lecture 14: classification thursday 19 february reading: “estimating sub-pixel surface roughness...
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Lecture 14: Classification
Thursday 19 February
Reading:“Estimating Sub-pixel Surface Roughness Using Remotely Sensed Stereoscopic Data” pdf preprint for RSE available on class website
Last lecture: Spectral Mixture Analysis
Classification vs.Spectral Mixture Analysis
In SMA, image pixels were regarded as being mixed from various proportions of common materials. The goal was to find what those materials were in an image, and what their proportions were pixel by pixel.
In classification, the image pixels are regarded as grouping into thematically and spectrally distinct clusters (in DN space). Each pixel is tested to see what group it most closely resembles. The goal is to produce a map of the spatial distribution of each theme or unit.
Forests – group 2
Water – group 1
Desert – group 3
=2
=48
=60
Multi-unit veg map
AVHRR Images with pixels similar to vegetation flagged according to distance
at different tolerances
What is spectral similarity?
X
Y
xA
B
Spectral distance: Spectral angle:
Spectral contrast between similar objects is small
Manual Classification
Seattle
1) association by spectral similarity of pixels into units
2) naming those units, generally using independent information- reference spectra
- field determinations- photo-interpretation
Basic steps in image classification:
1) Data reconnaissance and self-organization
2) Application of the classification algorithm
3) Validation
Reconnaissance and data organization
Reconnaissance What is in the scene?What is in the image?What bands are available?What questions are you asking of the image?Can they be answered with image data?Are the data sufficient to distinguish what’s in the scene?
Organization of dataHow many data clusters in n-space can be recognized?What is the nature of the cluster borders?Do the clusters correspond to desired map units?
UnsupervisedUnsupervised
Separate DataInto Groups
With Clustering
Classify DataInto Groups
Assign NameTo Each Group
Satisfactory?
Yes
No
Form ImagesOf Data
Choose TrainingPixels For
Each Category
CalculateStatistical
Descriptors
Satisfactory?
Classify DataInto Categories
Defined
Yes
No
SupervisedSupervised
Classification algorithmsClassification algorithms
Unsupervised Classification:K-Means algorithm
Pick number of themes; set distance tolerance° 1st pixel defines 1st theme° is 2nd pixel within tolerance?
- YES: redefine theme- NO: define 2nd theme
° Interrogate 3rd pixel…
° Iterate, using “found” themes as the new seed
How do you estimate thenumber of themes? - can be greater than number of bands
•Parallelipiped
•Minimum Distance
•Maximum Likelihood
•Decision-Tree
+x
““Hard” vs. “soft” classificationHard” vs. “soft” classification
Hard: winner take allSoft: “answer” expressed as probability x belongs to A, B
“Fuzzy” classification is very similar to spectral unmixing
Supervised Classification: What are some algorithms?
Parallelepiped Classifier
Assigns a DN range in each band for each class (parallelepiped)
Advantages: simple
Disadvantages: low accuracy - especially when the distribution in feature space has covariance or dependency with oblique axes.
Minimum-Distance Classifier
Uses only the mean of each class. The unknown pixel is classified using its distance to each of the class means. The shortest distance wins.
Decisionboundaries
Maximum Likelihood
The most commonly used classifier used. A pixel is assigned to the class based on statistical probability.
Based on statistics (mean; covariance)
A (Bayesian) probability function is calculated from the inputs for classes established from training sites.
Each pixel is then judged as to the class to which it most probably belong.
Maximum Likelihood
For each DN ntuple in the image, 1) calculate the distance to each cluster mean
2) scale by the number of standard deviations in the direction of the ntuple from the mean
3) construct rule images, pixel by pixel for each cluster, in which the number of std dev’s is recorded
4) threshold the rule images (null pixels too far from a cluster)
5) pick best match (least number of std dev’s and record it in the appropriate pixel of the output , image or map
Decision-Tree Classifier
Hierarchical classifier compares the data sequentially with carefully selected features.
Features are determined from the spectral distributions or separability of the classes.
There is no general procedure. Each decision tree or set of rules is custom-designed.
A decision tree that provides only two outcomes at each stage is called a “binary decision tree” (BDT) classifier.
One goal: reduce impact of topography on outcome
ratioing
NDVI
Spectral angle
Pre-processing - dimension transformation
Line of constant ratio
y
x
x/y
y/z
A
B
BA
Validation
PhotointerpretationLook at the original data:
does your map make sense to you?
Confusion matricesWell-named. Also known as contingency tables or error matricesHere’s how they work…
Training areasA B C D E F
A
B
C
D
EF
Cla
ssif
ied
data
Col sums
Row sums
Grand sum
All non diagonal elementsare errors
Row sums give “commission”errors
Column sums give “omission” errors
Overall accuracy is the diagonal sum over the grand total
This is the assessment only for the training areas
What do you do for the rest of the data?
p 586, LKC 6th
480 0 5 0 0 0 485
0
0
0
0
0
0
0
0
480
52
16
68 1992
0 20 0 0 72
A basic problem with classification
What’s actually on the ground –all three look similar (A) because they are grassy
meadow
golf course
cemetary
Mystery pixel X
is found to be spectrally similar to:
Theme A = grass
We tend to want to classify by land use, and from the remote sensing perspective this may lead to ambiguity
= bear habitat
≠ bear habitat
≠ bear habitat
I want to find bears. Bears like meadows. I train on a meadow (Theme A) and classify an image to see where the bears are. Pixel X is classified as similar to A. Will I find bears there?
Maybe not. 1) they might be somewhere else even they like the meadow. 2) What a meadow is from the RS perspective is a high fraction of GV. Other things share this equivalence. Therefore, X may indeed belong to A spectrally, but not according to use.
Thought exercise: what would you need to do in order to classify by land use?
Next class: Relative dating of surfaces on Mars – counting craters(Matt Smith, ESS)