Probabilistic graphical models for feature-based …probabilistic graphical models to find the minimum number of spectrally distinct signal sources (bands) or features that characterise

Visualisationtechnical

14 PositionIT – Jan/Feb 2014

The Kingdom of Swaziland, like many other countries, has been invaded by a variety of invasive

alien plants and in recent time these have caused widespread degradation of rangelands, water resources, and croplands culminating in their declaration as a national disaster. Therefore, it is imperative that alien plant invasions be controlled and that a strategic planning, management and implementation approach is adopted. A key element to this is information about their distribution, size and density. Although alien plant species invasions have been intensively and widely researched, a shortcoming is accurate mapping of the spatial distribution (range and abundance) data [1]. Early detection and a fast response to invasions are needed and remote sensing appears to be a relevant tool in order to develop national management strategies and policies and for the implementation and monitoring of control activities as well as to implement research and policy initiatives over time [2].

Remote sensing is a critical tool for detection, understanding and mapping invasive plant species and vegetation in general. Through the use of remote sensing technologies, it is now possible to undertake detailed species classification and extraction to better understand how individual species or groups of species penetrate indigenous plant populations. However, the typical need to balance spectral resolution, spatial resolution and project scale to determine the most appropriate image source has limited the applicability and effectiveness of most remote sensing platforms for invasive alien plant detection. WorldView-2 is the first very high-resolution multispectral satellite to provide eight spectral sensors in

Probabilistic graphical models for feature-based detection

by Wisdom Dlamini, Swaziland National Trust Commission

This article describes the use of probabilistic graphical models, in particular Bayesian networks (BN), for the detection of four problem invasive alien plants, Chromolaena odorata, Eucalyptus grandis, Lantana camara, and Pinus patula from 8-band WorldView-2 satellite imagery acquired over two characteristically different sites in Swaziland.

the visible to near-infrared range including the yellow and red-edge bands. The sensor’s imagery provides an unprecedented combination of both sub-metre spatial accuracy to assist in mapping the location and boundary of vegetation, coupled with improved spectral discrimination potential to map vegetation structure, composition, condition and rigour. The challenge is then to develop techniques that are able to handle the increasing spatial and spectral resolution whilst increasing the feature discrimination or classification accuracy from such imagery.

Artificial intelligence and machine learning techniques are increasingly being used to classify multispectral and even hyperspectral remotely-sensed data for various practical applications such as vegetation monitoring. Probabilistic graphical models, especially Bayesian networks (BNs), have become very popular as a graphical formalism for handling uncertainty and this is evidenced by the increasing number of practical applications. BNs [3] are based on Bayes’ rule which enables us to go from the more intuitive causal conditional probability to the more practically relevant conditional probability. The BNs are built upon the Bayes’ rule (Eqn. 1), which can be represented as:

(1)

where P(B|A) is the conditional probability of event B occurring given A, P(A|B) is the conditional probability of event A occurring given that event B occurred, and P(B) is the probability of event B occurring. In the invasive alien species classification problem, B in equation (1) corresponds to the

different species that occur in the study area, and A corresponds to the feature vector of an unknown pixel. Since we can easily estimate the quantities P(A|B) and P(B) and P(A) from known data values, we can use this equation to calculate a posterior probability distribution over B for any values of A. BNs are directed acyclic graphical models for reasoning under uncertainty, where the nodes represent random variables (discrete or continuous) and arcs (or links) represent direct causal connections between them [3]. Within BNs, the nodes and arcs provide a relatively intuitive semantics that helps users to understand and interpret the networks. The propagation of information in the form of instantiated variable states forward or backward through nodes allows both deductions and abductions.

Because of the symmetric nature of conditional probability, parameter estimation can be used to perform classification as successfully applied in remotely-sensed image and signal classification (e.g. [4 – 14]. The selected category 1 (most problematic) species were Chromolaena odorata (L.) R. M. King and H. Robinson , Eucalyptus grandis W. Hill ex Maiden, Lantana camara L. and Caesalpinia decapitala (Roth) Alston. The objective of this study was to test the feasibility and applicability of WorldView-2 imagery, to detect these species with the aim of creating distribution maps. The study aims at using a variety of probabilistic graphical models to find the minimum number of spectrally distinct signal sources (bands) or features that characterise the 8-band data from the target invasive alien species detection and classification point of view.

technicalVISUALISATION

PositionIT – Jan/Feb 2014 15

Methods

Study area

The study sites were distributed in different parts of central Swaziland, southern Africa and were characterised by different land uses, and included a nature reserve (Mantenga) and an urban area (Manzini). These areas varied from undulating to complex hilly terrain and were chosen because they have emerging to intense invasive alien plant infestations dominated by different land cover types. This offered an opportunity to test the application and effectiveness of the 8-band imagery to detect subtle and isolated patches of invasive alien plants in different landscapes using different probabilistic graphical models.

Field data collection

Field measurements of the distribution were recorded within the study sites in order to determine both the spatial and spectral variability of the four alien invasive species. The presence of each species was georeferenced using a differential GPS and every effort was also made to co-locate the individual clumps/bushes from the satellite imagery using photographs as a visual reference. As such, we ensured that every point captured in the field corresponded with corresponding pixels on the WorldView-2 images. All the points were mapped with ArcGIS 10 software [15]. The data was also supplemented with data from national survey data wherein at each point the presence of each species was recorded as well as the age class and density [16].

Image acquisition and pre-processing

The spectral information in the data is enhanced if the timing of the data acquisition maximises phenological differences between the invasive plant species and the native species. In this study, cloud-free WorldView-2 images were obtained from DigitalGlobe and the periods of image acquisition corresponded to the period from the early part of the dry season when most of the native vegetation begins to senescence, thus offering an opportunity to detect the four species, two of which (C. odorata and L. camara) are predominantly understorey species in forested or densely vegetated ecosystems. The bundled 8-band imagery, which was also radiometrically corrected and orthorectified, had a 2 m spatial

resolution and also included the 0,5 m panchromatic band. The multispectral bands were pan-sharpened to 0,5 m using the hyperspherical colour space (HCS) pan-sharpening method [17]. The HCS algorithm maintains the best balance between spectral and spatial quality and is currently implemented within the Erdas Imagine 2011 software. This was done to overcome the common difficulty when using spatial image analysis for target detection arising from the fact that the ground sampling distance (GSD) becomes generally larger than the size of targets of interest as may be the case with clumps of alien invasive plants. The 11-bit raw data in each band were converted to reflectance through applying the conversion equations using the calibration factors in the WorldView-2 metadata files. All the eight bands were combined within the geographic information system (GIS) software ArcGIS 10 to create case files, each consisting of eight feature variables and the presence/absence of each of the species. The case files were used for the development and parameterisation of the models at each site.

BN model development and parameterisation

BN modeling generally involves learning both the structure and parameters (probabilities) from data for which a number of algorithms have been developed. The arcs signify direct dependencies between the linked variables, and the strengths of these dependencies are quantified by conditional probabilities as represented in conditional probability tables (CPTs). Those variables that are not linked directly in the graph are conditionally independent of each other. Formally, a Bayesian network consists of two parts B= ⟨G,Θ⟩. The first part G is a directed acyclic graph consisting of nodes and arcs. The nodes are the variables X1,...,Xn in the data set whereas the arcs indicate direct dependencies between the variables. The graph G then encodes the independence relationships in the domain under investigation. The second part of the network, Θ, represents the conditional probability distributions. It contains a parameter

(2)

for each possible value xi of Xi, given each combination of the direct parent

variables of Xi, ∏xi of ∏Xi, where ∏Xi denotes the set of direct parents of Xi in G. The network B then represents the following joint probability distribution:

(3)

The first task when learning a Bayesian network is to find the structure G of the network. Once we know the network structure G, the parameters Θ need to be estimated. In general, these two estimation tasks are performed separately. Thus it was possible to efficiently compute probabilities of the presence of each of the species in the structure given the reflectance values (corresponding to an observed wavelength) from the WorldView-2 bands. Eight different BN structures were developed for each species and the multiple class case using data from the four sites investigated. The BNs were developed using jBNC [18, 19] software implemented within the Waikato Environment for Knowledge Analysis (WEKA), [20]. These algorithms differ in the trade-offs made between computational complexity and structural richness. The algorithms used were the general Bayesian network (GBN) [21], naïve Bayes (NB) [22], tree-augmented naïve Bayes (TAN) [21], selective tree-augmented naïve Bayes (STAN) [18, 19], selective tree augmented naive Bayes with node discarding (STAND), forest augmented naïve Bayes (FAN) [18, 19], the selected forest augmented naïve Bayes (SFAN) [18, 19], and selective forest augmented naive Bayes with node discarding (SFAND) [18, 19].

The selective BNs were created from operators which perform attribute selection and determined, using 10-fold cross-validation, which attributes do not contribute to the classification goal. Detailed description of the implemented classifiers and their benchmark tests can be found in [18] and [19]. In this application all features (class variable and attributes of the problem) are assumed to be discrete, that is, each variable has a finite set of possible values. Discretisation of the features (band reflectance values) was done using split point encoding within the Kononenko method [23] which assumes that the attributes are unconditionally independent of each other. The parameters of all the BN models, but the GBN, were



estimated applying the Heckerman [24] parameter estimation method which assumes that all features have unlimited multinomial distributions with Dirichlet priors and that parameters vector are mutually independent. The GBN was learned using the K2 search procedure [25] in conjunction with the Bayesian BDeu scoring metric [26]. In this study, we aimed at maximising the accuracy of the classifier whilst reducing the number of (irrelevant) bands for particular site and minimising the computational time. Fig. 1 illustrates the characteristic structural differences between all the models used in the study.

Accuracy assessment

The accuracy of each model was then assessed using 10-fold cross-validation, thus ensuring that the final calibration of every model used all of the data available. Testing the classification success rate can provide useful information on scoring success by using not the most likely state as a prediction of each case but rather the actual beliefs of each state. Hence, the logarithmic loss and spherical payoff [27] were calculated to compare the classification abilities of the models. These scores don't just take the most likely state (species presence/absence) as a prediction, but rather considers the actual posterior probabilities of the states in determining how well they agree with the values in the training data [27]. In general, these scoring

rules provide an evaluation of the predicted probabilities of states over a set of variables [28]. These results are calculated in the standard way for scoring rules and their respective equations are:

(3)

(4)

where M is the mean probability value of a given state averaged over all cases, Pc is the probability predicted for the correct state or class, Pj is the probability predicted for class j, n is the number of states for which the training data provides a value for the classification variable (or node). These measures are well explained in [27] and [3], and are suitable for the assessment of "soft" classifiers for which the traditional error matrix approach may not be appropriate [29]. The logarithmic loss (Eqn. 3), which has scores between 0 and 1, is a cross-entropy estimate which measures the additional penalty for using an approximation instead of the true model. According to Colwell [28], the logarithmic loss is the only scoring rule whose value is determined solely by the probability of the outcome that actually occurs. Therefore values closer to 0 indicate a lower penalty. The spherical payoff (Eqn. 4) is a very useful index which varies in the interval [0,1], with 1 representing best classifier performance. In addition to the above accuracy measures, we assessed the frequency with which

(b) (c) (d)

(e) (f) (g) (h)

a specific band was selected and included in the models, in order to ascertain their usefulness in species discrimination.

Results

The results of our first experiment in Fig. 2 show the Kappa values of the BN classifiers on the four sites for all species and their average logarithmic and spherical payoff values. We find a significant difference in average classification accuracy between the GBN, NB and each of the augmented classifiers, but insignificant differences between selective augmented classifiers. The results of our set of experiments show the robustness of the different classifiers to irrelevant features or bands. NB, TAN, and FAN all have significant accuracy degradations as the amount of irrelevant features increases, while the STAND and SFAND models effectively ignore the irrelevant features.

Despite the limited training data, all the models produced very high overall accuracies spherical payoff values of 0,95 and above (see Table 1). Figs. 4 and 5 show sample site results of the BN classifications of all the species. The comparison shows only slight differences between all the probabilistic graphical models. All of the models were computed relatively fast characterised low computation times with higher advantages of the STAND and SFAND models. In all the runs, the STAND and SFAND algorithms achieved very low logarithmic loss values sometimes

Fig. 1: Illustrations of the Bayesian networks used in this study. The node C represents the classification node and the other nodes are representative of the different bands of WorldView-2. (a) General Bayesian network (GBN), (b) Naïve Bayes (NB), (c) tree-augmented NB (TAN), (d) forest-augmented NB (FAN), (e) selective tree-augmented NB (STAN), (f) selective forest augmented NB (SFAN), (g) selective tree-augmented NB with node discarding (STAND), (h) selective forest-augmented NB with node discarding (SFAND).

a)



how 8-band WorldView-2 information affects spectral target detection, using four invasive alien plants as the targets. Several instances of the target species were hidden amidst other vegetation and land cover types in different scenes. The SFAND and STAND structures were found to have the edge over other BN structures with the same computational complexity and robustness. The main advantage of the selective augmented classifiers with node discarding was in cases where some bands and/or dependencies are irrelevant for predicting the occurrence of the species concerned. In such domains in addition to providing good predictive accuracy, their flexibility provides us with important feature dependencies/independencies.

What is also apparent is that different landscapes result in different accuracies and optimum band selections, although the newer red-edge and near infrared bands were automatically selected in almost all the resultant selective augmented models. It is evident that for topographically simpler (flat) landscapes and those areas with low flora species richness, the addition of extra attributes or bands and their reflectance values that are not related to any species does not improve classification results and may increase classification error. This is due to the fact that an increase in the number of parameters in a model, the variance in parameter estimation increases and each of the parameters is estimated with lower accuracy resulting in lower classification accuracy. It is clear from the results that a minimum of four bands or attributes gave optimum results for all species. This also implies that the addition of extra bands that are not directly related to the feature (species) being detected does not

Fig. 2: Average classification accuracy (spherical payoff) values of the BN classifiers for the four species in both sites.

Species Bayesian network Logarithmic loss Spherical payoff

C. decapetala

FAN 0,161 0,829GBN 0,161 0,829NB 0,166 0,824SFAN 0,161 0,829SFAND 0,131 0,859STAN 0,141 0,850STAND 0,131 0,859TAN 0,146 0,844

C.odorata


E. grandis


P. patula


Table 1: Average accuracy assessment results for the models.

nearing zero. Similarly, the spherical payoff values were both very high (>0,95) for the SFAND and STAND models indicating a very high degree of classification accuracy.

The results in Table 1 show the robustness of the different classifiers to irrelevant features or bands. NB, TAN, and FAN all have significant accuracy improvements as the amount of irrelevant features increases, while the STAND and SFAND models effectively ignore the irrelevant features or bands.

Fig. 3 shows the part of the image data as being identified as C. odorata by the most accurate BN.

Discussion

Despite the existence of several different spectral target detection algorithms [30], efforts to model optical and infrared imaging systems in simple target detection often limit the ability to separate the target from the background in a particular scene. This study was designed to assess

Band Frequency of selection

Red edge 16

NIR 2 13

Yellow 12

Red 11

Blue 8

Coastal 8

Green 5

NIR 1 4

Table 2: Frequency of selection of each band by all the selective BN models (out of a possible 16 selections).



Fig. 3: Result of the SFAND inference for the label (C. odorata) node of the graphical model on (a) Mantenga nature reserve and (b) Manzini urban area image data. Black indicates the algorithm gives a probability of 100% for the classification, and white 0%.

in the classification node’s Markov blanket.

Dimension reduction is often used in clustering, classification, and many other machine learning and data mining applications to retain the most important dimensions (attributes) and to remove the noisy dimensions (irrelevant attributes) and, hence, reduce computational cost. We have shown that the built-in feature selection of the selective augmented probabilistic graphical classifiers provide far greater robustness to noisy, irrelevant features. Another interesting characteristic of these classifiers is that, when computational time is a critical factor, the selective augmented classifiers were quickly learned from the training and calibration data by means of the original inductors. We believe this evidence and the similar run-time and implementation complexities suggest selective augmented probabilistic graphical classifiers are preferable for high spectral resolution satellite image classification.

The importance of the red-edge in the detection of all the species affirms the observed importance for this band for vegetative analysis, directly related to plant health revealed through chlorophyll production. The NIR-2 band, although overlapping with the NIR-1, is less affected by atmospheric influence and was observed to be very useful for C. odorata discrimination. The high sensitivity of the L. camara to the yellow band is largely due to the fact that the L. camara plants in the study area are mainly short which leads to an increase in reflectance within the yellow portion of the electromagnetic spectrum. This is also due to the fact that when the leaf begins to change, due either to dehydration or senescence resulting from the dry season, chlorophyll production slows in L. camara, and reflection in the blue and red bands is increased. When considering the logarithmic loss and Brier score results, the L. camara model slightly outperformed the C. odorata model. This implies that without taking into account the predicted plant cover, the actual parameters (posterior probabilities) of the plant cover of the L. camara model agreed slightly better with the values in the training data than those of the C. odorata and the multiple-class models. The reason for the differences in the

necessarily improve the classification results but may increase classification error particularly for sites with complex vegetation or land cover composition and topography. This is due to the fact that the larger the number of bands, the larger the number of parameters needed to describe a classifier. The models in the land cover feature rich urban area of Manzini, for instance,

resulted in relatively lower accuracies. From the findings it is also evident that a combination of a minimum of four bands seems to give the most optimal results. We believe the WorldView-2 imagery used in this study provide the discriminative benefit of including more potentially relevant bands and is balanced against the detrimental effect of including too many irrelevant bands

a)

b)



sensitivities is that the two species have different leaf pigmentations. The slight differences were also expected because the C. odorata has varied spectral signature due to the lower contrast with nearby vegetation and other objects thus reducing the spectral separation.

This is in line with the premise that subtle vegetation changes and characteristic variations are prominent in these portions of the electromagnetic spectrum. Hence, both species' attributes can be probabilistically determined in terms of various combinations of the red, red-edge and near infrared band reflectance. The near-infra red bands coupled with the red edge and yellow bands, therefore, contribute to vegetation mapping and offer broader discrimination than previously seen with other sensors. The incorporation of the red edge also offers more sensitivity to some of the exposed land patches, including those adjacent to the river channel, potentially reflecting differences in edaphic conditions. The results point to the efficacy and usefulness of the new bands in the detection of the selected invasive alien plants.

The low accuracies obtained from using the conventional bands demonstrate their limited spectral sensitivity for discriminating invasive alien species from native vegetation. The substantial increase in the Kappa values when incorporating the newer bands is only very slightly reduced when using the BN model-selected combinations of both the conventional and newer bands.

This demonstrates that BNs can achieve very good prediction accuracies even with a rather small sample training sizes. Since the logarithmic loss and Brier scores take into account the posterior probabilities, they can be regarded as very good measures for evaluating and comparing probabilistic or "soft" classifiers. The posterior probabilities from the BN models are also an indicator of the uncertainty in making a particular hard class allocation but provide a relative measure of class membership and can be used as an indicator of sub-pixel proportions [31]. Although there is not a direct link between the proportional coverage of a class and its posterior probability, in practice useful sub-pixel thematic information may be derived by this approach.

From the BN models, we can see that despite the similarities between the spectra of some of the vegetation, and most importantly, the appearance of the individual pixels for various class objects, the BN accurately separated most of the individual plant species. The success of the BN approach used in detecting all the species is due to the fact that they capitalised on probabilistically identifying unique phenological or reflectance properties that can be measured by the WorldView-2 imagery based on their spectral characteristics or their spatial patterns. The 11-bit radiometric resolution of WorldView-2 also enhanced the spectral separation of the species from the background information. The added advantage of the feature selective BN classification approach, therefore, was that the number of parameters to learn from the data is low, improving in this way the accuracy of the estimations. The BNs also have an important advantage in that they can also show which variables contribute most to classification accuracy. Compared with the field data, the probability maps reveal more details at the spatial level and are indicative of the level of uncertainties and confidence regarding each species’ presence.

In addition to providing insights into the spatial distribution of invasive alien plants, the WorldView-2 imagery was also able to provide the segmentation necessary to evaluate small scale details, like the identification of individual clumps within the studied landscape. Although the incorporating of other ancillary information such as texture and vegetation indices might also improve the classification accuracy, the additional bands from WorldView-2 were adequate.

The success achieved with the WorldView-2 multispectral data suggest that applying probabilistic graphic models with the very high spectral resolution of WorldView-2 may increase target recognition performance for broader remote sensing applications. The BN models can also be converted to dynamic BNs to possibly model and monitor the spatio-temporal dynamics of alien plant invasion. In future studies we plan to improve the accuracy rates through, for instance, the use of models such as mixtures of truncated exponentials [32] which avoid the discretisation of the continuous features

when learning BNs and testing other BN structures and ensembles.

Conclusion

In this study we showed empirically that the selective augmented BN classifiers work better than non-selective models on "noisy" and multi-dimensional/multispectral data. We believe that this feature selective robustness, along with the comparable run-time costs, and implementation complexity, make selective augmented BN classifiers preferable classifiers. The selective BN classifiers were found useful and more accurate because they reveal the probabilistic relationships among variables, whilst reducing the number of input variables required for classification. Furthermore, the study has demonstrated that the additional spectral information, coupled with the improved radiometric resolution, provided by the WorldView-2 data makes it possible to develop feature detection approaches that are based only on spectral information. The usefulness of the innovative partitioning of the electromagnetic spectrum through the addition of newer wavelengths bands such as the red edge, near-infrared 2, and yellow bands was found particularly effective for discriminating between invasive alien plant species. The findings are useful in broader applications such as automatic feature or band selection for most applications in remote sensing. This could include extending the general idea presented here into testing other parameter and structural learning approaches, thereby providing very useful and novel solutions for image classification and target detection tasks.

Acknowledgement

The author is grateful to DigitalGlobe for the complementary WorldView-2 imagery which was provided under the DigitalGlobe 8-Band Challenge Contest.

This paper was presented at GISSA Ukubuzana 2012 and is republished here with permission.

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Contact Wisdom Dlamini, Swaziland National Trust Commission, [email protected]

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Probabilistic graphical models for feature-based …probabilistic graphical models to find the minimum number of spectrally distinct signal sources (bands) or features that characterise