs to denote the space (spatial) and range (tonal) sampling rates. The timing and errors measurements corresponding to Figure 2 are given in Table 1 . Figures 3, 5 , and 6 demonstrate speed and accuracy advantages of our method over the approaches developed in [PvV05] , [PD06] , and [Por08] for varying bandwidth parameters. The graphs in Figures 3, 5 , and 6 correspond to [PvV05] (red), [Por08] (green), [PD06] with (1,1) abbreviating (s s , r s ) = (σ g1 , σ g2 ) (blue) and (0.1,0.1) staying for (ss, rs) = (0.1σ g 1 , 0.1σ g 2 ) (pink), and our method where (10,2) means (ε, r) = (10, 2) (orange), and (1,6) stays for (ε, r) = (1, 6) (sky-blue). We do not include detailed graphs for the ARE and L ∞ metrics because they are similar to the graphs for L 1 and MRE error metrics, respectively. Table 2 presents a computational time comparison of the methods for various image sizes (we use the same the enumeration notations and parameter settings as in Figure 2) . Table 3 displays summaries the bilateral filter approximation error results for the Lena image. As demonstrated by the top image of Figure 6 , the relation between the computational time and accuracy (we use L 1 metric in this case) for our method differ for different pairs of the bandwidth parameters. This is so because, for given bandwidth parameters, our FGT-based algorithm automatically adapts the necessary computational cost in order to satisfy a given precision. Tables 4 and 6 , respectively, for various volume sizes. Table 5 demonstrates how fast our method in processing large size volumetric images (512 3 voxels) for various sets of the bandwidth parameters. According to our estimates, a straightforward and exact bilateral filtering of a volume dataset consisting of 512 3 would take approximately 31 years of computational time.. When σ g 1 is small, our method requires greater computational time to compare with middle and large values of σ g1 for the same approximation accuracy.. As mentioned before, we have examined the fast bilateral filter of [PD06, PD09] with two parameter settings, (s s , r s ) = (σ g 1 , σ g 2 ) and (s s , r s ) = (0.1σ g 1 , 0.1σ g 2 ) (the image intensity range is supposed to be rescaled to [0, 1]). Although the first setting is recommended by the authors, we decided to test the second one since it delivers a much more accurate approximation to the bilateral filter. In our experiments with the histogram-based approach of [Por08] , we use the 256 bins, although following numbers of bins: 16, 32, and 64 are recommended by the author. Obviously the more bins are used, the more accurate approximation is achieved. In all numerical experiments presented in this paper, our method with (ε, r) = (1, 6) delivers a more accurate approximation of the bilateral filter w.r.t. L 1 , L ∞ , MNR, and PSNR error metrics than the methods of [PD06, PD09] and [Por08] with the highest accuracy settings. Setting (ε, r) = (10, 2) gives approximately the same accuracy as the above mentioned methods with the highest accuracy settings w.r.t. L 1 and PSNR metrics but our method is much faster. In addition, those highest accuracy settings may cause memory overflows when dealing with large-size images, as indicated by (b) and (d) of Table 2 . Overall, the numerical experiments show that our approach leads to fast and accurate bilateral and SCYaroslavsky image and volume filtering. For example, our fast bilateral filter processes 116K (71K), 474K (541K), 467K (812K), and 873K voxels (pixels) per second in average when (ε, r) is set to (1,6), (10,2), (10 2 ,2), and (10 4 ,2), respectively. Our fast SC-Yaroslavsky filter with (ε, r) = (1, 6) is highly accurate and processes images and volumes at high speed of 5.28M pixels/voxels per second.. The plots of Figure 4 illustrate timing and accuracy of our methods w.r.t. the FGT parameters (ε, r) and can serve as a guidance for choosing these parameters. It is well known that the r = 4 and r = 6 are sufficient to obtain single and double error precisions [GS98] . It is rather unexpected that using r = 2 delivers quite satisfactory results as demonstrated by Tables 1-5 and in Figures 2-8 and 10-12. We refer to [LKdF05] for an empirical study of how the computational cost depends on the FGT accuracy ε.

O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Object-based assessment of burn severity in diseased forests using high-spatial and high-spectral resolution MASTER airborne imagery Forest ecosystems are subject to a variety of disturbances with increasing intensities and frequencies, which may permanently change the trajectories of forest recovery and disrupt the ecosystem services provided by trees. Fire and invasive species, especially exotic disease-causing pathogens and insects, are examples of disturbances that together could pose major threats to forest health. This study examines the impacts of fire and exotic disease (sudden oak death) on forests, with an emphasis on the assessment of post-fire burn severity in a forest where trees have experienced three stages of disease progression prefire: early-stage (trees retaining dried foliage and fine twigs), middle-stage (trees losing fine crown fuels), and late-stage (trees falling down). The research was conducted by applying Geographic Object-Based Image Analysis (GEOBIA) to MASTER airborne images that were acquired immediately following the fire for rapid assessment and contained both high-spatial (4 m) and high-spectral (50 bands) resolutions. Although GEOBIA has gradually become a standard tool for analyzing high-spatial resolution imagery, high-spectral resolution data (dozens to hundreds of bands) can dramatically reduce computation efficiency in the process of segmentation and object-based variable extraction, leading to complicated variable selection for succeeding modeling. Hence, we also assessed two widely used band reduction algorithms, PCA (principal component analysis) and MNF (minimum noise fraction), for the delineation of image objects and the subsequent performance of burn severity models using either PCA or MNF derived variables. To increase computation efficiency, only the top 5 PCA and MNF and top 10 PCA and MNF components were evaluated, which accounted for 10% and 20% of the total number of the original 50 spectral bands, respectively. Results show that if no band reduction was applied the models developed for the three stages of disease progression had relatively similar performance, where both spectral responses and texture contributed to burn assessments. However, the application of PCA and MNF introduced much greater variation among models across the three stages. For the early-stage disease progression, neither band reduction algorithms improved or retained the accuracy of burn severity modeling (except for the use of 10 MNF components). Compared to the no-band-reduction scenario, band reduction led to a greater level of overestimation of low-degree burns and underestimation of medium-degree burns, suggesting that the spectral variation removed by PCA and MNF was vital for distinguishing between the spectral reflectance from disease-induced dried crowns (still retaining high structural complexity) and fire ash. For the middle-stage, both algorithms improved the model R 2 values by 2-37%, while the late-stage models had comparable or better performance to those using the original 50 spectral bands. This could be explained by the loss of tree crowns enabling better signal penetration, thus leading to reduced spectral variation from canopies. Hence, spectral bands containing a high degree of random noise were correctly removed by the band reduction algorithms. Compared to the middle-stage, the late-stage forest stands were covered by large piles of fallen trees and branches, resulting in higher variability of MASTER imagery. The ability of band reduction to improve the model performance for these late-stage forest stands was reduced, because the valuable spectral variation representing the actual late-stage forest status was partially removed by both algorithms as noise. Our results indicate that PCA and MNF are promising for balancing computation efficiency and the performance of burn severity models in forest stands subject to the middle and late stages of sudden oak death disease progression. Forests are an integral part of many terrestrial ecosystems, providing a wide range of ecological, economic, social and cultural services. The structure and function of forests result from a dynamic process of tree recruitment, growth, and death, and the influence of a variety of disturbances (e.g., fires, storms, and diseases) (Asner, 2013) . Major disturbance events could initially harm most of the ecosystem services delivered by trees. However, depending on the extent, severity and type of disturbance, some ecosystem services may be regained during forest succession, while the others may be permanently disrupted (Boyd et al., 2013) . Wildfires and invasive species (especially exotic disease-causing pathogens and insects) are examples of the disturbances that may cause permanent and unexpected changes to forest landscapes and the associated services. The U.S. Forest Service currently lists them as two of the four major threats to the health of the nation's forests (U.S. Forest Service, 2014). Although neither disturbance is new, a growing number of studies have found that their intensities and frequencies have substantially increased over the past decade, as a result of global change (Bergot et al., 2004; Wulder et al., 2006; Kurz et al., 2008; Aukema et al., 2010; Olsson et al., 2012; Boyd et al., 2013) . Fires of higher severity may also be more likely to occur in forests where invasive diseases or insects have caused high tree mortality (Jenkins et al., 2008; Harvey et al., 2013) . Furthermore, the interaction of fire and insects or disease disturbances may alter forest ecosystems in unexpected ways (Metz et al., 2013) , challenging our ability to predict the severity of burns across large infested landscapes.. Remote sensing has proven effective in large-area fire detection and burn severity mapping across a diversity of environments by linking the fire-induced physical changes in the land surface to variations in spectral reflectance from remotely sensed images (Hall et al., 1980; Milne, 1986; Jakubauskas et al., 1990; White et al., 1996; Hudak and Brockett, 2004; Lentile et al., 2006; Veraverbeke et al., 2012) . Two types of approaches are typically used to model burn severity: statistical regression (deriving continuous burn severity values) or classification (retrieving discrete burn severity classes). Compared to field efforts required to directly measure the post-fire burn effects, remote sensing offers a dramatically less expensive alternative that is especially appropriate for managing large and topographically complex landscapes. However, accurate burn severity assessment may become a challenging task if exotic diseases or insects have caused extensive pre-fire tree mortality. Disease-related mortality can lead to a significant rise in shortwave infrared surface reflectance and a decrease in the near infrared reflectance, which is similar to the reflectance created by ash or charred remains after combustion of vegetation (Guyot et al., 1989; Roy and Landmann, 2005) . Thus, pre-fire mortality may be confounded with burn severity in infested areas where low-severity fire also occurred. To understand the degree to which these factors may influence the accuracy of burn severity assessment, it is necessary to examine mapped burn severity across various stages of disease or insect progression; however, this has not been well investigated yet.. Recent developments in the sensor technologies used in remote sensing have made it possible to improve the accuracy of burn severity assessment using high-spatial and/or high-spectral resolution imagery. For example, Mitri and Gitas (2008) successfully mapped burn severity with an overall accuracy of 83% using 4 m IKONOS imagery, while Veraverbeke et al. (2012) found that the char fraction cover derived from 50-band MASTER data was strongly correlated with field-measured burn severity. High-spatial resolution imagery enables the evaluation of the degree of burn heterogeneity at the small patch level, which could aid in a better characterization of the complex effects from fire and disease/insect interactions (Turner et al., 1998; Lentile et al., 2006; Meentemeyer et al., 2012) . High-spectral resolution imagery may further improve the analysis of such effects due to its increased sensitivity to the spectral variations from terrestrial features (Thenkabail et al., 2012) . Since the early 2000s, Geographic Object-Based Image Analysis (GEOBIA) has been increasingly used to extract and analyze geographic objects from high-spatial resolution imagery (Blaschke et al., 2014) . Unlike the prevailing per-pixel methods, GEOBIA applies segmentation-generated image objects (i.e., aggregates of pixels) to mimic the human perception of the real objects on the ground . While promising results of applying GEOBIA have been reported in numerous studies from various fields (Blaschke et al., 2014) , less consideration has been given to the application of data sets featuring both high-spatial and high-spectral resolutions. Compared to the typical multispectral data with less than ten spectral bands (e.g., IKONOS, SPOT, and QuickBird), images with a high-spectral resolution contain dozens to hundreds of spectral bands. An immediate consequence is that the computation efficiency in segmentation (a common process in GEOBIA) could be dramatically reduced. Furthermore, compared to the per-pixel feature extraction, a greater number of post-segmentation object-based features (also called feature bands) are often extracted in order to better define ground objects and the spatial interactions between neighboring objects, such as shape, size, and object-based texture or patterns (Hay et al., 1996; Kelly et al., 2008; Chen et al., 2011) . Once all the spectral and feature bands are combined as inputs for subsequent modeling, selecting the optimal subset (from a pool of at least hundreds of objectbased bands) could pose major challenges (e.g., time-consuming and error-prone) to GEOBIA practitioners. Reducing the number of original spectral bands prior to GEOBIA processing is an intuitive solution to address this issue; however, it remains unclear how this procedure influences the precision in delineating objects (e.g., object size and shape) and the accuracy of burn severity modeling in disease-impacted forests.. Based on the above considerations, in this research we studied the 2008 Basin Complex Fire in the Big Sur, California ecoregion, which burned over 95,000 hectares of forest (USDA Forest Service, 2008) that was patchily infested by the exotic forest pathogen Phytophthora ramorum, the cause of sudden oak death (SOD; Rizzo et al., 2005) . This non-native pathogen is estimated to have killed hundreds of thousands of host trees in the Big Sur forests since the mid-1990s (Meentemeyer et al., 2008) . Interestingly, disease progression is not uniform across the landscape, resulting in forest stands experiencing varying stages of invasion and levels of disease-related mortality. This variability in disease progression and tree mortality has been linked to variation in field measurements of burn severity following the Basing Complex Fire (Metz et al., 2011 (Metz et al., , 2013 . Our interest in improving post-fire rapid assessment of burn severity across large forested landscapes heterogeneously impacted by pests or pathogens led us to explore two research questions: (i) How do different stages of SOD progression affect the accuracy of forest burn severity modeled with images having both high-spatial and high-spectral resolutions? (ii) How does spectral band reduction influence the delineation of image objects and the accuracy of subsequent object-based burn severity models? Increasingly, forest ecosystems are experiencing a variety of complex and interacting disturbances. Large fires are occurring more frequently and burning forest stands where invasive diseases have already caused high tree mortality. This study investigated the possibility of applying MASTER airborne imagery with both highspatial (4 m) and high-spectral (50 bands) resolutions to assess post-fire burn severity in forests affected by three different stages of pre-fire mortality (i.e., early -trees retaining dried foliage and fine twigs, middle -trees losing fine crown fuels, late -trees falling down) due to SOD. While GEOBIA is gradually becoming a standard tool for analyzing high-spatial resolution imagery, high-spectral resolution imagery with dozens to hundreds of bands can dramatically reduce computation efficiency and poses challenges to the object-based variable selection for accurate burn severity modeling. This study further evaluated the impacts of two widely used band reduction algorithms PCA and MNF on the delineation of image objects and the resulting accuracy of burn severity modeling. If no band reduction was applied, the models developed for the three stages of disease progression had relatively similar performance, suggesting that the invasion of SOD did not have a major impact on the performance of burn severity modeling using unreduced images of high-spatial and high-spectral resolutions, but this is computationally intensive. However, the application of PCA and MNF introduced substantial variability among the segmentation and modeling results across the three stages. Compared to the image objects generated using all the 50 spectral bands, our results show that the PCA components led to mild over-segmentation (i.e., smaller mean object sizes) and the shape of objects was marginally affected, while the MNF components resulted in notable under-segmentation (i.e., larger mean object sizes) and the shape of image objects exhibited reduced complexity by 24% and 29% using the top 5 and top 10 MNF components, respectively. Compared to PCA, MNF dramatically reduced image spectral variation, generating larger image objects with less complexity of object shapes. However, PCA-based models outperformed the MNF-based models in most cases, suggesting that MNF may have removed some variation that was vital for distinguishing between spectral reflectance from diseased trees and fire-induced ash or charred remains. Comparison of the early-stage burn severity models showed that both band reduction algorithms were typically unable to improve or retain the model performance over no-band-reduction, except for the model using 10 MNF components. Compared to the no-bandreduction scenario, band reduction led to a higher level of overestimation of low degrees of burns and underestimation of medium degrees of burns, probably due to the fact that both PCA and MNF enhanced the reflectance from dried tree crowns similar to the way fire-induced ash change the reflectance. For the middle and late stages, trees losing crowns allowed for improved signal penetration and a lower spectral variation in the MASTER image mosaic. Consequently, the two band reduction algorithms evaluated in this research (using 10 PCA/MNF components as input) showed promising results of balancing computation efficiency and the performance burn severity modeling in the forests stands subject to the middle and late stages of SOD progression. Finally, we note that the conclusions made from the burn severity models using PCA and MNF are scene-dependent. If the landscape is covered by forests with different structures and/or subject to distinct disease impacts, the post-fire spectral variation at various infestation stages may also differ from that observed in this study. Compared to the model involving PCA and MNF, the no-band-reduction models may have higher transferability across varying forest landscapes, but remain computationally expensive.

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