Automatic Geomorphic Mapping
of Mars Using Pattern
Recognition
Ricardo Vilalta
Dept. of Computer Science
University of Houston
Collaborators:
Planetary Scientist: Tomasz Stepinski
Lunar and
Planetary Institute
Graduate Student: Soumya Ghosh
Dept. of Computer Science
University of Houston
Automatic Geomorphic Mapping
of Mars Using Pattern
Recognition
• Basic concepts in pattern recognition
• Pattern recognition for Mars analysis
• Semi-supervised learning and metalearning
A Particular Example
™ Fish packing plant
™ Sort incoming fish on a belt according to two classes:
™ Salmon or
™ Sea Bass
Steps:
a) Preprocessing (segmentation)
b) Feature extraction (measure features or properties)
c) Classification (make final decision)
Figure 1.1
Histograms
We decide to use “length” as the first feature.
Classification is then easy:
Decide Salmon if length l < l*
Decide Sea Bass if length l > l*
(l* : critical threshold)
Some features may give poor results.
Part of the design of pattern recognition systems
is to find the right features to discriminate between classes.
What if we try lightness of fish scales?
Figure 1.2
Figure 1.3
Figure 1.4
Figure 1.5
Figure 1.6
Classification and Clustering
Classification: A function to predict the class of new examples
Let X be the space of possible examples
Let Y be the space of possible classes
Learn F : X
Y
Clustering: Find natural groups on unlabeled data
Let X be the space of possible examples
Let S be a sample of X
Find natural groups on S
Application 1
Automatic car drive (ALVINN 1989)
Train computer- controlled vehicle to steer correctly when
driving on a variety of road types.
computer
(learning algorithm)
class 2
class 1
steer to the right
steer to the left
class 3
continue straight
Application 2
Learning to classify astronomical structures.
galaxy
stars
Features:
o Color
o Size
o Mass
o Temperature
o Luminosity
unkown
Other Applications
ƒ Bio-Technology
ƒ Protein Folding Prediction
ƒ Micro-array gene expression
ƒ Computer Systems Performance Prediction
ƒ Banking Applications
ƒCredit Applications
ƒ Fraud Detection
ƒ Character Recognition (US Postal Service)
ƒ Web Applications
ƒ Document Classification
ƒ Learning User Preferences
Automatic Geomorphic Mapping
of Mars Using Pattern
Recognition
• Basic concepts in pattern recognition
• Pattern recognition for Mars analysis
• Semi-supervised learning and metalearning
Objective: automated creation of
geomorphic maps.
Martian landscape
Geomorphic map
shows landforms
chosen and
defined by a
domain expert.
Digital Elevation Map
Manually drawn geomorphic map of this landscape
Geomorphic Map
Definitions:
• Landscape:
• Landforms:
Background: Representation.
• Represent the surface of Mars as a quantized
rectangular space composed of pixels.
P1,1 P1,2 ....... P1,n
F1 …. …. ….. Fn
....... …… …… …..
…… …… …… ……
Pn,1 …… …… Pn,n
Pij represent pixels.
Fi represents features.
Previous Work.
• Each pixel has 6 features
• Clustering of pixels using
EM.
• The number of clusters is
calculated using crossvalidation.
• Landform categories are
identified with clusters.
Stepinski & Vilalta, “Digital Topography Models for Martian Surfaces”,
IEEE Geoscience and Remote Sensing Letters, 2(3), p260., 2005
Previous work # 1: results
• 12 resultant clusters
• Each cluster given a posteriori meaning by domain expert.
• After meaning is assigned 12 clusters are grouped into 4 superclusters based on meaning.
Previous work # 2: results
• Each pixel has 6 features
• Clustering of pixels using combination of selforganizing map (SOM) and the Ward
hierarchical clustering method.
• The number of clusters is chosen to be 20.
• Landform categories are identified with
clusters.
Bue & Stepinski, “Automated Classification of Landforms on Mars”,
IEEE Computers & Geoscience, 32, p604., 2006
Automatic generation of geomorphic
maps: unsupervised vs. supervised
learning
Clustering
•
•
•
•
Practical to use a pixel as a
basic unit .
Semantic meaning of resultant
landforms must be assigned a
posteriori by a domain expert.
Results in “general purpose”
geomorphic map with broadly
defined semantic meanings of
landforms.
Resultant map is not similar to
conventional geomorphic map.
Classification
•
•
•
•
Pixel is not a practical basic unit,
instead one should use bigger
segments.
Semantic meaning of resultant
landforms is assigned a priori by
a domain expert during a training
phase.
Results in “focused” geomorphic
map with narrowly defined
semantic meanings of landforms.
Resultant map is similar to
conventional geomorphic map.
Our Approach:
Pixel based
topographic
data
Segmentation
Object based
topographic
data
(DEMs)
Geomorphic
Map(s)
Supervised
Learning
Segmentation
Segmentation: Features.
Digital Elevation Map
Slope (Feature 1)
Curvature (Feature 2)
Flood (Feature 3)
Segmentation: Results.
2631 segments
homogeneous in
slope, curvature
and flood.
Displayed on an elevation background.
Segmentation: Results.
Landforms of Interest (Classes):
ƒCrater Floor.
ƒCrater Wall.
ƒConvex
ƒConcave
ƒFlat Plain.
ƒRidge.
ƒConvex
ƒConcave
Classification: Labeling.
• A representative subset
of objects are labeled as
one of the following six
classes:
– Plain
– Crater Floor
– Convex Crater Walls
– Concave Crater Walls
– Convex Ridges
– Concave Ridges
517 labeled segments.
Classification: Results.
– Plain
– Crater Floor
– Convex Crater
Walls
– Concave Crater
Walls
– Convex Ridges
– Concave Ridges
Perspective View.
Test Site: EvrovallisW.
Classification: Results.
– Plain
– Crater Floor
– Convex Crater
Walls
– Concave Crater
Walls
– Convex Ridges
– Concave
Ridges
Classification Performance
• Produce similar
accuracies. Difficult to
say which map is better.
• Maps are different.
Algorithm
Accuracy
SVM
84.61(4.89)
Bagging
83.02(5.30)
k-NN
78.77(5.15)
Automatic Geomorphic Mapping of
Mars Using Pattern Recognition
• Basic concepts in pattern recognition
• Pattern recognition for Mars analysis
• Semi-supervised learning and
meta-learning
Semi-supervised Learning
Different from supervised learning, the semi-supervised learning
scheme enables us to exploit segments that are both labeled and
unlabeled.
Labeled segments
Data Analysis
Unlabeled segments
Semi-supervised Learning
Common Assumption (Smoothness Assumption):
Knowledge of the distribution of unlabeled data carries
information about the posterior class probability P(y|x).
Any points close in X should be expected to have similar
output values Y.
Meta-Learning
Learning-to-Learn:
Model
Family of Models
Adapt to new landscapes.
Use model parameters on one landscape to learn to classify
landforms in other landscapes.
Meta-Learning
Training 2 (using knowledge
from training 1)
Training 1
Knowledge Transfer
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