Transcript Intro to Remote Sensing

Pixel-based image
classification
Lecture 8
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
…….
Example spectral plot
• Two bands of data.
• Each pixel marks a location in
this 2d spectral space
Band 2
• Our eye’s can split the data into
clusters.
• Some points do not fit clusters.
Band 1
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.

Advantages




Requires no prior knowledge of the region
Human error is minimized
Unique classes are recognized as distinct units
Disadvantages



Classes do not necessarily match informational
categories of interest
Limited control of classes and identities
Spectral properties of classes can change with
time


Distance Measures are used to group or
cluster brightness values together
Euclidean distance between points in space is
a common way to calculate closeness
K-means (unsupervised)
1.
2.
3.
4.
5.
A set number of cluster centers are
positioned randomly through the spectral
space.
Pixels are assigned to their nearest cluster.
The mean location is re-calculated for
each cluster.
Repeat 2 and 3 until movement of cluster
centres is below threshold.
Assign class types to spectral clusters.
Band 1
1. First iteration. The
cluster centers are set
at random. Pixels will
be assigned to the
nearest center.
Band 2
Band 2
Band 2
Example k-means
Band 1
2. Second iteration.
The centers move to
the mean-center of all
pixels in this cluster.
Band 1
3. N-th iteration. The
centers have
stabilized.
Band 1
1. Data is clustered but
blue cluster is very
stretched in band 1.
Band 2
Band 2
Band 2
Example ISODATA
Band 1
2.Cyan and green
clusters only have 2 or
less pixels. So they
will be removed.
Band 1
3. Either assign
outliers to nearest
cluster, or mark as
unclassified.
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)
Maximum Class Stdv (in pixel value). If the stdv of a class is larger than this threshold then the
class is split into two classes.
Minimum class distance (in pixel value) between class means. If the distance between two class
means is less than the minimum value entered, then ENVI merges the classes.
Optional Maximum stdev from mean (1 to 3σ) and maximum distance error (in pixel value). If
any of these two setup, the some pixels might not be classified.
5-10 classes, 8 iterations, 5 for change threshold, (MinP 5, MaxSD 1, MinD 5, MMP 2)
1-5 classes, 11 iterations, 5 for change threshold, (MinP 5, MaxSD 1, MinD 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

Advantages




Analyst has control over the selected classes
tailored to the purpose
Has specific classes of known identity
Does not have to match spectral categories on the
final map with informational categories of
interest
Can detect serious errors in classification if
training areas are missclassified

Disadvantages


Analyst imposes a classification (may not be
natural)
Training data are usually tied to informational
categories and not spectral properties




Remember diversity
Training data selected may not be representative
Selection of training data may be time consuming
and expensive
May not be able to recognize special or unique
categories because they are not known or small
Statistic extraction of each training site
Each pixel in each training site associated with a particular class (c) is
represented by a measurement vector, Xc; Average of all pixels in a training
site called mean vector, Mc; a covariance matrix of Vc.
 BVi , j ,1 


BV
 i, j,2 
 BV 
X c   i , j ,3 
.



.


 BVi , j ,k 


 c1 
 
 c2 
c3 
Mc   
. 
. 
 
 ck 
cov c11 cov c12 ... cov c1k 
cov cov ... cov 
c 22
c 2k 
 c 21

Vc  .


.

cov ck1 cov ck 2 ... cov ckk 


where BVi,j,k is the brightness value for the i,jth pixel in band k.
µck represents the mean value of all pixels obtained for class c in band k.
Covckl is the covariance of class c between bands l through k.
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.
 ck   ck  BVijk   ck   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 1-3
This method is a computationally efficient method. But an unknown pixel might meet the
criteria of more than one class and is always assigned to the first class for which it meets
all criteria. The Minimum Distance to Means can assign any pixel to just one class.
Parallelepiped example
Training classes plotted in spectral space.
In this example using 2 bands.
Parallelepiped example
continued
•Each class type defines a spectral
box
•Note that some boxes overlap even
though the classes are spatially
separable.
•This is due to band correlation in
some classes.
•Can be overcome by customising
boxes.
1 means 1 stdev from mean, 2 means 2 stdev from mean, 3 means 3 stdev from mean;
Use 1, you will classify the closest pixels to the class
Use 3, you will include some not so closest pixels to the class
2.2 Minimum distance
The distance used in a minimum
distance to means classification
algorithm can take two forms: the
Dist  BV
    BV
   on the
Euclidean
distance
based
Pythagorean theorem and the
“round the block” distance. The
Euclidean distance is more
computationally intensive, but it is
more frequently used
2
ijk
Dist 
BV
 ck   BVijl  cl 
2
ijk
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
ck
cl
 ck   BVijl  cl 
2
ijk
2
ijl
2
e.g. the distance of point a to class forest is
Dist 
40  39.12  40  35.52  4.6
If either Max stdev or Max distance error is not set, all pixels will be classified.
If the Max stdev from mean is set at 2 (stdev), then the pixels with values
outside the mean ± 2σ will not be classified.
If the Max distance error is set at 4.2 (pixel value), then the pixels with distance
larger than 4.2 will not be classified.
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 based on a normal probability density
function, and the pixel is then assigned to the class for which the
probability is the highest. probability
The estimated probability density function for class wi (e.g., forest) is computed using
the equation:
 1  x  ˆ i 2 
pˆ  x | wi  
exp 

1
2
2
ˆ
i

2 2 ˆ i 
1
where exp [ ] is e (the base of the natural logarithms) raised to the computed power, x
is one of the brightness values on the x-axis, ̂ i is the estimated mean of all the values
2
in the forest training class, and ˆ i is the estimated variance of all the measurements in
this class. Therefore, we need to store only the mean and variance of each training
class (e.g., forest) to compute the probability function associated with any of the
individual brightness values in it.
For multiple bands of remote sensor data for the classes of interest, we compute an ndimensional multivariate normal density function using:
p X | wi  
1
2 
n
2
| Vi |
1
2
 1

T
1
exp   X  M i  Vi  X  M i 
 2

1
where
is the determinant of the covariance matrix,
is the inverse of the
covariance matrix, and  X  M i T is the transpose of the vector  X  M i  . The mean
vectors (Mi) and covariance matrix (Vi) for each class are estimated from the training
data.
| Vi |
Vi
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

The assign the measurement vector X of
an unknown pixel to a class, the
maximum likelihood decision rule
computers the value pi for each class.
Then it assigns the pixel to the class that
has the largest value
Unless you select a probability threshold (0-1),
all pixels are classified. Each pixel is assigned
to the class that has the highest probability
Probability threshold from [0, 1]. 0 means zero probability of
similarity, 1 means 100% probability of similarity.
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 reflectance spectra to selected
reference reflectance spectra using a least-squares technique.
SFF is an absorption-feature-based methodology. Both
reflectance spectra should be continuum removed.
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.
Least square tech (regression)

A continuum is a mathematical function used
to isolate a particular absorption feature for
analysis
Supervised
classification
method:
Spectral Feature
Fitting
Source: http://popo.jpl.nasa
.gov/html/data.html