Transcript Basics:
Basics: Notation: Qi Pixelrow i ,col j band Q k Sum: i Q Q Q i 1 0, 1, 2. Qk PARAMETERS k MEAN: Q i 1 k * the statistical average i Q k Sample Variance: Standard Deviation: s S 2 Q Q 2 i 1 i k 1 2 Q * the central tendency 2 st . d . Q * 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 v1 v 2 v 3 v n Mean Vector 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 d i ei n 2 i 1 i a band (dimension) d valueof pixeld in band i e valueof pixele 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 Maximum likelihood (bayesian) B •probability •Bayesian, a prior (weights) Band B A Band A Minimum Distance SDxyc n i 1 ci X xyi 2 c class X xyi value of pixel x, y in i class Band B ci mean of valuesin i for samplefor 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 • Measurements of location (center of distribution n – mean (m µ x ) – median – mode i 1 n 2 st. d. • Measurements of shape (symmetry & length – coefficient of skewness – coefficient of variation i 1 / n xi n • Measurements of spread (variability) – variance – standard deviation – interquartile range x CS i 1 2 3 1 n xi n i 1 2 2 IQR Q Q 3 CV 1 Bivariate p Scatterplots Yin p Correlation x y n 1 n p i 1 i i x x y X in Linear Regression y 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 n 2n i 1 x y i 2 i 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