Digital Image Processing: A Remote Sensing PerspectiveFW5560FW5560LectureEvaluation of Training Sets (Training Signatures)Once training sets (training signatures) are created, they can be evaluated, deleted, renamed, and merged with signatures from other filesother files.Training set evaluation and editing permits complexTraining set evaluation and editing permits complex classifications with signatures that are derived from more than one training method (supervised and/or unsupervised, parametric dti)and nonparametric).A parametric signature is based on statistical parameters (e.g.,di i)fhilhihiimean and covariance matrix) of the pixels that are in the trainingsample or cluster.A parametric signature includes the following attributes in addition to the standard attributes for signatures:• the number of bands in the input image (as processed by the• the number of bands in the input image (as processed by thetraining program)• the minimum and maximum data file value in each band for hll(ii dieach sample or cluster (minimum vector and maximum vector)• the mean data file value in each band for each sample or pcluster (mean vector)• the covariance matrix for each sample or cluster•the number of pixels in the sample or cluster the number of pixels in the sample or clusterA nonparametric signature is based on an AOI that you define inA nonparametric signature is based on an AOI that you define in the feature space image for the image file being classified.A nonparametric classifier uses a set of nonparametric signatures to assign pixels to a class based on their location, either inside oroutside the area in the feature space image.pgALARMALARMThe alarm evaluation enables you to compare an estimated classification of one or more signatures against the original data, gg g,as it appears in the Viewer. All pixels are evaluated.Using a parallelepiped decision rule pixels that fittheUsing a parallelepiped decision rule, pixels that fit the classification criteria are highlighted in the displayed image. Evaluate individual or multiple training sets. Have the option to idi lbh ii i diff lindicate an overlap by having it appear in a different color.Min- maxStandard deviationDependent on user pattern recognition skills, or some ground truth data to determine the accuracy of atraining settruth data, to determine the accuracy of a training set.ELLIPSESELLIPSESEllipses of concentration are calculated with the means and standard deviations stored in the signature file. Also possible to generate parallelepiped rectangles, means, and labels.In this evaluation, the mean and the standard deviation of everysignature are used to represent the ellipse in 2-dimensional feature spaceThe ellipse is displayed in a feature space imagefeature space. The ellipse is displayed in a feature space image.By analyzing the ellipse graphs for all band pairs you canBy analyzing the ellipse graphs for all band pairs, you can determine which signatures and which bands provide accurate classification results.CONTINGENCY MATRIXThe pixels of each training sample are not always so homogeneous that every pixel in the training set is actually classified to that training set.Each sample pixel only weights the statistics that determine the pp y gclasses. However, if the signature statistics for each sample are distinct from those of the other samples, then a high percentage of eachsample’s pixels is classified asexpectedof each sample s pixels is classified as expected.A quick classification of the sample pixels is performed using the minimum distance, maximum likelihood, or Mahalanobisdistance decision rule. A contingency matrix is presented, which contains the number and percentages of pixels that are classified as expected.TRAINING SET SEPARABILITYIs a statistical measure of distance between two signatures and can be calculated for any combination of bands that is used in the classification, enabling you to rule out any bands that are not useful in the results of the classification.For the distance (Euclidean) evaluation, the spectral distancebetween the mean vectors of each pair of signatures is computed. If thespectral distance between two samples is not significant forIf the spectral distance between two samples is not significant for any pair of bands, then they may not be distinct enough to produce a successful classification. The spectral distance is also the basis of the minimum distanceclassification. Therefore, computing the distances between ,pgsignatures helps you predict the results of a minimum distance classification.DIVERGENCEThe formulas used to calculate divergence are related to themaximum likelihood decision rule. Therefore, evaluatingmaximum likelihood decision rule. Therefore, evaluating signature divergence helps predict the results of a maximum likelihood classification.There are three options for calculating the separability. All of these formulas take into account the covariances of the signatures in the bands being compared, as well as the mean vectors of thesignatures.DIVERGENCEDIVERGENCEThe formula for computing Divergence (Dij) is as follows:Where:iand j = the two signatures (classes) being comparediand j = the two signatures (classes) being comparedCi= the covariance matrix of signature iµi= the mean vector of signature itr = the trace function (matrix algebra)T = the transposition functionTRANSFORMED DIVERGENCEWhWhere:i and j = the two signatures (classes) being comparedCi= the covariance matrix of signature iµi= the mean vector of signature itr = the trace function (matrix algebra)T=the transposition functionT the transposition functionTransformed divergence “gives an exponentially decreasing weight to increasing distances between the classes.” The scale of the di ergence al es can range from 0 to 2 000 Interpretingthe divergence values can range from 0 to 2,000. Interpreting results after applying transformed divergence requires analysis of the numerical divergence values. Result is greater than 1,900, then the classes can be separated. Between 1,700 and 1,900, the separation is fairly good. Below 1,700, poor separation.Jeffries-Matusita DistanceThe formula for computing Jeffries-MatusitaDistance (JM) isThe formula for computing JeffriesMatusitaDistance (JM) is as follows:Where:Where:i and j = the two signatures (classes) being comparedChi ifiiCi= the covariance matrix of signature iµi= the mean vector of signature iln = the natural logarithm functiongf|Ci| = the