ImageClassificat...

Medical Image Analysis
Lecture 13b Image Classification (continued)
Unsupervised Posterior Space to Classes in the Image
Training
•Training: the process of defining criteria by
which patterns/features are recognized •Signature: result of training that defines a training sample or cluster
parametric-based on statistical
parameters that assume a normal
distribution (e.g., mean, covariance matrix)
nonparametric-not based on statistics but
on discrete objects (polygons) in feature
space
Supervised Training Set Selection •Objective: selecting a homogenous (unimodal)
area for each apparent cluster
•Digitized polygons: high degree of user control; often results in overestimate of cluster variability •Seed pixel: region growing technique to reduce within class variability; works by analyst setting threshold of acceptable variance, total #pixels, adjacency criteria (horiz/vert, diagonal)
Supervised Training Set Selection
Whether using the
digitized polygon or
seed pixel technique,
the analyst should
select multiple training
sites to identify the
many possible clusters
in each class of interest
Training Stage
•Training set ⇒training vector
•Training vector for each cluster -represents a sample in n-dimensional measurement space where n = #bands
for a given cluster j
X j= [ X1] X1= mean DN band 1
[ X]X= mean DN band 2
Classification Training Aids •Goal: evaluate cluster separability
•1) Graphical plots of training data
-histograms
-coincident spectral plots
-scatter plots
•2) Statistical measures of separability
-divergence
-Mahalanobis distance
•3) Training Area Classification
•4) Quick Alarm Classification
-paralellipiped
Training Aids
•Graphical portrayals of training data
–histogram (check for normality)
–ranges (coincident spectral plots)
–scatter plots (2D or 3D)
•Statistical Measures of Separability: expressions of statistical distance that are sensitive to
both mean and variance
-divergence
-Mahalanobis distance
•Scatter plots: each training sample-set constitutes an ellipse in feature space •Provides 3 pieces of information
-location of ellipse: mean vector -shape of ellipse: covariance
-orientation of ellipse: slope & sign of
covariance
•Need training vector and covariance matrix
Grass Trees Impervious Surface &Bare Soil
Spectral Feature Space
Examine ellipses for gaps and overlaps. Overlapping ellipses ok within classes; want to limit between Conifer
Broadleaf Mix: grass/trees
•Training/Test Area classification: look for
misclassification between classes; training areas can be biased;better to use independent test areas
•Quick alarm classification: on-screen evaluation of all pixels that fall within the training decision region (e.g. parallelipiped) Classification Decision Process •Decision Rule: mathematical algorithm that, using data contained in the signature, performs
the actual sorting of pixels into discrete classes •Parametric vs. nonparametric rules
Parallelepiped or box classifier •Decision region defined by the rectangular area defined by the highest and lowest DN’s in each band; specify by range (min/max) or std dev.•Pro: Takes variance into account but lacks sensitivity to covariance (Con)
•Pro: Computationally efficient, useful as first pass
•Pro: Nonparametric
•Con: Decision regions may overlap; some pixels may remain unclassified
Spectral Feature Space
Parallelepiped or Box Classifier
Upper and lower limit of each
box set by either range
(min/max) or #standard devs.
Note overlap in Red but not
Minimum distance to means •Compute mean of each desired class and then classify unknown pixels into class with closest mean using simple Euclidean distance
•Con: insensitive to variance & covariance •Pro: computationally efficient
•Pro: all pixels classified, can use thresholding to eliminate pixels far from means
Statistically-based classifiers
•Defines a probability density (statistical) surface •Each pixel is evaluated for its statistical probability of belonging in each category, assigned to class with maximum probability •The probability density function for each cluster can be completely described by the mean vector and covariance matrix
Parametric Assumption: each cluster exhibits a unimodal normal distribution
255
Digital Number
#pixels
Class 1Class 2
Bimodal histogram: Mix of Class 1 & 2
Red Reflectance
Spectral Feature Space Ellipses defined by class mean
and covariance; creates
likelihood contours around each cluster
Clusters as probability
surfaces
Red Reflectance
Spectral Feature Space Some classes may have large variance and greatly overlap the others
Sensitive to large covariance values
Maximum likelihood classifier
•Pro: potentially the most accurate classifier as it incorporates the most information (mean vector and COV matrix)
•Con: Parametric procedure that assumes the clusters are normally distributed •Con: sensitive to large values in the covariance matrix
•Con: computationally intensive
Hybrid classification
•Can easily mix various classification algorithms
in a multi-step process
•First pass: some non-parametric rule (feature space or paralellipiped) to handle the most obvious cases, those pixels remaining unclassified or in overlap regions fall to second pass
•Second pass: some parametric rule to handle the difficult cases; the training data can be derived from unsupervised or supervised techniques Example: GIS Rule-based approach •Unsupervised or supervised techniques to define
clusters
•Use of additional geo-spatial data sets to either pre-stratify image data set, for inclusion as additional band data in classification algorithm or post-processing
•Develop set of boolean rules or conditional statements
Region-based classification approaches •As an alternative to “per-pixel”classification approaches, region-based approaches attempt to include the local spatial context
•Textural channels approach: inclusion of texture (local variance) as an additional channel in classification; con: tends to blur edges
•Region growing: Image segmented into spectrally homogenous, spatially contiguous regions first, then these regions are classified using a classification approach; conceptually very promising but robust operational algorithms scarce
Post-classification “smoothing”•Most classifications have a problem with “salt and pepper”, i.e., single or small groups of mis-classified pixels, as they are “point”operations that operate on each pixel independent of its neighbors
•Majority filtering: replaces central pixel with the majority class in a specified neighborhood (3 x 3 window); con: alters edges
•Eliminate: clumps “like”pixels and replaces clumps under threshold-size with majority class in local neighborhood; pro: doesn’t alter edges
Accuracy Assessment •Various techniques to assess the “accuracy”of the classified output by comparing the “true”class-identity derived from reference data (observed) vs. the classified (predicted) for a random sample of pixels
•Contingency table: mxm matrix
where m = #classes –Columns: usually represent the reference data
–Rows: usually represent the classification results
Accuracy Assessment
•Sampling Approaches: to reduce analyst bias –simple random sampling: every pixel has equal
chance
–stratified random sampling: #points will be stratified to the distribution of the classes (larger classes, more points)
–equalized random sampling: each class will have
equal number of random points
Accuracy Assessment Issues •What constitutes reference data?-
higher spatial resolution imagery (with visual interpretation)
-“ground truth”
-existing “maps”, e.g. brain atlas
Errors of Omission vs.
Commission
•Error of Omission: pixels in class 1 erroneously assigned to class 2; from the class 1 perspective these pixels should have been classified as class1 but were omitted •Error of Commission: pixels in class 2 erroneously assigned to class 1; from the class 1 perspective these pixels should not have been classified as class 1 but were included
Accuracy Assessment Measures •Overall accuracy: divide total correct (sum of the major diagonal) by the total number of sampled pixels; can be misleading, should judge individual categories also
•Producer’s accuracy: measure of omission error; total number of correct in a category divided by the total # in that category as derived from the reference data •User’s accuracy: measure of commission error; total number of correct in a category divided by the total # that were classified in that category
Accuracy Assessment Measures •Kappa coefficient: provides a difference measurement between the observed agreement of two “maps”and agreement that is contributed by chance alone
•A Kappa coefficient of 90% may be interpreted as 90% better classification than would be expected by random assignment of classes
•Allows for statistical comparisons between matrices (Z statistic); useful in comparing different classification approaches to objectively decide which gives best results。