Multitemporal Crop Type Classification Using Conditional Random Fields .
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXVIII-4/W19, 2011ISPRS Hannover 2011 Workshop, 14-17 June 2011, Hannover, GermanyMULTITEMPORAL CROP TYPE CLASSIFICATION USING CONDITIONAL RANDOMFIELDS AND RAPIDEYE DATAT. Hoberg*, S. MüllerIPI - Institute of Photogrammetry and GeoInformation, Leibniz Universität Hannover, Germany(hoberg, mueller)@ipi.uni-hannover.deKEY WORDS: Crop, Agriculture, Classification, Multitemporal, SatelliteABSTRACT:The task of crop type classification with multitemporal imagery is nowadays often done applying classifiers that are originallydeveloped for single images like support vector machines (SVM). These approaches do not model temporal dependencies in anexplicit way. Existing approaches that make use of temporal dependencies are in most cases quite simple and based on rules.Approaches that integrate temporal dependencies to statistical models are very rare and at an early stage of development. Here ourapproach CRFmulti, based on conditional random fields (CRF), should make a contribution. Conditional random fields considercontext knowledge among neighboring primitives in the same way as Markov random fields (MRF) do. Furthermore conditionalrandom fields handle the feature vectors of the neighboring primitives and not only the class labels. Additional to taking spatialcontext into account, we present an approach for multitemporal data processing where a temporal association potential has beenintegrated to the common CRF approach to model temporal dependencies. The classification works on pixel‐level using spectralimage features, whereas all available single images are taken separately. For our experiments a high resolution RapidEye satellitedata set of 2010 consisting of 4 images made during the whole vegetation period from April to October is taken. Six crop typecategories are distinguished, namely grassland, corn, winter crop, rapeseed, root crops and other crops. To evaluate the potential ofthe new conditional random field approach the classification result is compared to a manual reference on pixel‐ and on object‐level.Additional a SVM approach is applied under the same conditions and should serve as a benchmark.of an existing GIS to evaluate the geometric quality. Theapproaches are demonstrated for a set of four multispectralRapidEye-images. Additionally a SVM-classification thatserves as a benchmark is performed.1. INTRODUCTIONIn 2008 the German RapidEye system in its constellation of fivesatellites launched. Each satellite has five spectral bands (blue,green, red, red edge and near infrared) with a GSD of 6.5 m.This system and many other recently launched high resolutionoptical remote sensing satellites allow a higher availability ofmultitemporal image data. These data can be used for enhancingthe classification accuracy and for analyzing land coverchanges. While in the latter case, one has to deal with potentialclass transitions, in the first case the class remains unchanged.Nevertheless the appearance of the individual classes at severalepochs might change and that can be used to achieve higherclassification accuracy.In chapter 2 an overview on related work on multitemporal croptype classification and on CRF is given. Next the data andextracted features for our tests are described. Chapter 4 dealswith the principle of CRF and our implementation. A briefoverview on the applied SVM can be found in chapter 5.Finally chapter 6 shows the results of our experiments.2. RELATED WORKIn this work we present two CRF-based approaches formultitemporal crop type classification of high resolution opticalremote sensing data. The first one, called CRFall, is a commonCRF approach with a 2D-grid graph structure. For thisapproach, all extracted features of all images are concatenatedin one feature vector per pixel. The second approach, CRFmulti,is based on an extension of the CRF concept by an additionaltemporal interaction potential. Here each pixel of each image isrepresented as one node in a 3D-grid. The decision for a pixelbelonging to one class is based on the extracted features at pixelsite and on spatial and temporal context. Although thisapproach was originally developed for change detection, in thiswork we investigate its potential for multitemporal crop typeanalysis where no class transitions occur during one vegetationperiod.For both approaches no existing land cover map is required.Nevertheless, finally the results are overlaid to cropland objects2.1 Multitemporal crop type classificationIn the field of multitemporal crop type classification three maindirections of approaches can be observed:In the first category powerful classifiers or combinations ofseveral classifiers that are developed originally for single imageclassification are used. The temporal dependencies are notmodeled in any way and are only implicit contained. To use atime series of images simultaneously, the multitemporal imagesare simply stacked to one image. The contributions of Bruzzoneet al. (2004), Gislason et al. (2006) and Waske andBraun (2009) as well as our approach CRFall belong to thiscategory. Bruzzone et al. (2004) propose a multi classifiersystem and apply three classifiers in parallel, one of themconsidering the k nearest neighbors of each pixel. Decisiontree-ensembles (Random-Forest) (Gislason et al., 2006) (Waskeand Braun, 2009) that are based on several parallel decision* Corresponding author.115
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXVIII-4/W19, 2011ISPRS Hannover 2011 Workshop, 14-17 June 2011, Hannover, ure 1. RapidEye images 2010 ( 2010 RapidEye AG, Germany. All rights reserved.)trees of weak classifiers are also discussed for some time in thefield of crop classification and show good results.2009). Roscher et al. (2010) classified crop types amongst otherland cover classes in monotemporal Landsat data and achievedan accuracy of approx. 70% for the crop type classes. Hoberg etal. (2010) applied CRF on multitemporal high resolution data inorder to enhance classification accuracy in no change areas aswell as to detect changes. In most approaches using CRF onimagery the graph is constructed as a regular grid with nodesrepresenting pixels or square patches. In contrast, Wegner et al.(2011) use an irregular graph derived from a mean-shiftsegmentation for their CRF-based approach for buildingdetection based on features generated from aerial images andairborne InSAR data.The second category of approaches model temporaldependencies by rules or comparison strategies to typicalphonological behavior. These models are explicit but in mostcases quite simple to stay handable. To this category belong thecontributions of Müller et al. (2010), Simonneaux et al. (2008),Lucas et al. (2007) and De Wit and Clevers (2004). Müller et al.(2010) use a classification based on weighting functions.Thereby feature vectors of different time are compared totypical phenological behavior that is learned from a learningsample. Similar Simonneaux et al. (2008) calculates NDVIprofiles that are evaluated using combinations of differentthresholds. Lucas et al. (2007) proposes a rule basedclassification applying the software eCognition. The approachleads to a quite complex rule basis that is difficult to handle. DeWit and Clevers (2004) apply a pixel-wise MaximumLikelihood classification and combine the result with anevaluation of the NDVI profiles concerning the phonologicalbehavior.3. DATA DESCRIPTION3.1 RapidEye dataRapidEye consists of a constellation of five satellites launchedin 2008. Each satellite has five spectral bands (blue, green, red,red edge and near infrared) with a GSD of 6.5 m and a dynamicrange of 12 bit. Parts of the used time series are depicted inFigure 1. For the experiments RapidEye orthophotosautomatically preprocessed are taken. The preprocessingincludes orthorectification, resampling to a pixel size of 5 mand applying an automatic atmospheric correction. The imagesare taken from April to October 2010.The third category of approaches integrates temporaldependencies to statistical models. This approach should becontinued in our work using conditional random fields with theapproach CRFmulti. To compare the results of the developedstatistical methodology a SVM-classifier as state of the art ischosen. Examples for the third category are Feitosa et al. (2009)and Melgani and Serpico (2004). Feitosa et al. (2009) modeltemporal dependencies by Markov chains for detecting landcover transitions in Landsat images, but spatial context is nottaken into account. In Melgani and Serpico (2004) the MarkovRandom Field (MRF) framework is extended by a temporalenergy term based on a transition probability matrix in order toimprove the classification results for two consecutive images.3.2 FeaturesThe spectral bands green, red, red edge and near infrared arecrucial during classification of vegetation classes. Only thesebands are taken as input for feature extraction. Inside a filterradius of 5 pixels resulting in a filter window of 11*11 pixelsthe mean value is calculated during feature extraction. Fouravailable images of 2010 lead to a total of 16 features. For bothapproaches (CRF and SVM) the same features are taken asinput to receive a direct comparison of both approaches.Because the focus of this work is not on feature selection andtests with gradient-based features did not improve our results,we decided to choose only these simple features.2.2 Conditional random fieldsThe interaction between neighboring image sites (pixels orsegments) in MRF is restricted to the class labels, whereas thefeatures extracted from different sites are assumed to beconditionally independent. This restriction is overcome byConditional Random Fields (CRF) that were introduced byLafferty et al. (2001) for classifying one-dimensional data. CRFprovide a discriminative framework that can also modeldependencies between the features from different image sitesand interactions between the labels and the features. They werefirst applied on image data by Kumar and Hebert (2003) for thedetection of man-made objects in terrestrial images.4. CONDITIONAL RANDOM FIELDS4.1 PrincipleIn many classification algorithms the decision for a class at acertain image site is just based on information derived at theregarded site, where a site might be a pixel, a square block ofpixels in a regular grid or a segment of arbitrary shape. In fact,the class labels and also the data of spatially and temporallyneighboring sites are often similar or show characteristicpatterns, which can be modeled using CRF. In monotemporalIn remote sensing CRF have been used for the classification ofsettlement areas in high-resolution optical satellite images(Zhong and Wang, 2007) (Hoberg and Rottensteiner, 2010) andfor generating a digital terrain model from LiDAR (Lu et al.,116
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXVIII-4/W19, 2011ISPRS Hannover 2011 Workshop, 14-17 June 2011, Hannover, Germanyis the temporal neighborhood of image site i at epoch t, thus k isthe time index of an epoch that is a “temporal neighbor” of t.The temporal interaction potential models the dependency ofclass labels at consecutive epochs and the observed data. In ourcase the image sites are chosen to be pixels and thus are orderedin a regular grid (Figure 2). We model the CRF to be isotropicand homogeneous, hence the functions used for Ait, ISijt and ITitkare independent of the location of image site i.classification, we want to determine the vector of class labels xwhose components xi correspond to the classes of image sitei S from the given image data y by maximizing the posteriorprobability P(x y) (Kumar and Hebert, 2006):P xy exp Z 1 Ai ( x i , y ) i S i S j NI ij x i , x j , y (1) i4.2 ImplementationThe image data are represented by a site-wise feature vectorfit(yt) that may depend on the whole image at epoch t, e.g. byusing features at different scales in scale space (Kumar andHebert, 2006).In Equation 1, Ni is the spatial neighborhood of image site i(thus, j is a spatial neighbor to i), and Z is a normalizationconstant, called the partition function. The association potentialAi links the class label xi of image site i to the data y, whereasthe term Iij, called interaction potential, models thedependencies between the labels xi and xj of neighboring sites iand j and the data y. The model is very general in terms of thedefinition of the functional model for both Ai and Iij; refer to(Kumar and Hebert, 2006) for details.For our task of mutlitemporal crop type classification we applytwo CRF-based approaches:CRFmulti: Implementation of the approach as described inEquation 2 and Figure 1. Each image site i at eachtime t is represented as one node in the graph with itsfeature vector fit. In general this approach allows classtransitions between epochs, in this work we have toavoid this by appropriate definition of the temporalinteraction potential.Figure 2. CRFmulti graph structure.Red node: processed primitive; orange nodes: spatial neighbors;green nodes: temporal neighborsThe association potential Ait(xit, yt) is related to the probabilityof label xit given the image yt at epoch t byAit(xit, yt) log{P[xit fit(yt)]}. We use a simple Gaussian modelfor P[xit fit(yt)] (Bishop, 2006):In the multitemporal case, we have M co-registered images. Thecomponents of the image data vector y are site-wise data vectorsyi consisting of M components yit, where yit is the vector of theobserved pixel values at image site i at epoch t T andT {1, M}. The components of x are vectorsxi [xi1, xiM]T, where xit describes the class of image site i atepoch t T. For each image site we want to determine its classxit for each time t from a set of C pre-defined classes. In order tomodel the mutual dependency of the class labels at an imagesite at different epochs, the model for P(x y) in Equation 1 hasto be expanded:P xy exp Z i S 1 tAi(txi,yt ) t T i S t T k KITiii S t T j Ntk x tikt, xi ,y ,yk IStij txitj, x ,ytThe extracted features fit of all images at each site areconcatenated in one feature vector fiall. So allinformation of one site is merged and no temporalstructure (e.g. order of images) is existent any more.This allows the use of standard classificationtechniques, here the application of a common CRFapproach with a 2D-grid structure as described inEquation 1. It should be noted that it would not bepossible to detect class changes between epochs withthis approach. Of course this is not wanted in thiscase.CRFall:Ai x1t,yi f t i2 t nlo g y Et 2 212tfc T Σt 1fc lo g d e t Σ t fi y Ettfctfc (3) In Equation 3, Etfc and tfc is the mean and co-variance matrixof the features of class c, respectively. For CRFmulti they aredetermined from the features fit(yt) in training sites individuallyfor each epoch t and each class c. With t 1 Equation 3 is alsoapplied for CRFall but using the concatenated feature vector fiall.The spatial interaction potential ISijt is a measure for theinfluence of the data yt and the neighboring labels xjt on theclass xit of site i at epoch t. For both approaches CRFall (witht 1) and CRFmulti we applied the identical implementation andparameters to ensure comparability of the results. The data arerepresented by site-wise vectors of interaction features ijt(yt)(Kumar and Hebert, 2006). We use the component-wisedifferences of the feature vectors fit respectively fiall, i.e. ijt(yt) [µij1t, µijRt]T, where R is the dimension of the vectors i(2) In Equation 2, yt and yk are the images observed at epochs t andk, respectively. The association potential Ait is identical to Ai forepoch t in Equation 1. The second term in the exponent, ISijt, isidentical to Iij for epoch t in Equation 1, but it is called spatialinteraction potential in order to distinguish it from the thirdterm in the exponent, the temporal interaction potential ITitk. Ki117
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXVIII-4/W19, 2011ISPRS Hannover 2011 Workshop, 14-17 June 2011, Hannover, Germanyfit / fiall, µijkt fikt(yt) – fjkt(yt) , and fikt(yt) is the kth component offit(yt). Introducing as a sensitiveness factor for the effect ofneighboring data being different, ISijt is modeled as:IStij txitjt,x ,y tt e x p µ ij y tt1 e x p µ ij y 2 2 tifxi xExact inference is computationally intractable for CRF (Kumarand Hebert, 2006). In (Vishwanathan et al., 2006), severalmethods for parameter learning and inference are compared. Inthis paper we use Loopy-Belief-Propagation (LBP) (Nocedaland Wright, 2006), which is a standard technique forperforming probability propagation in graphs with cycles.tj(4) tif xix5. SVMtjAs support vector machines (SVM) are successfully applied innumerous remote sensing applications (Mountrakis et al., 2011)a SVM-classifier should serve as a reference classificationoperator.In Equation 4, µijt(yt) is the Euclidean norm of µijt(yt). This isa very simple model that penalizes local changes of the classlabels if the data are similar. The only model parameter is . Itcould be determined from training data if fully labeled trainingimages were available, but currently it is defined by the user.The neighborhood Ni of image site i over which ISijt has to besummed in Equation 2 consists of the four neighboring imagesites in a regular grid (Figure 1).5.1 PrincipleIn principle, the SVM is a binary classifier. Therefore, samplesof two classes are used to train a model that separates theseclasses in feature space. Being a maximum margin classifier, theSVM maximizes the space between cluster borders. Based onthis, separating hyperplanes are defined by support vectorswhich are a subset of the training vectors. In order to allowseparation of non-linearly separable data, a common approachin machine learning is applied: The feature space is mapped to ahigher dimensional space, where classes become linearlyseparable. This is done by applying kernel methods (Hofmannet al., 2008).In our case, more than two classes have to be discerned. Thereare several strategies to transfer two-class problems to multiclass problems (Vapnik, 1998, Schölkopf and Smola, 2002).The most common are one vs. one and one vs. rest. The first oneuses a voting scheme that accumulates the number of wins in apairwise classification of each two classes. The second classifieseach class against all others. The highest output determines thewinning class. Here, the approach of (Chang and Lin, 2001) isapplied with the one vs. one strategy using the concatenatedfeature vector fiall. It performs similar to one vs. rest strategy forclassification, but is faster in the training process.The output of the classification process is a pixel-wiseclassification result. For more detail, in (Burges, 1998) acomprehensive tutorial about SVM is given.The temporal interaction potential ITitk that we use for CRFmultimodels the dependencies between the data y and the labels xitand xik of site i at epochs t and k. We apply a bidirectionaltransfer of temporal information, so the temporal neighborhoodKi of xit is chosen to contain the two elements xit-1 and xit 1. Dueto seasonal effects on the vegetation and due to differentatmospheric and lighting conditions it would not be sufficient toderive ITitk just from the difference of features vectors as forISijt. Instead this difference ditk(yt, yk) is set in relation to thedifferences Dfctk of the mean of the features of each class c(Equations 5-7). ytkdiDνtkfctkict,y E yt fi y fi y kttfc,yk E tkk(5)kfc(6)tkfcD dtki yt,yk (7)Using the difference measure νictk(yt, yk ) it is possible to supportthe decision for a site i to belong to a class c, if the features atthat site show a typical development for that class betweenepochs t and k. This is realized in Equation 8 when computingITictk.tkI T ic xtikt,x i ,y , yk 1 0 .0 1 0 c tktkifxi xiifxi xiiftxiand c 0 .9 9and c 0 .9 9 6. RESULTSBoth CRF-based approaches as well as the SVM-classifier areapplied to the data described in chapter 3.1.6.1 Description of classeskxiThe choice of crop type classes is based on expert knowledgeabout the most important categories of agricultural crops. Theclasses of interest are grassland, corn, winter crop, rapeseed, root crops and other crops.(8)withtk ( c ) ν ic yt,yk / (9)The temporal interaction potential ITitk is set to zero if theclasses assigned to xit and xik differ (Equation 8), so classtransitions can be avoided.The only parameter of our temporal model is ε (Equation 9).Using ε the effect for one site having a different developmentthan the average class development of any class can be adjusted.It could be estimated from training data, but currently it is set bythe user.Whereas the class winter crop consists in detail of the classesbarley, oat, rye, wheat and triticale. Other crops include in ourcase the classes asparagus and strawberries.118
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXVIII-4/W19, 2011ISPRS Hannover 2011 Workshop, 14-17 June 2011, Hannover, GermanyReferenceSVM-classificationLegend: grassland corn winter cropCRFall-classificationrapeseed root cropsCRFmulti-classificationotherFigure 3. Reference data and classification results in comparison6.2 Description of manual referenceA manual reference is used that was made in the same year 2010like the satellite images. It consists of 121 separate fields of anarea of about 322ha and has been acquired by field walking.The portion of the individual crop types of the whole area is12% grassland, 21% corn, 28% winter crop, 11% rapeseed,11% root crops and 17% other crops. In the process an existingGIS was used to define the borders of single fields. The manualreference builds the training and evaluation sample for the testclassifications.For our tests we applied the cross-validation method byseparation the learning sample into two equal parts. Tables 1-4show the results for the two CRF-approaches and the SVMclassification. Overall 129001 pixels were classified.Both of the CRF-based approaches slightly outperform theSVM classification with CRFall being best. For all approachesthe overall accuracy is far over 80%, only the class grassland isclassified with lower accuracy in each case. The classificationresults for a section of 21 fields are displayed in Figure .583.48.92.40.66.30.55.384.9Table 3. Confusion matrix for SVM-classification(Cla classification, Ref Reference, Gra Grassland, Cor Corn,Win winter crop, Rap rapeseed, Roo root crops, Oth othercrops.)In general there are two main reasons for misclassifications: Atfirst some fields show an “untypical” appearance for their class,e.g. most of the fields of one class are already harvested at onetime of image acquisition but on some fields the crop is stillpresent. Second some fields are very slender. So by using ourfeature extraction in an 11*11 window, their characteristicsbecome blurred.CorCorOthIn a next step, the majority of pixels belonging to a class in eachreference fields was determined. This gives an idea of how goodthis approach is suited for classifying complete fields, ignoringclassification errors at their borders. Applying CRFall 108 of the121 reference fields were classified correctly (89.3%), withCRFmulti 102 fields were correct (84,3%).GraGra1.57.43.40.37.180.4OthTable 2. Confusion matrix for CRFmulti-classification6.3 CRF vs. SVMClaRefGraClaRefGraoverall 9SVMTable 4. Overview on overall accuracy and kappa coefficient6.4 Comparison to GIS dataTo evaluate the results concerning geometric accuracy wesuperimposed them with a national GIS dataset artographic Information System (ATKIS). Among othersources ATKIS data are collected using aerial photography witha resolution of 20cm or 40cm supported by ground truth data,and set to be used in scale between 1:10.000 and 1:25.000.Objects of interest are point, line and area based objects listed at(AdV, 1997) with a minimum mapping unit of 0.1 ha to 1 ha.The geometric accuracy is 3m. Figure 4 illustrates that the classborders of the CRF-based approaches fit to boundaries of theGIS-dataset quite well.2.76.84.00.49.476.7OthTable 1. Confusion matrix for CRFall-classification119
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXVIII-4/W19, 2011ISPRS Hannover 2011 Workshop, 14-17 June 2011, Hannover, GermanyBy use of the temporal interaction potential (Equations 5-9)these results are set in temporal context and the overall accuracyis increased to 84.2%. Results of the CRFmulti-classification andthe corresponding reference can be seen in Figure 5 e) and f).7. CONCLUSIONgrassland corn winter cropIn this work we presented two CRF-based approaches formultitemporal crop type analysis and tested them on RapidEyedata of 4 epochs. Even with using just very few simple features,we achieved a classification accuracy of far over 80% for sixcrop type classes (grassland, corn, winter crop, rapeseed, rootcrops and other crops) with both approaches. Both of themperformed better than a SVM-classification that served as abenchmark with the “classic approach” CRFall being slightlybetter than CRFmulti. Nevertheless the CRFmulti approachgenerally has a higher potential for any kind of multitemporalanalysis. Because of its flexibility in the definition of thetemporal interaction potential, it is also applicable for tasks ofchange detection or multi-scale analysis.rapeseed root crops otherFigure 4. CRFmulti-classification superimposed by GIS croplandobject borders (black borders)ACKNOWLEDGEMENT6.5 Detailed results of CRFmultiThe implementation of the CRF-classification is based on“UGM: A Matlab toolbox for probabilistic undirected graphicalmodels” by Mark Schmidt, http://people.cs.ubc.ca/ schmidtm/Software/UGM.html.The association potential in CRFmulti is the context-free result ofa separate Maximum-Likelihood-classification for each epoch(Equation 3). A section of the ML-classification result for thefour individual epochs is displayed in Figure 5 a)-d). For mostof the pixels the classification results for the epochs differ,sometimes three or even four different classes are assigned.Moreover the classification result within many fields isinhomogeneous. Overall the classification accuracy for thesingle epochs is 59.6%.a)The research is funded by the Federal Ministry of Economicsand Technology (BMWi) via the German Aerospace Center(DLR e.V.) under the funding number 50EE0914 and by theGerman Science Foundation (Deutsche Forschungsgemeinschaft) under grant HE 1822/22-1.b)REFERENCESAdV, Arbeitsgemeindschaft der Vermessungsverwaltungen derLänder der Bundesrepublik Deutschland, 1997. ATKIS –Amtlich Topographisch-Kartographisches Informationssystem,Germany. http://www.atkis.de (accessed 2011-04-01).c)Bishop, C. M., 2006. Pattern recognition and machinelearning. 1st edition, Springer New York.d)Burges, C. J. C., 1998. A Tutorial on Support Vector Machinesfor Pattern Recognition. Data Mining and KnowledgeDiscovery, 2, pp. 121–167.Bruzzone, L., Cossu, R., Vernazza, G., 2004. Detection of landcover transitions by combining multidate classifiers. PatternRecognition Letters, 25(13), pp. 1491-1500.e)f)Chang, C.C. and Lin, C.J., 2001 LIBSVM: a library for supportvector machines. http://www.csie.ntu.edu.tw/ cjlin/libsvm/,accessed: 2011-04-01.De Wit, A. J. W. and Clevers, J. G. P. W., 2004. Efficiency andaccuracy of per-field classification for operational cropmapping. International Journal of Remote Sensing, 25(20), pp.4091–4112.grassland corn winter crop rapeseed root crops otherFeitosa, R. Q., Costa, G. A. O. P., Mota, G. L. A., Pakzad, K.,Costa, M. C. O., 2009. Cascade multitemporal classificationFigure 5 a)-d) Results of ML-classification for t 1.4;e) Result of CRFmulti-classification; f) Reference120
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXVIII-4/W19, 2011ISPRS Hannover 2011 Workshop, 14-17 June 2011, Hannover, Germanybased on fuzzy Markov chains. ISPRS J. PhotogrammetryRemote Sens. 64(2), pp. 159-170.Gislason, P. O., Benediktsson, J. A., and Sveinsson, J. R., 2006.Random Forests for land cover classification. PatternRecognition Letters, 27(4), pp. 294–300.Simonneaux, V., Duchemin, B., Helson, D., Er-Raki, S.,Olioso, A. and Chehbouni, A. G., 2008. The use of highresolution image time series for crop classification andevapotranspiration estimate over an irrigated area in centralMorocco. International Journal of Remote Sensing, 29(1), pp.95–116.Hoberg, T. and Rottensteiner, F., 2010. Classification ofsettlement areas in remote sensing imagery using ConditionalRandom Fields. Int. Arch. Photogrammetry, Remote Sens., SISXXXVIII (7A), pp. 53-58.Schölkopf, B. and Smola, A.J., 2002. Learning with Kernels:Support Vector Machines, Regularization, Optimization, andBeyond (Adaptive Computation and Machine Learning). TheMIT Press, Cambridge, MA, USA.Hoberg, T., Rottensteiner, F., Heipke, C., 2010. Classificationof Multitemporal Remote Sensing Data Using ConditionalRandom Fields. 6. IAPR TC 7 Workshop on PatternRecognition in Remote Sensing, Istanbul.Vapnik, V.N., 1998. Statistical Learning Theor
2.1 Multitemporal crop type classification In the field of multitemporal crop type classification three main directions of approaches can be observed: In the first category powerful classifiers or combinations of several classifiers that are developed originally for single image classification are used.
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Abstract: The determination of crop coefficients and reference crop evapotranspiration are important for estimating irrigation water requirements of any crop in order to have better irrigation scheduling and water management. The purpose of this study is to determine the crop water requirement of cauliflower, using single and dual crop coefficient
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J. Chil. Chem. Soc., 59, N 4 (2014) 2747 EXPERIMENTAL ACTIVITIES IN THE LABORATORY OF ANALYTICAL CHEMISTRY UNDER AN INQUIRY APPROACH HELEN ARIAS 1, LEONTINA LAZO1*, FRANCISCO CAÑAS2 1Intituto de Química, Facultad de Ciencias, Pontificia Universidad Católica de Valparaíso, Avenida Universidad 330, Curauma, Valparaíso, Chile. 2Universidad Andres Bello, Departamento de Química, Facultad de .
