it has now been clearly established that solar eruptive phenomena have multiple incidences on the heliosphere , and in particular on the earth space environment . along with coronal mass ejections ( cmes ,see * ? ? ?* ) , solar flares are one of the most dangerous space weather events . they are also systematically observed before a large cme is triggered .while cme - triggered energetic particles reach earth on time scales of tens of hours , high energy protons accelerated by a flaring process may reach 1 au few tens of minutes later , and the associated x - ray photons affecting the earth s ionosphere only 8 minutes later .no robust precursor of solar flares have been identified so far , preventing any efficient empirical forecast .an ongoing significant effort to predict when a flare of a given magnitude will occur have been pursued over the last decade ( for a recent review , see * ? ? ? * and references therein ) , with moderate success so far .any progress in this direction is thus highly valuable for risk management related to space weather .decades of flare observations have shown that the probability distribution function for flare energy takes the form of a power law , spanning some 8 orders of magnitude in energy , with estimated in the range  .avalanches provide one class of physical phenomena characterized by such scale - free energy release when driven slowly and continuously .many avalanche models have been developed to represent the solar flares distribution ( see * ? ? ?* and references therein ) , most of which are based on the concept of self - organized criticality ( hereafter soc ; see * ? ? ?* ; * ? ? ?* hereafter lh ) have proposed an avalanche - type model for solar flares that has become a reference model in the solar context , although numerous variations have now been developed over the intervening years .if flares are indeed accurately described by an avalanche - type model , forecasting them may appear dubious because of the stochastic driving from which they originate . in a lattice - based avalanche model such as the lh model , the size of an avalanche is controlled by ( i ) the starting position of the instability triggering it and ( ii ) the closeness to the threshold of the neighbor nodes . in the original lh model ,the starting position mainly depends on the stochastic driver while the state of the system is the complex result of past avalanching history .if a large portion of the system is close to the threshold , the short term avalanching behavior may depend marginally on the stochasticity of the driver .building on this idea , coupled the lh model to data assimilation technique to forecast solar flares .it remains unclear , though , whether a mean prediction ( _ i.e. _ , when varying the stochastic driver ) can generally be defined from such an avalanche model .this paper focuses on the following question : can avalanches models be used for predictive purposes in the context of solar flares ?we present a study of the predictive capabilities of a series of avalanches models , starting from the original lh model , in which we introduce variations in the stochastic components the latter , as expected , determining the predictive capability of the model .the models considered and their statistical properties are described in section [ sec : aval - models - solar ] and [ sec : model - properties ] .section [ sec : predictive - abilities ] provides a methodology to define a prediction from an avalanche model as well as estimates of the predictive capabilities of the models we considered .we conclude in section [ sec : conclusions ] by a discussion summarizing our results and the identification of subclasses of avalanche models most promising for the development of a solar flares prediction tool based on avalanche models .an avalanche model necessarily includes some kind of stochasticity . we develop different soc models by modifying how and where the stochasticity appears , which will lead to very different predictive capabilities ( see section [ sec : predictive - abilities ] ) . with one exception ( see section [ sec : georgoulis vlahos ] ) ,the models we use are described in details in .we summarize briefly their properties and defer the interested reader to this other paper .   following in part , have developed a soc avalanche model for solar flares that by now has become a kind of `` standard '' ( for a review , see * ? ? ?here we consider a version of the lh model defined over a 2d regular cartesian grid with nearest - neighbor connectivity over which a scalar field is defined .the superscript is a discrete time index , and the subscript pair identifies a single node on the 2d lattice . keeping on the lattice boundaries , the cellular automaton is driven by adding one small increment in per time step , at some randomly selected node that changes from one time step to the next . a deterministic stability criterion is defined in terms of the local curvature of the field at node : where the sum runs over the four nearest neighbors at nodes and .if this quantity exceeds some preset threshold then an amount of nodal variable is redistributed to the same four nearest neighbors according to the following discrete , deterministic rules : where .following this redistribution it is possible that one of the nearest - neighbor nodes now exceeds the stability threshold .the redistribution process begins anew from this node , and so on in classical avalanching manner .driving is suspended during avalanching , implicitly implying a separation of timescales between driving and avalanching dynamics , and all nodal values are updated synchronously during avalanche to avoid introducing a directional bias in avalanche propagation .it is readily shown that these redistribution rules , while conservative in , lead to a decrease in summed over the five nodes involved by an amount : with the energy released being `` assigned '' to the unstable node . if one identifies with a measure of magnetic energy ( see * ? ? ?* ) , the total energy liberated by all unstable nodes at a given iteration is then equated to the energy release per unit time in the flare . a natural energy unit here ( used for normalization in all that follows ) , is the quantity of energy liberated by a single node exceeding the stability threshold by an infinitesimal amount .this very simple model yields a good representation of flare statistics , namely the observed power - law form ( and associated exponents ) of the frequency distributions of flare peak energy release , duration , and total energy release  .* ; * ? ? ?* hereafter gv ) have developed a variation of the lh model based on the work of by adding anisotropic stability criterion and redistribution rules .this model is known to generate a double power - law frequency distribution of avalanche parameters e , p and t , with a steeper power law for the smaller events .then , they introduced a modified driving scheme using a power - low random number generator for the small increments of .the increments follow the probability distribution they showed that the power law indexes of the avalanche parameters e , p and t vary roughly linearly with the parameter .this method provides a very interesting mean of controlling the power - law indexes of soc models .we choose , for the present study , to retain only this modified driving scheme leaving out the anisotropic stability criterion and redistribution rules from the complete original gv model .in addition to the gv model , also developed a modified driving scheme by rendering it non - stationary .this work was motivated initially by the results of , who showed that the waiting time distribution of solar flares should be characterized by a power - law tail for long waiting times , rather than by an exponential decay which is obtained from the lh model .finally , re - analyzed the solar flare data from various source and concluded that the waiting time distribution of solar flares is indeed consistent with a non - stationary poisson process , and can well be described with an avalanche model possessing a non - stationary driver .a biased driving scheme could in principle make the model either more or less robust with respect to various random number sequences , and hence improve or decrease its predictive capabilities . in order to simplify the discussion we only detail the results obtained with the gv model in this work .similar analysis made with the model of lead to the same conclusions regarding its predictive capabilities ( not shown here ) . in the following we use a gv model with a parameter .the random driver of the lh and gv models can be nicely linked to the parker picture of random shuffling of a loop s magnetic footpoint by photospheric flows . for loop diameters smaller than this scale ,though , the granular flow displaces the footpoints in a spatially coherent manner far removed from random shuffling .one particularly interesting form of such global forcing is a twisting of the loop s footpoints , which then propagates upwards and accumulates along the length of the loop .this form of global forcing has a direct equivalent in our 2d cellular automaton through the driving rule where the parameter ( ) is a measure of the driving rate . as in the lh model , driving is interrupted during avalanching , which amounts to assuming that the driving timescale is much longer than the avalanching timescale , a reasonable assumption in the solar coronal context ( for a discussion , see * ? ? ?the stochastic component of the deterministically driven model can appear in the threshold definition , in the extraction or in the redistribution rule .in all rules discussed so far , redistribution is conservative , in that whatever quantity of being extracted from an unstable node ends up in the nearest neighbors .this conservation property is basically inspired by the sandpile analogy , where avalanches redistribute sand grains without creating or destroying any .a nonconservative version of the lh redistribution rules can be defined as follows : where  ] .a nonconservative model of this type , using fully deterministic driving , and random redistribution and stability criteria , has been studied extensively in .we consider here three deterministically driven models ( hereafter d1 , d2 and d3 , or d models ) with different levels of stochasticity .model d1 corresponds to model nc6 in and includes random extraction , random redistribution and random non - conservation components .model d2 corresponds to model nc0 , which involves only one type of stochastic process located in the non - conservative redistribution rule ( ) .finally , model d3 is equivalent to d2 with a significantly lower non - conservation degree ( ) .in the following analysis , we test the predictive capabilities of the five models by combining different random number sequences for different initial conditions for a total of runs of ( on average ) iterations .the statistical properties of each model ( described hereafter ) are obtained from longer individual runs of more than iterations .the large number of runs we considered is necessary for assessing the predictive skills of each model but precludes the use of large lattices .we run the five models on a mid - size [ lattice which represents a good computational compromise since the power - law exponents and global properties of the models were shown to vary only marginally for larger lattices in the considered models .[ fig : lh_example ] shows a small sample of a time series for the lattice energy ( a ) and avalanche energy release ( b ) in the lh model .the lattice energy fluctuates around a mean state and energy is released by avalanches of various duration and size .  . ]the total energy release ( e ) , duration ( t ) and peak energy ( p ) of avalanches are distributed as a power - law over several decades ( see the probability distribution functions pdfs in fig .[ fig : mod_properties ] ) .the d models have an anomalous non - power law component for very small avalanches , and model d3 also exhibit and small excess of large avalanches ( for a complete discussion on these models , see * ? ? ?* ) . in this workwe assess the capability of avalanche models to predict large avalanche .hence , the peculiar small avalanches population does not affect the results of this paper .the gv model possess a significantly different waiting time statistics ( not shown here ) . because of all these differences , we need to precisely define the time intervals and avalanches properties on which we characterize the predictive capabilities to ensure that some specificities of the models do not include some bias to our analysis. these definitions will naturally change from one model to the other ( see section [ sec : predictive - abilities ] ) .the five models are characterized by different power - law exponents , which are listed in table [ tab : props_mods ] .the power - law exponents characterizing the lh , gv and d3 models stand at the very low end of the observationally - inferred value for solar flares , citep[e.g . , }$ ] in the hard x - rays data , see][]aschwanden:2014wg , and fall significantly below this range for the d1 and d2 models .we will see that the predictive capabilities of the avalanches models are rather insensitive to these power - law exponents , but rather strongly depend on their embedded stochasticity note that it is in principle possible to alter the components of the model to better reproduce the observationally - inferred power - law indices ( see * ? ? ? * ; * ? ? ? * ; * ? ? ?* ) .   and the fits are plotted ( solid lines ) . ].statistical properties of the five models used for this study .the normalization energy and time windows are also indicated ( see section [ sec : predictive - abilities ] ) .all models are defined on a 2d cartesian lattice with four - nearest - neighbour connectivity . [ cols="<,>,>,>,>,>",options="header " , ]predicting the occurrence of an event requires the definition of the time window on which the prediction is given .the largest events which we want to predict are rare but obey specific statistical rules which depend on the avalanche model considered .we define a cumulative waiting time defined by the averaged waiting time between avalanches of energy higher than .we display the cumulative waiting times as a function of the corresponding energy for the model we considered in fig .[ fig : time_properties ] .the d models have an almost - constant waiting - time distribution for the population of small avalanches ( see * ? ? ?* ) . then , the models exhibit of a power - law part ( except for model d3 ) followed by an exponential part for the highest energies .this change reflects the energy limit the avalanches can access due to the finite size of the lattices .  for each model, we identify the time window and its corresponding energy at which the slope of the cumulative waiting times changes ( these quantities are model - dependent and are used to normalize the axes in figure [ fig : time_properties ] ) .we are interested in the capability of the models to predict the largest avalanches , hence we consider here avalanches of energy higher than .we use in the following the time window to asses the predictive capabilities of the models . because of the known statistical distribution of avalanches , most of the runs carried over will trigger at least an avalanche of energy . in order to ensure that the predictive skills of the models are not the result of a simple statistical occurrence of an avalanche over , we aim at determining the predictability of avalanches of energy ( and higher ) that statistically occur on time windows larger than .this will ensure that the observed avalanche results from a particular lattice state and/or a particular random number sequence ( see section [ sec : mean - prediction - from ] ) , and is not the result of a climatological forecast based on the overall properties of the statistical soc model ( see also * ? ? ?avalanche models always include a stochastic component , the realization of which varies from one run to one another . a prediction from a soc - type modelshall be composed of a sufficient number of runs varying the stochastic component of the model .bearing in mind the analogy with solar flares prediction , we want to predict what will be the energy of the largest avalanche in the next , and the time at which it will occur . for one fixed initial condition, we use different random number sequences and store for each of them the starting time and release of energy of the largest avalanche over the time window .the resulting pdfs are shown in fig .[ fig : pred_example ] for the models lh , gv , d1 and d2 for a representative initial condition of each model ( model d3 gives very similar results to d2 ) .the left panels display the pdf of the occurrence time of the largest avalanche in the time window , and the right panels the pdf of the largest avalanche energy . in all models ,we notice that the energy is regularly distributed around a mean value . while the d models are well fitted by gaussian ( blue lines ) , the first two models have non - gaussian tails .we chose to fit those resulting pdfs with a weibull function which give satisfying fits ( red lines ) .the best of the two fits is shown with a solid bulleted line and the other is shown in dashed thin line , for reference .the mean predicted value from the model is defined as the peak location of the best of the two fits .the fact that a mean can always be defined confirms the intuition that the stress pattern embedded in an instantaneous soc state indeed determines the shape and size of upcoming avalanches , regardless of the stochastic component of the model .the departure of lh and gv models from a gaussian behaviour nonetheless reveal an interesting property , which shall be confirmed in the following .we observe that the pdf is heavy tailed on the high energy side compared to a classical gaussian distribution .on the one hand , the stochastic process tend to give the climatological prediction of the model ( , vertical solid grey line in fig .[ fig : pred_example ] ) .on the other hand , the initial stress pattern allows ( or not ) for very large avalanches to be triggered ( , vertical dashed grey line ) .the heavy - tail part of the pdf directly derives from this latter property and is obtained only for a few favorable random number sequences , while the stochastic process is strong enough to severely alter the mean prediction towards the climatological forecast ( vertical solid gray line ) .we clearly see that this property of the stochastic process is very strong in the lh and gv , and significantly weaker in models d. hence , the gaussian shape obtained in the d models simply indicative of marginal dependency upon the random number sequence : very large avalanche are triggered only when the adequate stress pattern exists in the lattice .the left panels reveal another fundamental difference in the context of predictability between the models we considered .the lh and gv models show pdfs of spanning the whole time window , which means that the stochastic process determines when the largest avalanche will occur in the next time window .hence , a mean is generally hard to define , although with some particular initial condition a slight peak value can be observed ( not shown here ) .conversely , the d models show pdfs peaked for a few values of which results in a very good confidence in the predicted time for the maximal avalanche .we note nonetheless that the multiplicity of peaks generally exhibited by the d1 model leads to a small but significant uncertainty on the occurrence time of the avalanche considered .models d2 and d3 are the only models from which one can confidently predict an occurrence time .the profound difference between the d models and the others is naturally explained by the deterministic character of their driving process . being deterministic , the driver dictates unambiguously the next avalanching node which will be marginally affected by the choice of random number sequence ( we recall here that in models d2 and d3 , the stochastic process is only acting during avalanches and hence the driver completely determines the next avalanching node ) .if this node is likely to trigger a large avalanche , it will do so for most of the random number sequences . as a consequence, the pdf of for the d models will always be peaked . for small avalanchesthe stochastic elements embodied in the d models will significant impact the unfolding of a given avalanche , but for large avalanches , where many hundreds of nodes are involved many avalanching repeatedly in the course of the same avalanche , these stochastic fluctuations will tend to `` even out '' and have a limited impact on global avalanching characteristic , including the amount of released energy .random number sequences using a common initial condition .left panels display the pdfs of the predicted arrival time of the largest avalanche , and right panels the pdfs of the predicted energy .the peak is identified by a vertical red dashed line on left panels .the red and blue lines on the right panel label the weibull and gaussian fits of the energy pdf .the solid and dashed vertical grey lines respectively label the normalization energy ( the climatological forecast ) and the target energy .results from d3 ( not shown here ) closely resemble d2 ., title="fig : " ]  random number sequences using a common initial condition .left panels display the pdfs of the predicted arrival time of the largest avalanche , and right panels the pdfs of the predicted energy .the peak is identified by a vertical red dashed line on left panels .the red and blue lines on the right panel label the weibull and gaussian fits of the energy pdf .the solid and dashed vertical grey lines respectively label the normalization energy ( the climatological forecast ) and the target energy .results from d3 ( not shown here ) closely resemble d2 ., title="fig : " ]  random number sequences using a common initial condition .left panels display the pdfs of the predicted arrival time of the largest avalanche , and right panels the pdfs of the predicted energy .the peak is identified by a vertical red dashed line on left panels .the red and blue lines on the right panel label the weibull and gaussian fits of the energy pdf .the solid and dashed vertical grey lines respectively label the normalization energy ( the climatological forecast ) and the target energy .results from d3 ( not shown here ) closely resemble d2 ., title="fig : " ]  random number sequences using a common initial condition .left panels display the pdfs of the predicted arrival time of the largest avalanche , and right panels the pdfs of the predicted energy .the peak is identified by a vertical red dashed line on left panels .the red and blue lines on the right panel label the weibull and gaussian fits of the energy pdf .the solid and dashed vertical grey lines respectively label the normalization energy ( the climatological forecast ) and the target energy .results from d3 ( not shown here ) closely resemble d2 ., title="fig : " ]    independent events .the predicted energy ( defined as the peak of the best fit of the pdf in the right panels of fig . [ fig : pred_example ] ) is shown against the predicted time significance ( see text ) .the closer the points are from unity , the higher the predictive capability .the dashed horizontal line corresponds to the climatological forecast of the model , the thin light lines correspond to the targeted energy for event prediction in each model . ]we performed the statistical analysis described in section [ sec : mean - prediction - from ] for independent initial conditions and associated large events for each of the models .for each event , we define the predicted energy by the mean of the best fit to the pdf of the predicted avalanche energy .we also define the predicted time significance by estimating the significance of the largest peak in the distribution .a significance of corresponds to one and only one peak at one particular time , while a significance of corresponds to a purely flat pdf ( see the top two left panels of fig .[ fig : pred_example ] ) .we display the results of the cases for the five models in fig .[ fig : combine_preds ] .the horizontal solid lines correspond to the values of , and the dashed line to the energy threshold .the intuition we got from fig . [ fig : pred_example ] is confirmed : the arrival time prediction is very good for d models ( ) , while lh and gv models rank poorly for almost all events ( ) .the energy predicted by the lh and gv models lies in between the `` climatological forecast '' ( , dashed line ) of the model and the target energy which they almost never predict correctly .this implies that they are unable to predict reliably the very large avalanches .conversely , large avalanches occurring in d models are generally recovered regardless the particular random sequence .model d1 exhibits intermediate behavior with instances of both good and bad prediction , and model d3 performs extremely well , with for all the events considered here .   is plotted against the occurrence time of the predicted avalanche , normalized to the prediction time window .the thick lines represent the best fit of the data ( eqs .[ eq : fits_lin]-[eq : fits_lin_end ] ) , and the corresponding shaded areas the estimated error of the fit . ]some events of the lh and gv models have good significance and the corresponding predicted energy is significantly larger than the other cases .they can be explained by taking a close look at fig . [fig : combine_preds2 ] which displays the same results as on fig .[ fig : combine_preds ] but against the largest avalanche occurrence time ( normalized to the time window ) rather than .the successfully predicted events of the lh and gv models correspond to runs where the large avalanches took place at the very beginning of the runs .hence , they occurred in runs where almost no random numbers were involved , which is why they have very good predictive capability .we observe that the later the large avalanche occurs in the run , the lesser lh , gv and d1 models are able to predict an avalanche different from the climatological forecast ( dashed line ) .the d2 model is , in contrast , predicting large avalanches fairly accurately regardless of the occurrence time in the prediction time window , again proving its high predictive capabilities .finally , the d3 model ( not shown here ) exhibit almost no dependency of the event occurrence upon the time window .the dispersion of the predicted energies is nevertheless comparable in all the d models . to confirm this interpretation, we further fit a linear relation between and for each of the models ( thick lines in fig .[ fig : combine_preds2 ] ) .we obtain , with energies normalized to for each model :    again , only models d2 and d3 exhibit a small dependency of the predicted energy on the avalanche occurrence time .the other models are clearly too sensitive to this parameter to be considered for reliable forecasts .in this paper , we have assessed the predictive capabilities of a representative set of avalanches models for solar flares .starting from the reference model of lu & hamilton , we modified the type of stochasticity embedded in the avalanche model and subsequently characterized their predictive capabilities .we focused our study on the prediction of large events , which are the rarest and presumably the hardest and most important to predict .we showed that only the purely deterministically driven model is able to predict a large event reliably , while the classical lu & hamilton model generally fails .we recall that the deterministically driven models show a deficit in term of small avalanches ( fig .[ fig : mod_properties ] ) and hence depart from the classical soc state .however , this property does not modify the predictive capabilities of the model , which were assessed for the larger , rarer avalanches , traditionally the hardest to predict .avalanche models always include the two conflicting aspects ( in terms of predictive capabilities ) of stochasticity and long - term correlations . by exploring the physical interpretation of avalanche models in the context of solar flares , we modified the stochastic process location in the model which lead to the development of a deterministically - driven model .we empirically demonstrated that this model possess the required properties to be used as a predictive tool : it is able to unambiguously predict the large avalanche occurrences over a given time window , well above the `` climatological forecast '' .we were able to demonstrate that the deterministically driven model has very little bias with the event occurrence time over a selected time - window .all the other models we considered are significantly affected by they stochastic component which makes them impossible to use for any practical prediction of large events .computationally , avalanche models also have the significant advantage of being extremely inexpensive to run ( this naturally results from their low dimensionality and their simplicity ) .those unexpected properties promote a further investigation for the development of a near - real time prediction tool of large solar flares based on deterministically driven avalanche models .we envision this a a two - steps process .first , as noted already the deterministically driven models considered here produce either power - law exponents ( e.g. , for the avalanche / flare energy distribution function ) that are significantly lower than the real solar flare distribution exponents , or a small excess of large events .these different deterministically - driven models all possess good predictive capabilities for large events , which is probably one of their robust features . as a result ,variations of the d model could be explored ( e.g. , in the spirit of * ? ? ?* ) to produce a model combining good predictive capabilities with statistical properties closer to the real solar flare data .the second step consists in the coupling of data assimilation techniques ( see , e.g. * ? ? ?* ) to the chosen deterministically - driven model , and use observed times series ( such as the geostationary operational environmental satellite goes x - ray time series ) to assess quantitatively the predictive skills of the model .our approach is complementary to the approach of who also used the statistical properties of solar flare to predict the whole - sun large events occurrence . in our case, the avalanche model can be viewed as a representation of one particular active region from which we will assimilate data .the use of selected data assimilation techniques will allow us to automatically adapt the driver and/or lattice state of the model , so that the output of the model matches the observed data .we show in figure [ fig : ex_da ] an example of such data assimilation run using a simulated annealing method .the goes flux ( blue line in top panel ) is transformed following to the method described in into a distribution of delta - functions ( black lines ) filtered for flares of class c8 and above .we make the conversion of the goes time sequence in terms of avalanche energy and model iterations using the typical waiting times of flares above c8 in model d3 . in the bottom panel ,we show three random realizations of model d3 ( sets of light colored vertical lines ) and one realization of model d3 using data assimilation ( da , red peaks ) with the observed goes time series ( gray boxes ) . herethe assimilation technique succeeds in capturing the two clusters of flares exceeding c8 at and hr , without generating spurious ( c8 ) flares before , after , or in between .the energy levels of the four reproduced flares also match very well with observations .the details of this assimilation technique will be described in details in .these preliminary results suggest that the lattice configuration resulting from the data assimilation run combined with the predictive capabilities of the model we demonstrated in this work could be used to carry out quantitative predictions of solar flares through direct simulation .we believe that such a model could lead to significant improvements of the current predictions of large ( typically x - class ) solar flares .   range during the flaring events of the active region 1045 between february 6 and february 9 , 2010 .the top panel show the goes flux ( blue ) and the processed signal ( see * ? ? ?* ) ( black ) for flares of class c8 and above .the bottom panel shows the goes signal ( grey boxes ) used in the data assimilation run . the assimilated sequence ( da ) is shown in red along with three random realizations of the model in orange , green and magenta .]  the author thank the anonymous referee for valuable comments .the authors acknowledge stimulating discussions during the issi workshops on turbulence and self - organized criticality ( 2012 - 2013 ) held in bern ( switzerland ) ; and during the `` festival de thorie '' ( 2013 ) held in aix - en - provence ( france ) . this research has made use of http://sunpy.org/[sunpy ] , an open - source and free community - developed solar data analysis package written in python .we also acknowledge support from the natural sciences and engineering research council of canada . as acknowledges finanical support from cnes via solarorbiter grant .29 # 1isbn # 1#1#1#1#1#1#1#1_#1_#1*#1*#1#1#1#1#1#1#1#1#1#1#2#1#1#1#1#1_#1_#1#1#1*#1*#1#1#1_#1_#1#1#1#1#1#1#1#1#1#1#1 # 1http://dx.doi.org/#1 [ ] # 1http://arxiv.org / abs/#1 [ ] # 1http://adsabs.harvard.edu / abs/#1[]#1#1#1#1#1#1#1#1#1#1 # 1#1

Abstract: we assess the predictive capabilities of various classes of avalanche models for solar flares . we demonstrate that avalanche models can not generally be used to predict specific events due to their high sensitivity to their embedded stochastic process . we show that deterministically driven models can nevertheless alleviate this caveat and be efficiently used for large events predictions . our results promote a new approach for large ( typically x - class ) solar flares predictions based on simple and computationally inexpensive avalanche models .


in the kind of delay tolerant networks ( dtns )  that we consider in this paper , nodes are mobile and have wireless networking capabilities .they are able to communicate with each other only when they are within transmission range .the network suffers from frequent connectivity disruptions , making the topology only intermittently and partially connected .this means that there is a very low probability that an end - to - end path exists between a given pair of nodes at a given time .such dtns can be consider in ad hoc networking when connectivity is very low ( e.g. in tactical military communications ) , in transportation systems as in the dieselnet project  or in pocket switched networks ( psn )  which are formed by devices that people carry everyday ( cell phones , pdas , music players ) .in all these contexts , end - to - end paths can exist temporarily , or may sometimes never exist , with only partial paths emerging .this paper addresses the extreme case , where only temporal paths exist .we call such networks _ temporal dtns _ , or _t - dtns_. when a node in a t - dtn receives a `` bundle '' of information from a neighboring node , it keeps it until it meets another node which provides an opportunity to relay the bundle .the bundle is transfered from one node to another instantly and this transfer is atomic .prior work on routing in t - dtns has commonly made the assumption that each pair of nodes shares the same inter - contact time distribution as every other pair .the main argument in this paper is that researchers should also be looking at cases in which inter - contact time distributions are heterogeneous .chaintreau et al . posit that there might be heterogeneity , but we show it and characterize it .we also show how exponential distributions can be composed to yield the heavy - tailed distributions that chaintreau et al . observed .as we shall see , the heterogeneity that we highlight allows us to usefully extend the work of spyropoulos et al . , which analyzes numerous routing schemes for t - dtns , but that uses mobility models that yield homogeneous distributions .we show , on the well known dartmouth wi - fi data set  , that despite the existence of a heavy - tailed distribution when inter - contact times are considered in the aggregate , a large portion of the node pairs present inter - contact time distributions that can be well fitted by an exponential distribution .we found these distributions to be heterogeneous , with a wide variation in exponents .we also provide the first formal analysis of the impact of heterogeneous exponential inter - contact time distributions on simple single - copy routing schemes .we show that routing strategies can benefit , in terms of delay , from this heterogeneity , and in particular from knowing these distributions .a node can choose among possible relay nodes based upon their expectations for meeting other relays or the destination .this section presents the model we use to analytically derive the delay expectations for the routing protocols we study later in this paper .we consider a network composed of _ n _ nodes .let s first look at the inter - contact time between two individual nodes : are the successive instants at which a contact between and occurs . is the inter - contact time between the and contact instants .we assume that the are samples from independent and identically distributed random variables that follow an exponential law with parameter , which we note .the mean inter - contact time between and is thus given by = 1/\lambda_{ij} ] , the expected inter - contact time for the pair of nodes .this plot has been computed over all the source - destination pairs that experienced an average inter - contact time lower than one week within the two months period that we considered in dartmouth data .we can see that the distributions are heterogeneous with expectations varying over three orders of magnitude .the average ].,width=188 ]  then , we test for whether the inter - contact process between any two nodes can be modelled by an exponential process with a parameter  ] matrix .more precisely , the tail cumulative distribution of the aggregated inter - contact times is given by the laplace transform of the distribution of the parameters .a pareto law of the form , , with shape parameter and scale parameter , is observed if and only if the follow a gamma distribution , .  to verify this on the data set we proceed in the following way : we estimate parameters and from the cumulative distribution of the parameters for pairs that were shown to follow an exponential behavior ( the ones that pass the cramer hypothesis test ) .we find and .[ lambda_th ] shows the estimated cumulative gamma distribution with the experimental lambda cumulative distribution for all pairs that have shown to be exponential .then , we plot in fig . [ interc_th ] the corresponding power - law with cumulative distribution of aggregated inter - contact times .as one can see , the two experimental curves fit the theoretical curves .what this result shows is that when one considers an exponential t - dtn , we can regain the power law behavior for the aggregated inter - contacts when the distribution of the parameters is a gamma , which is the case in the data we used when considering the subset of pairs that have inter - contact times exponentially distributed .having defined a stochastic model that is realistic for the data set under study , we now examine different simple single copy routing strategies .we derive analytical formulas that we will use to study the impact of heterogeneous parameters on routing .  in all routing strategies, we consider that nodes know all pairwise mean inter - contact times for all nodes in the network , i.e. , each node knows the matrix .this knowledge could be diffused through an epidemic type of routing , or learned by each node from past contacts .   under the wait routing strategy ,the source node waits until it meets , the destination , to deliver the bundle in one hop .  if the bundle is injected at time , its delivery time is equal to , the remaining inter - contact time before the next contact between nodes and .the memoryless nature of exponentials implies that also follows an exponential distribution with the same parameter .the mean expected delivery is thus given by :  = 1/\lambda_{sd}\ ] ]  this straightforward result gives an upper bound on the delivery time that a routing strategy should meet , since the wait strategy is the most rudimentary one hop single copy scheme .the minimum expected delay ( med ) routing strategy was first introduced by jain et al .this strategy , similar to source routing , defines which path the bundle will follow from to , that is , the ordered list of intermediate relay nodes it will have to go through .the list is chosen to provide minimum expected end - to - end delay .if a path is given by the following ordered list of nodes , and relaying occurs at time instants , the total delivery time along path is given by the remaining inter - contact time after each relaying instant , that is :   using the fact that = 1/\lambda_{ij} ] .following the same line of reasoning as in sec .[ sec_sw ] , and defining , one finds that the expected delivery time is given by : = \frac { ( 1 + \sum_{r \in r } \frac{\lambda_{sr}}{\lambda_{rd } } ) } { \sum_{r \in r } \lambda_{sr}}\ ] ]  we performed simulations using dartmouth traces ( see sec .[ sec : fitting ] ) to study how the algorithms behave in the case of heterogeneous connectivity .we simulate the following protocols : wait and 1-sw which are naive schemes , and , 1-sw and med that are designed to take advantage of heterogeneity .we slightly modified 1-sw , to better compare it with 1-sw : a node is a potential relay only if , i.e. , if it has a chance of meeting the destination . in med , we authorized intermediary relays to directly transfer bundles to the destination whenever met .we choose at random different source destination pairs and replay the contacts between the nodes present in the data to see how for each pair a bundle , generated at the beginning of the two months period , is delivered . values used for route selection in 1-sw and med , and to determine theoretical delays of 1-sw , 1-sw and med have been computed over the data filtered due to the ping - pong effect ( see sec.[sec : fitting ] ) . however , the contacts replayed in simulations were that in the original traces as it does not impact the results and because filtering was only of interest for modelling ..[res_simus]simulation results with dartmouth data . [ cols="^,^,^,^,^,^,^,^,^ " , ]   table [ res_simus ] presents the simulation results averaged over runs with the % confidence levels that are obtained using the student distribution .it presents , for each of the protocols , the average delivery ratio , the average delay ( `` a delay '' ) and the median delay ( `` m delay '' ) computed over the delivered bundles , the average theoretical delay over all the bundles generated ( infinite delay is assumed to be the length of the simulated period , i.e. days ) , and the average hop count , also obtained on delivered bundles .  the major result in table [ res_simus ]is that schemes that make use of heterogeneity of inter - contact times ( 1-sw and med ) perform better , either in delivery ratio or delay , than the ones that do not exploit it ( wait and 1-sw ) .wait only delivers 11.2% of bundles because most of the source , destination pairs selected at random satisfy ( e.g. they never met ) .1-sw , 1-sw and med achieve almost the same delivery ratios with respectively 87.3% , 86.9% and 87.9% .about 13% of the bundles were thus not delivered . in terms of delay , among these last three protocols , 1-sw plots the highest with a mean of 23.0 and a median of 22.7 in days , 1-sw the lowest with a mean of 18.8 and a median of 15.4 .med appears to be in the mid - range with a mean of 20.9 and a median of 18.0 in days .the difference between the modified 1-sw and 1-sw gives a further insight on the type of heterogeneity that should be considered .the modified 1-sw is a one hop strategy that uses only true relays to the destination : relay nodes in 1-sw must meet both the source and the destination .the scheme is not completely ignorant of heterogeneity , as it exploits binary connectivity information , the fact that not all nodes meet one another .1-sw goes beyond that and differentiates between neighboring nodes based on the quantitative expected inter - contact time .the fact that 1-sw ourperforms the modified 1-sw thus indicates that routing actually benefits from the quantitative inter - contact time heterogeneity , and not just from node connectivity .table [ res_simus ] shows a descrepancy between the theoretical and the experimental delays .this can be first explained by the presence of node pairs that do not have an exponential behavior .this is particularly true for 1-sw . in this casethe computation of expected delays on mean inter - contact times misses possible inter - dependencies of node contacts .simulation artifacts also come into play .the routing simulation is carried out on a limited time scale .the values are computed over the entire data set in a prior pass , so a relay node may meet the destination for the last time before having met the source for the first time . this pre - computation being not realistic , we could have used on - line predictive or learning methods .however , as they are challenging to define , we let this study for future work and intend here to provide early validation results to motivate research in the domain . the fact that 1-sw delivers slightly less bundles than 1-sw is clearly due to this artefact . indeed , because in 1-sw , the source transfers more rapidly the bundle to a relay , we have a lower probability to contacts between that relay and the destination . also , med suffers from the same simulation artefact, it would have delivered % of bundles otherwise .  through these simulations ,we validate the natural feeling that we should take into account the heterogeneity of inter - contact time distributions in the design of routing solutions for t - dtns . furthermore , because 1-sw , which is only a two - hop protocol , achieves better performance than med by delivering bundles with lower delays and a lower impact on network resources ( med delivers bundles in 7.2 hops in average while 1-sw uses only 2 ) , we expect promising future work inspired from 1-sw to be done .the opportunistic nature of 1-sw is the main reason of this superiority over med , in which bundles follow a strict sequence of relays , in a network which is not a perfect exponential t - dtn .we have first shown that , in a widely - used t - dtn data set , distributions of inter - contact times are heterogeneous . as a consequence, one has to take it into account while modeling .second , we have validated the insight that considering heterogeneity in routing improves performance .we presented a simple routing strategy , 1-sw , adapted from the spray and wait scheme , which is capable of using only a subset of relays to improve routing performance , measured in term of average delay .clearly , our work , based as it is upon one data set , will benefit from validation against others as mentioned in sec .[ sec : fitting ] .work also needs to be done to examine why a memoryless model fits so many node pairs in an environment in which one would expect to find more temporal correlations .finally , formal studies and validations should be conducted with more elaborate schemes , in terms of number of copies distributed or in terms of the number of hops traversed .we gratefully acknowledge david kotz for enabling our use of wireless trace data from the crawdad archive at dartmouth college .we also thank augustin chaintreau for his valuable comments .

Abstract: prior work on routing in delay tolerant networks ( dtns ) has commonly made the assumption that each pair of nodes shares the same inter - contact time distribution as every other pair . the main argument in this paper is that researchers should also be looking at heterogeneous inter - contact time distributions . we demonstrate the presence of such heterogeneity in the often - used dartmouth wi - fi data set . we also show that dtn routing can benefit from knowing these distributions . we first introduce a new stochastic model focusing on the inter - contact time distributions between all pairs of nodes , which we validate on real connectivity patterns . we then analytically derive the mean delivery time for a bundle of information traversing the network for simple single copy routing schemes . the purpose is to examine the theoretic impact of heterogeneous inter - contact time distributions . finally , we show that we can exploit this user diversity to improve routing performance .


detecting road borders has broad applications in future autonomous vehicles and intelligent transportation systems as an important component of scene understanding .it can provides cues about road structure that benefit motion planning and cruise behavior control . in autonomous driving , the detection of road border is often done by gps , high quality road map and some other active sensors such as radar and lidar .this , however , can sometimes be limited by the accuracy of gps positioning signal as well as the resolution of active sensors .a natural question is whether we can address the problem with computer vision .  besides detecting the physical road border , part of our taskalso includes robustly detecting the shoulder region in order to provide necessary maneuver guidance for future autonomous driving systems . in the united states ,highways often contain a so - called `` shoulder region '' usually defined as the region between the outer - most solid lane marking and the physical road border .this shoulder region serves as a buffer zone before the physical limit of the road .non - emergency vehicles are mostly not allowed to drive on shoulder regions .but under emergency conditions , they may be allowed on shoulder regions for purposes such as evasive maneuver and emergency parking .[ fig1a ]   we start from the most basic setting where a side - view production camera looks out from the right side of a vehicle , as illustrated in fig.[fig1 ] .the detection problem is approached as the problem of detecting the road border ( e.g. , guard rails , concrete barriers , etc . ) and detecting the closest lane marking on the shoulder - side of the vehicle .the expectation is that the algorithm will return an estimate of the drivable regions before the physical road border .if the vehicle is on the right - most lane , the shoulder region is expected to be detected , while if the vehicle is on inner lanes , the detection also include available lanes on the right .we will assume that the shoulder is on the right side of the car , but we can easily apply our approach to the shoulder on the left side provided that the side camera is mounted on the left side of the vehicle .we emphasize that the current system is just one part of a future surround view system where side - view detection and front - view detection can jointly support and improve each other .the current system can also benefit future autonomous driving systems by providing information about road structure .our goal is to achieve robust detection within 0.5 to 6 meters detection range , while being able to handle various challenging scenarios including strong shadows , diverse border types / appearances and complicated scenarios such as highway entrances and exits .  in the united states , typical highway borderscan be classified into three types : concrete barrier , guard rail and soft shoulder . given this observation ,our key assumption is that the types of highway border are not as diverse as the borders in urban or other uncontrolled scenarios and can be learned from a set of labelled images .this assumption , however , by no means makes the problem trivial : the border and shoulder detection problem still needs to address the limited resolution challenge , meet the required speed constraints , deal with complicated border situations and contend with a number of other challenges such as strong shadows , dynamic appearances and other patterns that look like borders .we show that our problem can be theoretically formulated as a joint detection - and - tracking problem under a graphical model called `` structured hough voting '' .our contribution in this paper lies in the fact that the proposed structured hough voting model exploits a variety of inter - frame and intra - frame structural information to achieve very robust performance , while using multiple candidate hypotheses and mode selection to retain necessary flexibility .we will show that the proposed model performs very well on the highway border and shoulder detection problem .the problem of vision - based scene understanding for autonomous driving has been widely studied .many seek to address the problem of general object detection , such as the detection of pedestrians , bicycles , motorcycles and vehicles .there has also been a considerable amount of work regarding scene parsing where each pixel / superpixel in an image is labeled with a certain object class . however , most of them focus on the understanding of general objects and the algorithms are often not possible to run in real - time on a regular cpu .some relevant works try to understand the structure of road and these works are indispensable parts of the autonomous driving system .considerable effort has been devoted to automatically detect roads and lane markings , or to find vanishing points .others have addressed the problem by exploring more capable sensors , including stereo vision sensors and lidar sensors .these sensors provide extra depth information which makes the tasks considerably easier .thus they have been adopted in some autonomous systems . while these sensors are able to provide more information than monocular cameras , their costs are often very high .the problem of road border detection has been previously addressed but none has addressed the highway scenario where border detection can become particularly difficult with concrete barriers due to their textureless nature .in addition , most of them focus on features and detectors while our work also presents a novel robust model .given a video from the side camera , we investigate both the inter - frame and intra - frame structural information instead of performing hough voting independently for each frame .our high - level intuition here is that these structural cues are the key to robust performance . to utilize such cueswe formulate our model under a conditional random field ( crf ) .we shall see that independent hough voting corresponds to unary prediction in our crf model , returning how likely the hypotheses are .the inter - frame and intra - frame structural information corresponds to pairwise potentials , introducing additional constraints to refine the results .geometrically , a straight line in a 2-d space can be represented by the following equation : where is the algebraic distance between the line and the origin , is the angle of the vector orthogonal to the line .voting points are the points indicating where a line should be .given a set of voting points whose coordinates are , the voting weight is defined as : where is the weight associated with each voting point . is the bandwidth parameter that adjusts how sensitive voting is to relatively far away voting points and is empirically fixed as 5 in this work for its good performance .let , conventional hough voting seeks to find a hypothesis that maximizes the voting weight : finding with continuous optimization is difficult as it is non - convex .a common way is to discretize and search for the one with the maximum vote weight .the remaining questions are : 1 .how are the voting points defined ? 2 . how to obtain these voting points ?* type 1 voting points : * voting points are returned by triggered border or lane marking detectors . herewe adopt scanning window detection where each detected positive window returns an equally weighted voting point estimating where the border / lane marking is .we deliberately allow multiple dense triggers ( see fig .[ fig5 ] ) and the returned voting points are the main source of detection information .* type 2 voting points : * these are voting points whose coordinates are simply the coordinates of all pixels , while the hough voting is now weighted by the gradient of each pixel .the intuition is obvious : borders and lane markings often have relatively strong vertical gradients . in case where detectors have failed and very few type 1 voting points are returned , estimating with gradient might be a good approximate strategy to obtain a reasonable result .we seek to treat the hough voting hypotheses jointly , exploring their probabilistic and structured relations with a graphical model .crf is a highly suitable model for our problem .suppose denotes the aggregate of observations ( i.e. , the coordinates and weights of voting points ) in all the frames and the aggregate of all the hough hypotheses , crf discriminatively defines the joint posterior probability and the inference of crf is to find the joint hypothesis configuration that maximizes :   different from many conventional models , our structured hough voting model first generates three different candidate hypotheses in every frame ( except the initial one ) .we will show how they are generated later .the intuition is that we want to handle certain situations where : 1 .borders and lane markings can `` jump '' suddenly due to entrances and lane changes and 2 .failures of border / lane marking detectors can return very few type 1 voting points .we hope that at least one of them can return a good `` guess '' of the border / lane marking in every situation and that the model can appropriately select the best expert .once the candidate hypotheses are obtained , the model selects the best one as the detection output .finally , we also check whether the chosen hypotheses for border and lane marking in each frame have violated certain structure restrictions ( e.g. , whether they have intersected ) .if violations occur , perturbation is performed on the border hypothesis candidates to guarantee that such structural restrictions are followed .again , one of the perturbated hypothesis candidates is selected as the final detection result .let `` bd '' and `` ln '' denote `` border '' and `` lane marking '' for short , we define the following notations to better describe our model . in the ( ) frame , we have : + * bd candidate hypotheses : * + * ln candidate hypotheses : * + * selected bd / ln hypotheses : * + * observations ( bd , ln , grad ) : * .+  let be the number of video frames .we model the log crf conditional probability as a set of potentials :  the graphical model is shown in fig .[ model ] .let denote , and similarly for , , and , we will give detailed definition and intuition for each term in our model .to better illustrate each term , we decompose the model and show them in fig .[ model_decompose ] .the term seeks to generate multiple candidate border hypotheses based on the observations in current frame and the selected hypotheses in the previous frame .the intuition here is that the first hypothesis candidate is generated by performing unconstrained hough voting with type 1 bd voting points .it is able to discover sudden border changes . the second candidate is also generated by hough voting with type 1 bd voting points , but is additionally constrained ( smoothed ) by the previous frame .the third candidate concerns the constrained hough voting with type 2 voting points ( image gradients ) .it specifically handles the case of very few returned type 1 voting points due to occlusions and faded lane markings .the graphical representation is shown in fig .[ model_decompose ] ( a ) .note that the unit is not a clique potential .however , it is a composition of a set of potential functions : where is the hough voting function defined in eq .( [ weighted_hough ] ) .let and , is the inter - frame pairwise potential defined as a binary loss function : where and are the potential parameters to be learned .they respectively describe the tolerance of the inter - frame offset and angle difference of the hypotheses .similarly , is defined as :    the mode selection potential seeks to select the best candidate bd hypothesis .a decision tree is used to guide the selection .since the voting weights of candidates can indicate the hypotheses confidence , the decision tree takes such input to predict the best candidate .let be denoted as for short , the decision tree diagram for border is shown in fig .[ model_decision_tree ] :  let denote the candidate selected by the decision tree , and the candidates not selected by the decision tree .the mode selection potential is defined as : where is a nonnegative penalty parameter to be learned .it controls how sensitive the model is to the violation of decision tree output .the mode selection potential basically forces the output to be one of the candidate hypotheses , but allows discrepancy with the decision tree prediction with a penalty . the graphical model of the mode selection potentialis shown in fig .[ model_decompose ] ( b ) .the decision tree for lane marking is similarly defined .the condition for the root decision node is chosen as : and the conditions for the two child decision nodes are respectively and .the coupled structure potential further regularizes the results by exploiting the intra - frame structure . with this potential ,border and lane marking are no longer independent but coupled and it can significantly improve the results under certain cases . the graphical representation of the coupled structure potential is illustrated in fig .[ model_decompose ] ( c ) .the potential mainly captures two properties of structural restrictions between border and lane marking : + * parallelism : * the border and lane marking hypotheses are approximately parallel to each other .the closer they are , the stronger such property holds .most important of all , they can not intersect .+ * distance : * a border often keeps certain distance from the lane marking . they can not be too close to each other .let and . the coupled structure potential is defined as :    where and are the potential parameters learned from training data to control the level of parallelism . , and are empirically set to 10 , 17 and 35 respectively . is a piecewise - linear function defined as : where and are parameters that can also be learned through a linear regression from training data .the online updating nature ( real - time requirement ) of this problem limits our scope of observations to the past frames .suppose at time the set of available observations is denoted as .the inference problem is to :   however , conducting the above whole inference each time given a new frame is computationally infeasible .a relaxation is to initialize with the inferred state variable configuration of the previous frames and infer the current state variables , updating in an incremental way . at ,the inference is to optimize the following problem : this is to search the maximum hough voting for border and lane marking based on type 1 voting points , subject to the constraint from the coupled structure potential .  at , the log probability can be represented as : since we reuse the previously inferred results , the inference problem becomes : where .the penalty in the potential functions essentially serve as hard constraints on the search space of hough voting hypotheses . to perform inference one needs to follow these constraints and conduct the following 4-step optimization :   * step-1 * : optimize with and . given from the previous frame , generate the candidate hypothesis using unconstrained hough voting and and using constrained hough voting .similar for lane marking candidate hypotheses .* step-2 * : optimize with . step selects the candidate indicated by the decision tree for both border and lane marking .   * step-3 * : back perturbation with .( optional )  check whether equals to .if it is then one needs to go back adjust such that the three candidates also follow the structure restriction with :   * step-4 * : optimize with .( optional )  given the adjusted border hypotheses , again perform mode selection with the decision tree .much of the potential parameters in our model can be automatically learned from training data .we use gaussian models to fit the differences of and from ground truth hypotheses in consecutive frames .this gives a statistical estimate of how quick the hypotheses can change .thus , , and are learned as twice of the model standard deviation .the estimation of and is conducted similarly . is learned to be larger than the largest vote weight loss caused by back perturbation , such that one would not risk violating the decision tree to generate a candidate that does not follow the coupled structure restriction but with a larger voting weight .we first describe how to obtain the type 1 voting points .we extract the filter bank responses and histogram of oriented gradient ( hog ) to perform scanning window detection .the filter bank we used is the same as in , while the adopted hog descriptor follows the work of .we divide each image patch into upper and lower two cells , and concatenate their mean filter bank responses .in addition , we also divide each image patch into 8 cells for hog , where the normalized gradient histogram of all the cells are concatenated .the final feature for each detector window is the concatenation of the above filter bank responses and hog features .[ fig6 ] illustrates our feature extraction method .it is worth mentioning that the computation of filter bank and hog features for scanning windows can be conducted in an extremely efficient way using integral image .thus the proposed feature extraction method has the potential to work real time .we train two classifiers , one for border detection and the other for lane marker detection . in detail, we perform fisher discriminant analysis on both the border training set and the lane marker training set , where the features of each training set are extracted as described previously . then , we train two radial basis function ( rbf ) kernel svms on the dimensionality reduced training sets .in addition to the basic border and shoulder detection , we include highway entrance detection and lane state tracking which allow us to jointly estimate the position of merging / neighboring lane and tracking the lane state of the vehicle ( e.g. , whether it is the right - most lane ) .figure [ addfeat ] shows some example results returned by the algorithm , where yellow regions in ( a ) and ( b ) indicate non - shoulder merging / neighboring lanes .the true shoulders on the other hand are detected as green regions in ( c ) .we collected 4200 highway road shoulder images . among them , 1592 images are used for training where the images come from the frames of multiple video segments .the remaining 2608 images are used for testing and all the images form a complete video .the dataset contains many challenging and complicated scenarios .example images from the dataset are shown in fig .[ fig2 ] ( a)-(d ) .the number of training images containing concrete barriers , guard rails and soft shoulders are 839 , 300 and 453 , respectively .we use the mit labelme open annotation tool to label borders and lane markings .we label the borders into `` concrete barriers '' , `` guard rails '' and `` soft shoulders '' .a set of well - aligned border image patches can be extracted from each annotated border and lane marker region ( see fig .[ fig2 ] ( e ) ) .these patches form the positive training samples for the scanning window detectors , while negative samples are randomly mined from the background of the training images . the ratio between the number of positive samples and number of negative samplesis set as .[ fig4 ] illustrates some examples of the training patches .  for test sequence ,we label shoulder regions where the upper edges are the ground truth of highway borders . in the experimental section, we will use such ground truth to generate a set of benchmarks for quantitative comparison .we conducted an experiment on the 2608 frames of the test video using structured hough voting .the test sequence contains a variety of challenging situations , including complicated scenarios such as entrances and exits , as well as interfering visual manifestations such as strong shadows , dynamic appearances , drastic illumination change , weak border / lane marking and fake border / lane marking patterns .  to illustrate the performance of the proposed method, we compare our method with 3 baseline methods : 1 .independent hough voting in each frame using the fired detector voting points , 2 .hough voting using the triggered detector voting points constrained by previous frame and 3 .adding gradient tracking to baseline 2 .we also compare to results obtained by the kalman filter which is a standard method widely used in lane marking tracking .we first illustrate examples that show the difference brought by the coupled structure restrictions .one can see that such restrictions have successfully corrected results where the detection of border failed .some typical examples are illustrated in fig .[ fig10 ] .the first row corresponds to the method without coupled structure restriction , while the second row corresponds to the method with such restriction .we conducted a series of evaluations based on the annotated test sequence ground truth and benchmarks . + * ln_pen * : defined similarly to * bd_pen * for lane markings .+ * accept_ratio * : percentage of good frames defined by thresholding both * bd_pen * and * ln_pen*. a frame is `` good '' if both are within the threshold . + * overlap_score * : . ] .the quantitative results of the baselines and the proposed method ( proposed2 denotes with coupled structure restriction , while proposed1 denotes without the restriction . ) are listed in the table in table [ table1 ] .again , one can see the performance of the proposed method is the best one .we also select some challenging frames where the baseline methods usually fail .the results obtained by the baseline methods and the proposed method are shown in fig .the 6 sets of images ( from left to right and top to bottom ) correspond to ground truth , baseline1 , baseline2 , baseline3 , kalman filter and the proposed method .one can see that our model performs more robustly than the baseline methods in normal situations and is more responsive to drastic border changes in case of highway entrance due to the model flexibility achieved by the scheme of generating multiple hypothesis candidates .+  +      +  +         [ cols="^,^,^,^,^,^,^",options="header " , ]   we finally show some failure cases in fig .the failure cases are mostly caused by false positive voting points and there is little a model could do given such input .this shows that the next step to the improve the method is to enhance the quality of voting point input .in this paper , we have proposed a novel model called structured hough voting , and reported its application on vision - based highway border and shoulder detection .experimental results have validated the good performance of the proposed model and its superiority over some popular models such as kalman filter .our proposed method is also computationally efficient .first , the feature extraction unit can be implemented with integral image operations where the extraction of both mean filter bank responses and hog in every scanning window is extremely fast .second , our proposed inference method performs incremental ( online ) update , which also requires very few computation .the algorithm complexity of hough voting is where is the number of possible hypotheses and the number of voters .voting with image gradients takes the most computation among the three candidate hypotheses generation methods .but it is still highly efficient since both hypotheses and voting points are significantly truncated by previous frame . in general , the method is able to run real - time without any gpu acceleration .

Abstract: we propose a vision - based highway border detection algorithm using structured hough voting . our approach takes advantage of the geometric relationship between highway road borders and highway lane markings . it uses a strategy where a number of trained road border and lane marking detectors are triggered , followed by hough voting to generate corresponding detection of the border and lane marking . since the initially triggered detectors usually result in large number of positives , conventional frame - wise hough voting is not able to always generate robust border and lane marking results . therefore , we formulate this problem as a joint detection - and - tracking problem under the structured hough voting model , where tracking refers to exploiting inter - frame structural information to stabilize the detection results . both qualitative and quantitative evaluations show the superiority of the proposed structured hough voting model over a number of baseline methods .