Basics: Notation: Qi Pixelrow i ,col j band Q k Sum: i Q 0, i 1 Q1,Q2. Qk PARAMETERS k MEAN: Q i 1 * the statistical average i k k
Sample Variance: Standard Deviation: s 2 2 Q Q i 1 i k1 2 S Q Q st .d . 2 Q * the central tendency
* the spread of the values about the mean Covariance * measures the tendencies of data file values for the same pixel, but in different bands, to vary with each other in relation to the means of their respective bands. Q R k C QR i 1 i Q k i R
Dimensionality N = the number of bands = dimensions . an (n) dimensional data (feature) space Measurement Vector Mean Vector v1 v2 v 3 vn 1 2 3 n Feature Space - 2dimensions 190 85
Band B Band A Spectral Distance * a number that allows two measurement vectors to be compared D n d i ei 2 i 1 i a band (dimension) d value of pixel d in band i e value of pixel e in band i i i terms Parametric = based upon statistical parameters (mean & standard deviation) Non-Parametric = based upon objects (polygons) in feature space Decision Rules = rules for sorting pixels into classes
Clustering Minimum Spectral Distance - unsupervised ISODATA I - iterative S - self O - organizing D - data A - analysis T - technique A - (application)? Band B Band A Band B Band A 1st iteration cluster mean 2nd iteration cluster mean Classification Decision Rules If the non-parametric test results in one unique class, the pixel will be assigned to that class. if the non-parametric test results in zero classes (outside the decision boundaries) the the unclassified rule applies either left unclassified or classified by the parametric rule if the pixel falls into more than one class the overlap rule applies left unclassified, use the parametric rule, or
processing order Non-Parametric parallelepiped feature space Unclassified Options parametric rule unclassified Overlap Options parametric rule by order unclassified Parametric minimum distance Mahalanobis distance maximum likelihood Parallelepiped Band B Maximum likelihood (bayesian) B probability Bayesian, a prior (weights) A
Band A Minimum Distance SD xyc n i 1 ci X xyi 2 c class Band B X xyi value of pixel x, y in i class ci mean of values in i for sample for class c Band A cluster mean
Candidate pixel GeoStatistics Univariate Bivariate Spatial Description Univariate One Variable Frequency (table) Histogram (graph) Do the same thing (i.e count of observations in intervals or classes Cumulative Frequency (total below cutoffs) Summary of a histogram n Measurements of location (center of distribution mean (m x ) median mode Measurements of spread (variability) variance standard deviation interquartile range
n 2 Measurements of shape (symmetry st.d . & length coefficient of skewness coefficient of variation CS 1 n 1/n n x i 1 2 i
IQ R i n x i 1 2 i 1 xi 2 Q Q 3 3 CV
1 Bivariate p Scatterplots Y i n p X Correlation n 1 n p x i 1 i x y
x y i y i n Linear Regression y ax b slope constant a p y x b y a x
Spatial Description - Data Postings = symbol maps (if only 2 classes = indicator map - Contour Maps - Moving Windows => heteroscedasticity (values in some region are more variable than in others) - Spatial Continuity (h-scatterplots * Xj,Yj Spatial lag = h = (0,1) = same x, y+1 h=(0,0) h=(0,3) h=(0,5) tj hij=tj-ti * Xi,Yi correlation coefficient (i.e the correlogram, relationship of p with h * (0,0) ti Correlogram = p(h) = the relationship of the correlation coefficient of an h-scatterplot and h (the spatial lag) Covariance = C(h) = the relationship of thecoefficient of variation of an h-scatterplot and h Semivariogram = variogram = ( h ) = moment of
inertia moment of inertia = 1 2n n x i 1 i y i 2 OR: half the average sum difference between the x and y pair of the h-scatterplot OR: for a h(0,0) all points fall on a line x=y OR: as |h| points drift away from x=y