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Pixel-based image
classification
Lecture 7
March 4, 2005
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.
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.
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.
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 0.61 × 0.61 m Digital Globe QuickBird).
Knowledge-based information
extraction: Artificial Intelligence
†
†
†
†
Neural network
Decision tree
Support vector machine (SVM)
…
Purposes of classification
Land use and land cover (LULC)
Vegetation types
Geologic terrains
Mineral exploration
Alteration mapping
…….
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.
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)
5-10 classes, 8 iterations, 5 for change threshold, (MP 5, MSD 1, MD 5, MMP 2)
1-5 classes, 11 iterations, 5 for change threshold, (MP 5, MSD 1, MD 5, MMP 2)
5 classes
10 classes
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
Statistic extraction of each training site
Each
Each pixel
pixel inin each
each training
training site
site associated
associated with
with aa particular
particular class
class (c)
(c) isis
represented
Average of
of all
all pixels
pixels inin aa
represented by
by aa measurement
measurement vector,
vector, XXc;c; Average
training
covariancematrix
matrixof
ofVVc. .
trainingsite
sitecalled
calledmean
meanvector,
vector,M
Mc;;aacovariance
c
⎡ BVi , j ,1 ⎤
⎢
⎥
BV
⎢ i, j ,2 ⎥
⎢ BV ⎥
X c = ⎢ i , j ,3 ⎥
⎢.
⎥
⎢
⎥
.
⎢
⎥
⎢ BVi , j ,k ⎥
⎣
⎦
⎡ µ c1 ⎤
⎢µ ⎥
⎢ c2 ⎥
⎢µc3 ⎥
Mc = ⎢ ⎥
⎢. ⎥
⎢. ⎥
⎢ ⎥
⎢⎣ µ ck ⎥⎦
c
⎡cov c11 cov c12 ... cov c1k ⎤
⎢cov cov ... cov ⎥
c 22
c2k ⎥
⎢ c 21
⎥
Vc = ⎢.
⎢
⎥
.
⎢
⎥
⎢cov ck1 cov ck 2 ... cov ckk ⎥
⎣
⎦
ththpixel in band k.
where
isisthe
brightness
value
for
the
i,j
whereBV
BVi,j,k
the
brightness
value
for
the
i,j
pixel in band k.
i,j,k
µµck represents
the mean value of all pixels obtained for class c in band k.
ck represents the mean value of all pixels obtained for class c in band k.
Cov
Covckl isisthe
thecovariance
covarianceof
ofclass
classccbetween
betweenbands
bandsl lthrough
throughk.k.
ckl
Selecting
ROIs
Alfalfa
Cotton
Grass
Fallow
Spectra of ROIs
from ETM+ image
Spectra from library
Resampled to match
TM/ETM+, 6 bands
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 Xc 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
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
Lck ≤ BVijk ≤ H ck
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
Scann a table here p372
2.2 Minimum distance
The
Thedistance
distanceused
usedininaaminimum
minimum
distance
distancetotomeans
meansclassification
classification
algorithm
algorithmcan
cantake
taketwo
twoforms:
forms:the
the
(
)
(
)
Dist
=
BV
−
µ
+
BV
−
µ
Euclidean
Euclideandistance
distancebased
basedon
onthe
the
Pythagorean
Pythagoreantheorem
theoremand
andthe
the
“round
“roundthe
theblock”
block”distance.
distance.The
The
Euclidean
Euclideandistance
distanceisismore
more
computationally
computationallyintensive,
intensive,but
butititisis
more
morefrequently
frequentlyused
used
2
ijk
Dist =
(BV
ijk
− µ ck ) + (BVijl − µ cl )
2
2
Dist =
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.
(BV
ijk
ck
2
ijl
cl
− µ ck ) + (BVijl − µ cl )
2
2
e.g. the distance of point a to class forest is
Dist =
(40 − 39.1)2 + (40 − 35.5)2
= 4.6
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, and the pixel is then assigned to the class
for which the probability is the highest. probability
The
Theestimated
estimatedprobability
probabilitydensity
densityfunction
functionfor
forclass
classwwi i(e.g.,
(e.g.,forest)
forest)isiscomputed
computedusing
using
the
theequation:
equation:
⎡ 1 ( x − µˆ i )2 ⎤
exp ⎢−
pˆ ( x | wi ) =
⎥
2
1
2
ˆ
σi
⎦
(2π )2 σˆ i ⎣
1
where
er, xx
whereexp
exp[[]]isisee(the
(thebase
baseof
ofthe
thenatural
naturallogarithms)
logarithms)raised
raisedtotothe
thecomputed
computedpow
power,
isisone
the
xx-axis,
-axis, µ̂i isisthe
oneof
ofthe
thebrightness
brightnessvalues
valueson
on
the
theestimated
estimatedmean
meanof
ofall
allthe
thevalues
values
2
ˆ
σ
ininthe
e of
theforest
foresttraining
trainingclass,
class,and
and i isisthe
theestimated
estimatedvarianc
variance
ofall
allthe
themeasurements
measurementsinin
this
this class.
class. Therefore,
Therefore, we
we need
need toto store
store only
only the
the mean
mean and
and variance
variance ofof each
each training
training
class
ted with
class (e.g.,
(e.g., forest)
forest) toto compute
compute the
the probability
probability function
function associa
associated
with any
any ofof the
the
individual
valuesininit.
it.
individualbrightness
brightnessvalues
For
Formultiple
multiplebands
bandsof
ofremote
remotesensor
sensordata
datafor
forthe
theclasses
classesof
ofinterest,
interest,we
wecompute
computean
annndimensional
dimensionalmultivariate
multivariatenormal
normaldensity
densityfunction
functionusing:
using:
p( X | wi ) =
1
(2π )
n
2
| Vi |
1
2
⎤
⎡ 1
T
−1
(
)
(
)
exp ⎢− X − M i Vi X − M i ⎥
⎦
⎣ 2
Vi
−1
where
isisthe
isisthe
inverse
of
where
thedeterminant
determinantof
ofthe
thecovariance
covariancematrix,
matrix,
the
inverse
ofthe
the
(
)
X
−
M
T
i
covariance
. .The
covariancematrix,
matrix,and
and ( X − M i ) isisthe
thetranspose
transposeof
ofthe
thevector
vector
Themean
mean
vectors
vectors(M
(Mi)i)and
andcovariance
covariancematrix
matrix(V
(Vi)i)for
foreach
eachclass
classare
areestimated
estimatedfrom
fromthe
thetraining
training
data.
data.
| Vi |
IfIf we
we assume
assume that
that there
there are
are mm classes,
classes, then
then
p(X/w
p(X/wi)i) isis the
the probability
probability density
density function
function
associated
associated with
with the
the unknown
unknown measurement
measurement
vector
vectorX,
X,given
giventhat
thatXXisisfrom
fromaapattern
patternininclass
class
wwi. . InIn this
this case
case the
the maximum
maximum likelihood
likelihood
i
decision
decisionrule
rulebecomes:
becomes:
X
∈
w
i if, and only if,
Decide
Decide
if, and only if,
p( X | wi ) ⋅ p(wi ) ≥ p(X | w j )⋅ p(w j )
for
forall
alli iand
andj jout
outofof1,1,2,2,......mmpossible
possibleclasses.
classes.
Without Prior Probability Information:
Decide unknown measurement vector X is in
class i if, and only if,
pi > pj
for all i and j out of 1, 2, ... m possible classes
and
pi =
1
⎡1
⎤
T
−1
log e | Vi | − ⎢ ( X − M i ) Vi ( X − M i )⎥
2
⎣2
⎦
Therefore,
Therefore, toto classify
classify aa pixel
pixel inin the
the
multispectral
multispectral remote
remote sensing
sensing dataset
dataset with
with an
an
unknown
unknown measurement
measurement vector
vector X,
X, aa maximum
maximum
likelihood
likelihooddecision
decisionrule
rulecomputes
computesthe
theproduct
product
for
for each
each class
class and
and assigns
assigns the
the pattern
pattern toto the
the
class
classhaving
havingthe
thelargest
largestproduct.
product.This
Thisassumes
assumes
that
that we
we have
have some
some useful
useful information
information about
about
the
the prior
prior probabilities
probabilities ofof each
each class
class i i (i.e.,
(i.e.,
p(w
p(wi)).
)).
i
Unless you select a probability threshold (0-1),
all pixels are classified. Each pixel is assigned
to the class that has the highest probability
2.4 Mahalanobis Distance
†
M-distance is similar to the Euclidian distance
Dist =
( X − M i )T • V −1i • ( X − M 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)
2.5 Spectral Angle Mapper
2.6 Spectral Feature Fitting
†
†
compare the fit of image spectra to selected reference spectra
using a least-squares technique.
technique SFF is an absorption-featurebased methodology. The reference spectra are scaled to match
the image spectra after continuum removal from both data sets.
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.
Supervised
classification
method:
Spectral Feature
Fitting
Source: http://popo.jpl.nasa
.gov/html/data.html
3. Application:
LULC classification
†
Land cover refers to the type of material present on the
landscape (e.g., water, sand, crops, forest, wetland, humanmade materials such as asphalt).
†
Land use refers to what people do on the land surface (e.g.,
agriculture, commerce, settlement).
†
The pace, magnitude, and scale of human alterations of the
Earth’s land surface are unprecedented in human history.
Therefore, land-cover and land-use data are central to such
United Nations’ Agenda 21 issues as combating
deforestation, managing sustainable settlement growth, and
protecting the quality and supply of water resources.
USGS LULC levels
MODIS globe land cover product (1km)
†
Landcover:
MOD12Q1
(96 days)
†
Land cover
dynamics:
MOD12Q2
water 0
evergreen needleleaf forest 1
evergreen broadleaf forest 2
deciduous needleleaf forest 3
deciduous broadleaf forest 4
mixed forests 5
closed shrubland 6
open shrubland 7
woody savannas 8
savannas 9
grasslands 10
permanent wetlands 11
croplands 12
urban and built-up 13
cropland/natural vegetation mosaic 14
snow and ice 15
barren or sparsely vegetated 16
unclassified 254