DZD DPZ 9 Clasification. Jiří Horák - Tomáš Peňáz Institut geoinformatiky VŠB-TU Ostrava

Transcription

1 DZD DPZ 9 Clasification Jiří Horák - Tomáš Peňáz Institut geoinformatiky VŠB-TU Ostrava

2 Basic principles of classification Classification process assigning certain information meaning to image elements Goal to substitute radiometric features of the image by information classes (i.e. land cover) Type and content of new information depends on the purpose. What we need to obtained should be specified in the beginning of the classification process Classification is usually iterative process

3 Dobrovolný

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8 Classifiers decision rules A feature space image is a graph of the data file values of one band against another (basically a scatterplot with a dot for every pixel in the image). The pixel position in the feature space image is defined by the spectral values for the two chosen bands. The feature space image is shown as a raster image and has a color associated with each pixel. The colors (or grayscale intensity) represent the cumulative frequency (i.e. the number of pixels in the original image which have the given (x,y) combination). Bright tones represent a high density of points, dark tones represent a low density. (The pixel values can also be colored according to thematic layers assigned to the same image.) /ex5a_classification1_fs.pdf

9 Classification

10 Information classes Usable information obtained by processing of image data Often land cover categories In most cases they are not directly readable from image data (multispectral image record) Obtained indirect way using radiometric features of pixels/objects

11 Classifiers decision rules Decision rules enable to classify (assign) image elements into certain classes (classifiers) classifiers are based on various properties of objects and phenomena in the image. The condition is that the values of explored properties are significantly different for different classes. 3 types of classifiers based on: Spectral behaviour Spatial behaviour Temporal behaviour

12 Classifiers of spatial behaviour Classification of an object/phenomenon based on the relationships to surrounding pixels Features of classifiers of spatial behaviour texture proximity size shape repeatability context

13 Classifiers of temporal behaviour Use temporal changes of objects/phenomena for classification Important for vegetable (agriculture, forestry) spatial and spectral feature of vegetation are variable in time Using image records from different time periods

14 Classifiers of spectral behaviour Spectral classification Differences in reflectance and/or emittance of objects in different part of spectra data One-band multiband

15 Spectral classification Setting: What type of distance in image space? What kind of decision rule? What threshold value for the decision rule?

16 Classification using one-band data Only for cases of good separability (distinguishability) in one-band rules: thresholding Density slices see radiometric enhancement

17 Classification using multispectral data spectral response

18 Landsat TM

19 Spectral space Classification using multispectral data

20 Spectral signature specific combination of emitted, reflected and absorbed radiation of different wavelengths enabling to determine the object. For object identification we need some indicators measured or calculated from several intervals of EMG spectra

21 pixels cluster Spectral signature

22 Feature space Defined by all bands in which it is possible to measure or calculate some characteristics (indicators)

23 Spektrální variabilita

24 Extension of the feature space Important part of classification process Data preparation Selection of the best suitable bands for classification Elimination of the correlation between bands (see analysis and transformation of the principal components)

25 Spectral classes Do not confuse with information classes!!! Homogeneous parts of the image from the point of view of spectral behaviour Classification = searching all spectral classes corresponding to certain information class

26 Obr. Spectral classes

27 Classification Per-pixel Object-based Supervised Classification Unsupervised Classification hybrid

28 Per-pixel classification Only values in one pixel (on various layers) are utilized, not values of surrounding pixels Use classifiers of spectral and temporal behaviour Also classifiers of spatial behaviour recalculate characterics for 1 pixel (kernel function)

29 Per-pixel classifiers of spectral behaviour Often used condition and prerequisites: Fixed sensitivity of the sensor for all bands Each pixel correspond perfectly to well defined area of the land (Earth surface) Each pixel represents a homogeneous area for spectral behaviour Normal distribution of measured data in each band One pixel has to be assigned (classified) to one class

30 Object based classification See OBIA Image segmentation Identification of typical values of features for objects/segment from the point of view: Spectral Temporal Spatial behaviour classification

31 Supervised and Unsupervised Classification

32 Supervised Classification Training stage Classification stage using: Minimum Distance to the centre Parallelpiped Maximum Likelihood K nearest pixels Verification of results (accuracy, reliability)

33 Supervised Classification Definition of training sites Calculation of statistical characteristics (spectral features) for training sites, editing Selection of suitable bands for classification Selection of good classifier suitable to assign all image pixels into individual classes Assigning all pixels into classes (classification) Modification, evaluation (verification) and presentation on classification results

34 Training Delimitation of training sites for each class Representative areas large enough, homogeneous, from more than 1 areal, placement. Ability to identify and verify in the field. Minimal number of pixels (at least n+1 where n is the number of bands, recommended 10n to 100n) Create training set Land cover knowledge from field exploration or other sources of data is required

35 Training Requirements of completeness and representativeness completeness identify behaviour of all searched classes Representativeness training sites are typical for the given class

36 Selection of training set manual automated Problem of mixed pixels

37 Manual selection of training set Identify homogeneous groups of pixels (similar DN in individual bands) Elimination of mixed spectral information like border pixels

38 Automated selection of training set Cooperation of the user and software Setting of the seed pixel (Seed Pixel Method) - user Automated selection of surrounding pixels with similar spectral behaviour - SW

39 Number of pixels in the training set The smallest number (theoretically) of pixels = N + 1 where N = number of classified spectral bands Recommended 10N to 100N Towards the best statistical delimitation of each class in multidimensional space Selection of more areas for one class is recommended

40 Create training sites: Dobrovolný

41 Success of training Sufficient number of pixels in each training site Suitable size of training sites Suitable place of training sites Distribution of training sites in each class Level of homogeneity of training sites from their spectral behaviour

42 Statistical characteristics of classes For pixels of the image parts in training sites (masks) For several bands of the multispectral image Expressed by Average vector Standard deviations Covariance matrix Prerequisite data should fit to the normal distribution Enable to evaluate: Ability of training sites to represent classes Level of class separation based on spectral behaviour

43 Suitability of training set Prerequisite normal distribution of DN values in each class of the training data Deal with histogram of DN of training data Bimodal distribution divide into 2 classes define new, maximal and minimal DN value of pixels Increase separation level using various transformation of multispectral image

44 Statistical evaluation of proposed classes Explore following tools for each class and combination: Histogram Coincidence graph scatter plot Are homogeneous? Does not include outliers? Is it possible to separate these classes?

45 Evaluating Signatures methods: alarm Contingency matrix masking feature space to raster image Feature objects histograms Signature separability statistical evaluation

46 Evaluation of training data - histogram Dobrovolný

47 Evaluation of train.data-spectrographs Dobrovolný Spectrographs for classes A, B, C and 3 bands (TM2, TM4 and TM5)

48 Evaluation of train.data scatter plots Evaluation of separation using scatter plot and ellipses of training data Dobrovolný

49 Hodnocení trénovací etapy příznakové objekty angl. signature separability signalizace

50 Alarm Signalization of one or more selected information classes in the image according to training sets Create approximate idea of the user about distribution in the space

51 Ukázka signalizace

52 Signature separability Calculate some of statistical distances Euclidean spectral distances between average vectors Jeffries-Matusita distance Divergence Transformed divergence

53 Transformed divergence theory: ERDAS Field Guide Statistician textbooks Comparison of statistical distances between training sets

54 Band selection Evaluation of divergences between bands Selection of suitable bands for classification

55 Classification stage classifier selection Perform classification

56 Classification rules Image elements representing certain class will cluster in certain part of the multidimensional image space Create clusters Pixels of 1 class usually create a cluster with some variability

57 Clusters of image elements centroids (means) of clusters The location of the centroid is done by the average value of pixels in used bands Average value of bands in classification for the given cluster average vector

58 Application of classification rules Govern the membership of the non-classified pixels to certain cluster or class resp. Some pixels may be leaved as non classified their membership were not decided Rules: Parametric Non-parametric

59 Parametric classification rules Known statistical characteristics (average vector, variance, covariance) Evaluation of the statistical distance in the feature space

60 Non-parametric classification rules (non)linear function or mathematical/geometrical subdivision of the feature space Evaluation of Euclidean distance in the feature space

61 Classification rules minimum distance classifiers: to means classification K nearest neighbours minimal Mahalanobis distance parallelepipeds maximum likelihood Bayesian classifier Decision tree and more...

62 Minimum distance to means classification Nonparametric rule Pixel membership to a class is decided according to its distances to all centroids of clusters Euclidean distance (normalised Euclidean, Mahalanobis distance recommended when a correlation between axes in feature space exists) pros Fast calculation Cons Small sensitivity to the level of variance

63 Normalised minimum distance Modification of the minimum distance to means classification rule Distance normalization using multiples of standard deviation Presented by isolines parametric rule Pixel membership is given by: Distance to cluster centroids Variability of clusters are taken into account Pros Fast calculation Increased sensitivity to the level of variance

64 Distances Euclidean: Normalized Euclidean: Mahalanobis:

65 Dobrovolný

66 K-nearest neighbour classification Nonparametric rule modification of the minimum distance to means classification rule Pixel membership to a class is decided according to distances to nearest pixels K neighbours Possibility to apply some distance threshold

67 Dobrovolný

68 Parallelepiped (box) classification Nonparametric rule Boxes (parallelepipeds, multi-level slicing) are delimited by: maximal and minimal values Multiple of standard deviation Pixel membership to a class is determined by its position to boxes pros The most fastest calculation cons The accuracy depends on the selection of the lowest and highest values in consideration of the population statistics of each class (has to well understood) Bad assignment of pixels with values in distant corners of boxes Improvement orthogonalization using PCA

69 Dobrovolný

70 Modified parallelepiped (box) classification Create delimiting polygon in the scatter plot (vector) ERDAS Imagine Pros: Fast calculation Improved classification

71 maximum likelihood classification parametric rule Posterior probability of a pixel belonging to class k P(k) prior probability of class k (usual equal to all classes) P(X/k) conditional probability to observe X from class k (probability density function) Assumption of the normal distribution Normal distribution function is created using average vector and covariance matrix Calculate probability of pixel membership to each class Highest value -> classified class pros The best results when good training sites are used cons The slowest calculation

72 maximum likelihood classification

73 Dobrovolný

74 Dobrovolný

75 Decision tree classifier Hierarchical based classifier Binary Decision Trees Rules defined by experts. Rules usually include features like: Spectral value Indexes PCA components

76 Bayes classifier A priori probability of class occurrence. Setting based on various criteria (i.e. typical coverage, typical occurrence i.e. sand is less probable than urban area) Probability of membership to the class is driven by probability classification => resulting probability of the classification to the class parametric rule pros Variability of classes is taken into account (covariance matrix) Good results for classification of problematic pixels (using with combination with other classifiers) cons The slowest calculation

77 Output Assign pixels according to classification scheme and create a thematic map

78 Unsupervised classification Basic process: 1. Cluster analysis 2. Assign classes to clusters (determine the information value to the artificial categories) 3. reclassification (classes merge)

79 Unsupervised classification Do not use training sets No preliminary information about properties of searched classes is required Basic principles all members (pixels) of one class have similar values of DN and they are located close each other in multidimensional space -> create a cluster Members (pixels) of different classes are more distant and it is possible to separate them 1st stage create spectral classes 2nd stage merge and interpret spectral classes into information classes Dobrovolný

80 Unsupervised classification - clusters

81 Dobrovolný

82 Unsupervised classification - process 1. Define approximate number of resulting clusters 2. Generate initial location of a centroid for each cluster 3. Iterative assignment of all pixels to the closest clusters 4. Calculation of the new location of centroids for each cluster with newly assigned pixels 5. Repeating 2 steps until the changes of cluster location in the image space are not significant or the number of pixels in the cluster are the same 6. Assign the meaning to the stabile clusters 7. Create information classes merging spectral (or other) classes

83 Parameters Initial location of centroids Using diagonal of the feature space Using seed file approximate number of resulting clusters minimal distance of 2 clusters Threshold of distance difference between 2 clusters (in iteration) Maximal number of iterations

84 Cluster analysis spectral distance D n i 1 ( d i e i 2 ) in 2D (n = 2) D 2 d e 2 d e 2 i i j j D = spectral distance n = number of bands i = index of band d i = DN value of pixel d in band i e i = DN value of pixel e in band i

85 Algorithms of cluster analysis K-Means ISODATA (Iterative Self-Organizing Data Analysis Technique) algoritmus Narendra a Goldberg (PCI) AMOEBA RGB Clustering (ERDAS Imagine)

86 Cluster analysis Clustering grouping of data with similar characteristics Hierarchical Agglomerative disintegrative Non-hierarchical ISODATA K-means Optimised Dobrovolný

87 Flow and example of hierarchical clustering

88 Dobrovolný

89 K means Set the number of clusters and optional their centres (centroids) Centroids can be defined by regular placing in the space Each pixel is classified into the closest cluster according to a vector of means New centroids are calculated Iteration until satisfactory results or maximal number of iteration Convergence criteria: 1. Not significant number of changes in pixels classification 2. Vector of means are not change significantly

90 ISODATA Set the number of clusters and iterations If no seed file of centroids, create it using regular spacing Classification in iterations with rules: Heterogeneous cluster (high standard deviation) is divided Clusters with centroids closer than given threshold are merged Clusters containing number of pixels less than given threshold are dissolved and its members are assigned to other clusters

91 ISODATA

92 ISODATA algoritmus

93 ISODATA algorithms All members are relocated into the closest clusters by computing the disstance between the member and the clusters The center of gravity of all clusters is recalculated and the above procedure is repeated until convergence If the number of clusters is within a certain specified number, and the distance between the clusters meet a prescribed threshold, the clustering is considered complete

94 Algorithm Narendra and Goldberg Non-parametric method Set borders between clusters according to histograms of processed bands Non-iterative calculation impossible to specify requested number of resulting clusters

95 Algorithm AMOEBA parametric method amoeba Parameter - variability in assignment of the pixel in the given spectral class Using setting variance or standard deviation

96 RGB Clustering Simple classification and compress technique for 3 bands, 8-bits Fast calculation Draw pixels into 3-dimensional scatter Data is divided into intervals in scatter diagram to create clusters by boxes

97 Hybrid classification Results of cluster analyses are used for training stage of the supervised classification Or Data from training sites are used as an input of unsupervised classification (f.e. identification of linear objects)

98 Classification using neural networks Artificial intelligence (expert systems, neuron) neuron vs. artificial neurons Neuron network Input layer Hidden layer Output layer

99 Neural networks neuron the node of the network Node output (output signal): Defined by F(x) function Generated for values above some threshold F x i w i x i x i value of i input w i weight of i input

100 Classification process: supervised unsupervised combined Implementation in: TOPOL RS MUTISPEC ERDAS Imagine Neural networks

101 Neural networks Improvement of classification results Possibility to combine various data types: data from optical part of spectra Radar data morfometric data derived from DMR Possibility to weights to input data Do not use specific mathematical model Data normality is not required No extended training process are required Output information classes

102 Classification by neural networks Algorithm with backward propagation (supervised classification.) 2 layers (Kohonen and Grossberg) which are trained separately. Kohonen unsupervised classification of the input, Grossberg supervised classification of the output Alg. with reversed process the net is created by the input nodes = pixels. Next, the division to clusters are applied, iterative agglomeration until required number of clusters

103 Extension of per-pixel classification Utilization of information from surroundings after transformation a new value in the pixel = image preprocessing Some classification method follows Using classifiers of spatial behaviour i.e. textural, spatial context

104 Contextual classifiers Ability to utilize other landscape properties: texture Functional relationships context spatial pattern recognition Classification according to relations with surroundings surroundings is not explored using kernel (window) but in the full range of image Using map algebra and analytical techniques in GIS

105 context and structure Contextual classifiers Properties usually used for visual interpretation Import topological properties: Distance searched object has to be placed to some distance from another object direction or orientation - searched object only in some direction from another object Connectivity - 2 objects are/ are not connected with other object Touching (neighbourhood) - 2 objects do /do not touch each other Inclusion 1 object is / is not included in another object

106 Hard and soft methods of image classification

107 traditional hard classifiers Hard Classifiers Each classification unit (pixel, segment) belongs to only one class Do not solve mixed pixels

108 Soft Classifiers alternative and complementary methods of classification Each classification unit (pixel, segment) belongs to more than one class solve mixed pixels membership degree of the pixel into each class 0;1 Probability, evidence Combination with vector data in GIS additional information and evidences At the end you can use hard classifiers

109 Evaluation of running classification Improvement of classification Combination of soft and hard classifiers soft classifiers provide information about class uncertainty Problem cases high uncertainty high uncertainty when: Pixels seem to contain the mixture of classes because of: Bad training sample data is not separated Mixed behaviour on the microscale level Pixels belongs to unknown classes (unknown spectral signature) Create the new class collect appropriate training data

110 Hard and soft classifiers Output class membership images One image (map) hard classifiers More images (thematic maps) soft classifiers

111 soft classifiers Various metrics for membership Idrisi Selva (Taiga, TerrSet) selected soft classifiers based on: Bayes theory (BAYCLASS) Dempster-Shafer theory (BELCLASS) Mahalanobis distance fuzzy set theory model of linear mixing

112 soft classifiers Classification output = class membership images Idrisi stored in the raster image group file (.rgf) Values of membership can be obtained using questions numerical graphical

113 soft classifiers Classification Uncertainty image Level in which the membership of the pixel to the class is better/worse than to other classes where max = maximal membership for the pixel sum = sum of memberships to all classes for the pixel n CU = number of classes 1 max 1 sum n 1 n

114 Examples of classification uncertainty Example: Classification into 3 classes rules: - membership 0;1, - sum of membership values 0;1), Reasoning of classification uncertainty: - Need to collect more evidence (data) - Obtaining new information

115 Example: memberships to 3 classes and resulting CU ) 0,0 0,0 1,0 ( ) 0,05 0,05 0,9 ( ) 0,0 0,1 0,9 ( ) 0,1 0,3 0,6 ( ) 0,0 0,3 0,6 ( ) 0,3 0,3 0,3 ( ) 0,1 0,1 0,1 ( ) 0,1 0,0 0,0 ( ) 0,0 0,0 0,0 ( 0,00 0,15 0,15 0,60 0,55 1,00 1,00 0,90 1,00 CU CU CU CU CU CU CU CU CU

116 BAYCLASS Similar to Maximum Likelihood Classifier Express posterior probability for pixel membership into the given class according to Bayes probability theory Relationship between the probability and ratio of chances prior probability comes from existing knowledge (i.e. existing thematic maps)

117 BAYCLASS where p h e p(h /e) = resulting posterior probability of the hypothesis p(e /h) = probability of finding that the evidence is true i p( e p( e h). p( h) p(h) = prior probability - probability that the hypothesis is true (evidence is not taken into account) h ). p h i i

118 BAYCLASS p(e /h) based on the covariance matrix of the training data p(h /e) = posterior probability represents the membership level to the given class Precondition no other possible classes exist Assign pixels to classes using even a weak evidence sub-pixel classification output is separated images BAYCLASS in Idrisi Identify well basic components of mixed pixels Not well measure the real share of each class in the mixels

119 BELCLASS Similar to Maximum Likelihood Classifier Dempster-Shafer theory (DST) DST x BPT BPT no ignorance exists disadvantage!!! DST admit a possibility of non-completeness of existing information Shortage of evidence supporting the hypothesis does not mean the evidence against the hypothesis

120 BELCLASS See Data processing in GIS lessons: basic probability assignment (BPA) Ignorance missing information in the whole system, = 1-BPA(system) Belief (BEL) disbelief (DISBEL) Plausibility (PLA) interval of belief <Bel(A); Pl(A)>

121 DST BELCLASS Integrate various evidence easy way Integrated evidence: independent Not redundant

122 4 classes BELCLASS - example Evidence support the class No.1 with probability of 0.3 and 0 for other classes Result of BPT pixel is assigned to 1st class with 1.0 probability

123 BELCLASS Pixel X classified into 4 classes: List of evidence 1st class belief =0.3 Other classes (2, 3, 4) belief =0 X pixel assigned to 1st class: belief = 0.3 Plausibility = 1 interval of belief = <0.3; 1>, the range = 0,7 X pixel assigned to another class belief = 0 Plausibility = 0.7

124 BELCLASS New situation a new evidence for 2nd class (0.6): X pixel assigned to 1st class: belief = 0.3 Plausibility = 0.4 interval of belief = <0.3; 0.4>, the range = 0.1 X pixel assigned to 2nd class belief = 0.6 Plausibility = 0.7 X pixel assigned to 3rd or 4th class belief = 0 Plausibility = 0.1 New evidence causes the decrease of uncertainty

125 For each class produce: BELCLASS image of belief image of plausibility classification uncertainty image Reasons for using BELLCLASS Check the quality of training data (if some class is missing?) During classification When some class may missing use class OTHER

126 Comparison of BAYCLASS and BELCLASS BAYCLASS Belief to training sets No ignorance of some training sets BELLCLASS Not fully dependent on training sets Admit ignorance of some training sets

127 Postclassification modifications 1. Issues in the size of created spatial objects 2. Issues in classification Ad 1) A) too small and fragmented i.e. Sieve filtration B) Pepper and salt isolated pixels with different value Low frequency filters with appropriate operator mode, median,..

128 Issues of postclassification filtration Classified images contain qualitative characteristics Danger to create a new information class modal filter Improvements: Use different weights Elimination of some classes Multiple filtration A criteria of minimal area Respecting the border between classes

129 Properties of postclassification errors in the image Wrongly classified pixels: Connected usually only with some classes Occured in groups, not isolated Usually create a specific spatial arrangement (texture) in the final image Occur in typical parts of classified objects

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131 Detection of classification errors Large water body on the top or slopes of mountains Use DMR Error in classification?! Or icefield? Wetland forest distant to water streams Use buffer

132 Evaluation of classification accuracy Testing areas Contingency table Kappa index

133 Error matrix Counts placed out of main diagonal = errors Average accuracy = sum of diagonal counts/number of pixels Dobrovolný

134 Error matrix CHZ - errors of commision (1st type) CHO - errors of omission (2nd type) PU accuracy for users PZ accuracy for proccessor Dobrovolný

135 Kappa index Compare used classification with random classification (random assignment of pixels into classes) Even in random classification some part will be properly classified PP obtained accuracy PO accuracy of random classification