Pixel-based image classification. Lecture 8 March 4, 2008

Transcription

1 Pixel-based image classification Lecture 8 March 4, 2008

2 What is image classification or pattern recognition Is a process of classifying multispectral (hyperspectral) images into patterns of varying gray or assigned colors that represent either clusters of statistically different sets of multiband data, some of which can be correlated with separable classes/features/materials. This is the result of Unsupervised Classification, or numerical discriminators composed of these sets of data that have been grouped and specified by associating each with a particular class, etc. whose identity is known independently and which has representative areas (training sites) within the image where that class is located. This is the result of Supervised Classification. Spectral classes are those that are inherent in the remote sensor data and must be identified and then labeled by the analyst. Information classes are those that human beings define.

3 unsupervised classification, The computer or algorithm automatically group pixels with similar spectral characteristics (means, standard deviations, covariance matrices, correlation matrices, etc.) into unique clusters according to some statistically determined criteria. The analyst then re-labels and combines the spectral clusters into information classes. supervised classification. Identify known a priori through a combination of fieldwork, map analysis, and personal experience as training sites; the spectral characteristics of these sites are used to train the classification algorithm for eventual land-cover mapping of the remainder of the image. Every pixel both within and outside the training sites is then evaluated and assigned to the class of which it has the highest likelihood of being a member.

4 Hard vs. Fuzzy classification Supervised and unsupervised classification algorithms typically use hard classification logic to produce a classification map that consists of hard, discrete categories (e.g., forest, agriculture). Conversely, it is also possible to use fuzzy set classification logic, which takes into account the heterogeneous and imprecise nature (mix pixels) of the real world. Proportion of the m classes within a pixel (e.g., 10% bare soil, 10% shrub, 80% forest). Fuzzy classification schemes are not currently standardized.

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6 Pixel-based vs. Object-oriented classification In the past, most digital image classification was based on processing the entire scene pixel by pixel. This is commonly referred to as per-pixel (pixel-based) classification. Object-oriented classification techniques allow the analyst to decompose the scene into many relatively homogenous image objects (referred to as patches or segments) using a multiresolution image segmentation process. The various statistical characteristics of these homogeneous image objects in the scene are then subjected to traditional statistical or fuzzy logic classification. Object-oriented classification based on image segmentation is often used for the analysis of highspatial-resolution imagery (e.g., 1 1 m Space Imaging IKONOS and m Digital Globe QuickBird).

7 Knowledge-based information extraction: Artificial Intelligence Neural network Decision tree Support vector machine (SVM)

8 Purposes of classification Land use and land cover (LULC) Vegetation types Geologic terrains Mineral exploration Alteration mapping.

9 1. Unsupervised classification Uses statistical techniques to group n-dimensional data into their natural spectral clusters, and uses the iterative procedures label certain clusters as specific information classes K-mean and ISODATA For the first iteration arbitrary starting values (i.e., the cluster properties) have to be selected. These initial values can influence the outcome of the classification. In general, both methods assign first arbitrary initial cluster values. The second step classifies each pixel to the closest cluster. In the third step the new cluster mean vectors are calculated based on all the pixels in one cluster. The second and third steps are repeated until the "change" between the iteration is small. The "change" can be defined in several different ways, either by measuring the distances of the mean cluster vector have changed from one iteration to another or by the percentage of pixels that have changed between iterations. The ISODATA algorithm has some further refinements by splitting and merging of clusters. Clusters are merged if either the number of members (pixel) in a cluster is less than a certain threshold or if the centers of two clusters are closer than a certain threshold. Clusters are split into two different clusters if the cluster standard deviation exceeds a predefined value and the number of members (pixels) is twice the threshold for the minimum number of members.

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12 ISODATA: Initial Cluster Values (properties) number of classes maximum iterations pixel change threshold (0-100%) (The change threshold is used to end the iterative process when the number of pixels in each class changes by less than the threshold. The classification will end when either this threshold is met or the maximum number of iterations has been reached) initializing from statistics (Erdas) or from input (ENVI) (the initial values to put in for ENVI are minimum # pixel in class, maximum class stdv, minimum class distance, maximum # merge pairs)

13 Maximum Class Stdv (in pixel value). If the stdv of a class is larger than this threshold then the class is split into two classes. Minimum class distance (in pixel value) between class means. If the distance between two class means is less than the minimum value entered, then ENVI merges the classes. Optional Maximum stdev from mean (1 to 3σ) and maximum distance error (in pixel value). If any of these two setup, the some pixels might not be classified.

14 5-10 classes, 8 iterations, 5 for change threshold, (MinP 5, MaxSD 1, MinD 5, MMP 2)

15 1-5 classes, 11 iterations, 5 for change threshold, (MinP 5, MaxSD 1, MinD 5, MMP 2)

16 5 classes 10 classes

17 2. Supervised classification: training sites selection Based on known a priori through a combination of fieldwork, map analysis, and personal experience on-screen selection of polygonal training data (ROI), and/or on-screen seeding of training data (ENVI does not have this, Erdas Imagine does). The seed program begins at a single x, y location and evaluates neighboring pixel values in all bands of interest. Using criteria specified by the analyst, the seed algorithm expands outward like an amoeba as long as it finds pixels with spectral characteristics similar to the original seed pixel. This is a very effective way of collecting homogeneous training information. From spectral library of field measurements

18 Statistic extraction of each training site Each Each pixel pixel in in each each training site site associated with with a particular class class (c) (c) is is represented by by a measurement vector, X c ; c ; Average of of all all pixels in in a training site site called mean vector, M c ; c ; a covariance matrix of of V c. c. X c = BV BV BV.. BV i, j,1 i, j,2 i, j,3 i, j, k M c = µ c µ c µ c.. µ ck V c = cov cov.. cov c11 c21 ck1 cov cov cov c12 c22 ck 2...cov...cov...cov c1k c2k ckk where BV BV i,j,k is i,j,k is the the brightness value for for the the i,j i,j th th pixel pixel in in band band k. k. µ ck represents ck the the mean mean value value of of all all pixels pixels obtained for for class classcc in in band band k. k. Cov Cov ckl is ckl is the the covariance of of class class ccbetween between bands bands llthrough through k. k.

19 Selecting ROIs Alfalfa Cotton Grass Fallow

20 Spectra of ROIs from ETM+ image

21 Spectra from library Resampled to match TM/ETM+, 6 bands

22 Supervised classification methods Various supervised classification algorithms may be used to assign an unknown pixel to one of m possible classes. The choice of a particular classifier or decision rule depends on the nature of the input data and the desired output. Parametric classification algorithms assumes that the observed measurement vectors X c obtained for each class in each spectral band during the training phase of the supervised classification are Gaussian; that is, they are normally distributed. Nonparametric classification algorithms make no such assumption. Several widely adopted nonparametric classification algorithms include: one-dimensional density slicing parallepiped, minimum distance, nearest-neighbor, and neural network and expert system analysis. The most widely adopted parametric classification algorithms is the: maximum likelihood. Hyperspectral classification methods Binary Encoding Spectral Angle Mapper Matched Filtering Spectral Feature Fitting Linear Spectral Unmixing

23 If a pixel value lies above the low threshold and below the high threshold for all n bands being classified, it is assigned to that class. If the pixel value falls in multiple classes, ENVI assigns the pixel to the last class matched. Areas that do not fall within any of the parallelepipeds are designated as unclassified. In ENVI, you can use 1-3σ 2.1 Parallepiped This is a widely used digital image classification decision rule based on simple Boolean and/or logic. µ + ck σ ck BVijk µ ck σ ck L ck BV ijk H ck

24 This method is a computationally efficient method. But an unknown pixel might meet the criteria of more than one class and is always assigned to the first class for which it meets all criteria. The Minimum Distance to Means can assign any pixel to just one class.

25 1 means 1 stdev from mean, 2 means 2 stdev from mean, 3 means 3 stdev from mean; Use 1, you will classify the closest pixels to the class Use 3, you will include some not so closest pixels to the class

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27 2.2 Minimum distance ( BV ) ( ) 2 ijk µ + BV 2 ck ijl cl Dist = µ The The distance used used in in a minimum distance to to means classification algorithm can can take take two two forms: the the Euclidean Dist = ( BV ) 2 ( ) 2 ijk µ ck + BVijl µ cl distance based on on the the Pythagorean theorem and and the the round the the block distance. The The Euclidean distance is is more more computationally intensive, but but it it is is more more frequently used used All pixels are classified to the nearest class unless a standard deviation or distance threshold is specified, in which case some pixels may be unclassified if they do not meet the selected criteria. Dist = ( BV ) ( ) 2 ijk µ + BV ck 2 ijl cl Dist = µ e.g. the distance of point a to class forest is 2 2 ( ) + ( ) = 4. 6

28 If either Max stdev or Max distance error is not set, all pixels will be classified. If the Max stdev from mean is set at 2 (stdev), then the pixels with values outside the mean ± 2σ will not be classified. If the Max distance error is set at 4.2 (pixel value), then the pixels with distance larger than 4.2 will not be classified.

29 2.3 Maximum likelihood Instead based on training class multispectral distance measurements, the maximum likelihood decision rule is based on probability. The maximum likelihood procedure assumes that each training class in each band are normally distributed (Gaussian). Training data with bi- or n-modal histograms in a single band are not ideal. In such cases the individual modes probably represent unique classes that should be trained upon individually and labeled as separate training classes. the probability of a pixel belonging to each of a predefined set of m classes is calculated based on a normal probability density function, and the pixel is then assigned to the class for which the probability is the highest. probability

30 The The estimated probability density function for for class class w i (e.g., i (e.g., forest) is is computed using the the equation: pˆ ( x w ) i 1 1 exp ˆ σ 2 ( x ˆ µ ) i = 1 2 ( 2π ) 2 ˆ σ 2 i i where exp exp [ [] ] is is e (the (the base base of of the the natural logarithms) raised to to the the computed power, x is is one one of of the the brightness values on on the the x-axis, µˆi is is the the estimated mean of of all all the the values in in the the forest training class, and and σˆi 2 is is the the estimated variance e of of all all the the measurements in in this this class. Therefore, we we need need to to store store only only the the mean and and variance of of each each training t class class (e.g., (e.g., forest) to to compute the the probability function associated with with any any of of the the individual brightness values in in it. it.

31 For For multiple bands of of remote sensor data data for for the the classes of of interest, we we compute an an n- n- dimensional multivariate normal density function using: p ( X w ) i = ( 2π ) 1 n 2 V i 1 2 exp 1 2 T 1 ( X M ) V ( X M ) i i i 1 where V is is the the determinant of of the the covariance matrix, V i i is is the the inverse of of the the covariance matrix, and and ( ) is is the the transpose of of the the vector ( T X M X M i ) i.. The The mean vectors (M (M i ) i ) and and covariance matrix (V (V i ) i ) for for each each class class are are estimated from from the the training data. data.

32 Without Prior Probability Information: Decide unknown measurement vector X is in class i if, and only if, p i > p j for all i and j out of 1, 2,... m possible classes and p i = 1 2 log e V i 1 2 T 1 ( X M ) V ( X M ) i i i The assign the measurement vector X of an unknown pixel to a class, the maximum likelihood decision rule computers the value pi for each class. Then it assigns the pixel to the class that has the largest value Unless you select a probability threshold (0-1), all pixels are classified. Each pixel is assigned to the class that has the highest probability

33 Probability threshold from [0, 1]. 0 means zero probability of similarity, 1 means 100% probability of similarity.

34 2.4 Mahalanobis Distance M-distance is similar to the Euclidian distance Dist = ( ) T 1 X M V ( ) i X M i i It is similar to the Maximum Likelihood classification but assumes all class covariances are equal and therefore is a faster method. All pixels are classified to the closest ROI class unless you specify a distance threshold, in which case some pixels may be unclassified if they do not meet the threshold (in DN number)

35 2.5 Spectral Angle Mapper

36 2.6 Spectral Feature Fitting compare the fit of image reflectance spectra to selected reference reflectance spectra using a least-squares squares technique. SFF is an absorption-feature-based methodology. Both reflectance spectra should be continuum removed. A scale image is output for each reference spectrum and is a measure of absorption feature depth which is related to material abundance. The image and reference spectra are compared at each selected wavelength in a least-squares sense and the root mean square (rms) error is determined for each reference spectrum.

37 Least square tech (regression)

38 A continuum is a mathematical function used to isolate a particular absorption feature for analysis

39 Supervised classification method: Spectral Feature Fitting Source: