Robotics 2 AdaBoost for People and Place...
Transcript of Robotics 2 AdaBoost for People and Place...
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Giorgio Grisetti, Cyrill Stachniss,
Kai Arras, Wolfram Burgard
Robotics 2 AdaBoost for People and Place Detection
v.1.0, Kai Arras, Oct 09, including material by Luciano Spinello and Oscar Martinez Mozos
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Contents
Motivation
AdaBoost
Boosting Features for People Detection
Boosting Features for Place Labeling
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People tracking is a key technology for many problems and robotics-related fields:
People detection is a key component therein.
Motivation: People Detection
Human-Robot-Interaction (HRI)
Social Robotics: social learning, learning by imitation and observation
Motion planning in populated environments
Human activity and intent recognition
Abnormal behavior detection
Crowd behavior analysis and control
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Motivation: People Detection
Where are the people?
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Motivation: People Detection
Where are the people?
Why is it hard?
Range data contain little information on people
Hard in cluttered environments
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Motivation: People Detection
Appearance of people in range data changes drastically with: - Body pose - Distance to sensor - Partial occlusion and self-occlusion
2d data from a SICK laser scanner
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Motivation: People Detection
Appearance of people in range data: 3d data from a Velodyne sensor
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Motivation: People Detection
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Motivation: People Detection
Freiburg main station
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Motivation: People Detection
Freiburg Main Station data set: raw data
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Motivation: People Detection
Freiburg Main Station data set: labeled data
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Motivation: People Detection
Freiburg Main Station data set: labeled data
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Contents
Motivation
AdaBoost
Boosting Features for People Detection
Boosting Features for Place Labeling
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Boosting
Supervised Learning technique user provides <input data x, label y>
Learning an accurate classifier by combining moderately inaccurate “rules of thumb”
Inaccurate rules: weak classifiers
Accurate rule: strong classifier
Most popular algorithm: AdaBoost [Freund et al. 95], [Schapire et al. 99]
AdaBoost in Robotics:
[Viola et al. 01], [Treptow et al. 04], [Martínez-Mozos et al. 05], [Rottmann et al. 05] , [Monteiro et al. 06] , [Arras et al. 07]
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AdaBoost
What AdaBoost can do for you:
1. It tells you what the best "features" are
2. What the best thresholds are, and
3. How to combine this to a classifier
It's a non-linear classifier
Robust to overfitting
Very simple to implement
Classifier design becomes science, not art
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A machine learning ensemble technique (also called committee methods)
There are other ensemble technique such as Bagging, Voting etc.
Combines an ensemble of weak classifiers (weak learners) to create a strong classifier
Prerequisite: weak classifier better than chance, that is, error < 0.5 (in a binary classification problem)
AdaBoost
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Classification
Linear vs Non-Linear Classifier
NL L
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Classification
Overfitting
Overfitting occurs when a model begins to memorize the training data rather than learning the underlying relationship
Occurs typically when fitting a statistical model with too many parameters
Overfitted models explain training data perfectly
But: model does not generalize!
There are techniques to avoid overfitting such as regularization or cross- validation
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Error types
Sensivity (True Positive Rate) = TP / T
Specificity (True Negative Rate) = TN / N
many more measures...
Classification
True Positive False Positive
False Negative True Negative
True value
Pred
icte
d v
alue
of
the
clas
sifier
T'
N'
T N
Detected Not Detected
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Classification
Classification algorithms are supervised algorithms to predict categorical labels
Differs from regression which is a supervised technique to predict real-valued labels
Formal problem statement:
Produce a function that maps
Given a training set labels
values
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Alternatives
Decision stump: Single axis-parallel partition of space
Decision tree: Hierarchical partition of space
Multi-layer perceptron: General non-linear function approximators
Radial basis function: Non-linear expansions based on kernels
AdaBoost: Weak Classifier
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Decision stump
Simple-most type of decision tree
Equivalent to linear classifier defined by affine hyperplane
Hyperplane is orthogonal to axis with which it intersects in threshold θ
Commonly not used on its own
Formally,
where x is training sample, j is dimension
AdaBoost: Weak Classifier
€
h(x; j,θ) =+1 x j > θ
−1 else
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Given the training data
1. Initialize weights
2. For m = 1,...,M
• Train a weak classifier on weighted training data minimizing
• Compute error of :
• Compute voting weight of :
• Recompute weights:
3. Make predictions using the final strong classifier
AdaBoost: Algorithm
€
wi =1 n
€
hm (x)
€
hm (x)
€
hm (x)
€
αm = log(1− emem
)
€
wi = wi exp αm ⋅ Ι(yi ≠ hm (xi){ }€
em = wi Ι(yi ≠ hm (xi))i=1
n
∑ wii=1
n
∑€
Σi wi Ι(yi ≠ hm (xi))
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Computing the voting weight of a weak classifier
AdaBoost: Strong Classifier
€
α m
error
€
αm = log(1− emem
)
€
α m
chance: em= 0.5
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Training is completed...
The weak classifiers and their voting weight are now fix
The resulting strong classifier is
Weighted majority voting scheme
AdaBoost: Strong Classifier
€
H(xi) = sgn αmhm (xi)m=1
M
∑
Put your data here
Class Result {+1, -1}
€
h1...M (x)
€
α 1....M
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Train a decision stump on weighted data
This consists in...
Finding an optimum parameter θ* for each dimension j =1…d and then select the j* for which the cost is minimal.
AdaBoost: Weak Classifier
€
( j*, θ*) = argmin j ,θ
wi Ι(yi ≠ hm (xi))i=1
n
∑
wii=1
n
∑
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∀ j = 1...d
Sort samples xi in ascending order along dimension j
∀ i = 1...n Compute n cumulative sums
end
Threshold θj is at extremum of
Sign of extremum gives direction pj of inequality
end
Global extremum in all d sums gives threshold θ* and dimension j*
A simple training algorithm for stumps:
AdaBoost: Weak Classifier
€
wcumj (i) = wk yk
k=1
i
∑
€
wcumj
€
wcum
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Training algorithm for stumps: Intuition
Label y : red: + blue: –
Assuming all weights = 1
AdaBoost: Weak Classifier
€
θ*, j* = 1
€
wcumj (i) = wk yk
k=1
i
∑
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Given the training data
1. Initialize weights
2. For m = 1,...,M
• Train a weak classifier on weighted training data minimizing
• Compute error of :
• Compute voting weight of :
• Recompute weights:
3. Make predictions using the final strong classifier
AdaBoost: Algorithm
€
wi =1 n
€
hm (x)
€
hm (x)
€
hm (x)
€
αm = log(1− emem
)
€
wi = wi exp αm ⋅ Ι(yi ≠ hm (xi){ }€
em = wi Ι(yi ≠ hm (xi))i=1
n
∑ wii=1
n
∑€
Σi wi Ι(yi ≠ hm (xi))
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Training data
AdaBoost: Step-By-Step
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Iteration 1, train weak classifier 1
AdaBoost: Step-By-Step
Threshold θ* = 0.37
Dimension j* = 1
Weighted error em = 0.2
Voting weight αm = 1.39
Total error = 4
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Iteration 1, recompute weights
AdaBoost: Step-By-Step
Threshold θ* = 0.37
Dimension j* = 1
Weighted error em = 0.2
Voting weight αm = 1.39
Total error = 4
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Iteration 2, train weak classifier 2
AdaBoost: Step-By-Step
Threshold θ* = 0.47
Dimension j* = 2
Weighted error em = 0.16
Voting weight αm = 1.69
Total error = 5
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Iteration 2, recompute weights
AdaBoost: Step-By-Step
Threshold θ* = 0.47
Dimension j* = 2
Weighted error em = 0.16
Voting weight αm = 1.69
Total error = 5
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Iteration 3, train weak classifier 3
AdaBoost: Step-By-Step
Threshold θ* = 0.14
Dimension, sign j* = 2 , neg
Weighted error em = 0.25
Voting weight αm = 1.11
Total error = 1
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Iteration 3, recompute weights
AdaBoost: Step-By-Step
Threshold θ* = 0.14
Dimension, sign j* = 2 , neg
Weighted error em = 0.25
Voting weight αm = 1.11
Total error = 1
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Iteration 4, train weak classifier 4
AdaBoost: Step-By-Step
Threshold θ* = 0.37
Dimension j* = 1
Weighted error em = 0.20
Voting weight αm = 1.40
Total error = 1
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Iteration 4, recompute weights
AdaBoost: Step-By-Step
Threshold θ* = 0.37
Dimension j* = 1
Weighted error em = 0.20
Voting weight αm = 1.40
Total error = 1
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Iteration 5, train weak classifier 5
AdaBoost: Step-By-Step
Threshold θ* = 0.81
Dimension j* = 1
Weighted error em = 0.28
Voting weight αm = 0.96
Total error = 1
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Iteration 5, recompute weights
AdaBoost: Step-By-Step
Threshold θ* = 0.81
Dimension j* = 1
Weighted error em = 0.28
Voting weight αm = 0.96
Total error = 1
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Iteration 6, train weak classifier 6
AdaBoost: Step-By-Step
Threshold θ* = 0.47
Dimension j* = 2
Weighted error em = 0.29
Voting weight αm = 0.88
Total error = 1
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Iteration 6, recompute weights
AdaBoost: Step-By-Step
Threshold θ* = 0.47
Dimension j* = 2
Weighted error em = 0.29
Voting weight αm = 0.88
Total error = 1
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Iteration 7, train weak classifier 7
AdaBoost: Step-By-Step
Threshold θ* = 0.14
Dimension, sign j* = 2 , neg
Weighted error em = 0.29
Voting weight αm = 0.88
Total error = 1
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Iteration 7, recompute weights
AdaBoost: Step-By-Step
Threshold θ* = 0.14
Dimension, sign j* = 2 , neg
Weighted error em = 0.29
Voting weight αm = 0.88
Total error = 1
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Iteration 8, train weak classifier 8
AdaBoost: Step-By-Step
Threshold θ* = 0.93
Dimension, sign j* = 1 , neg
Weighted error em = 0.25
Voting weight αm = 1.12
Total error = 0
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Iteration 8, recompute weights
AdaBoost: Step-By-Step
Threshold θ* = 0.93
Dimension, sign j* = 1 , neg
Weighted error em = 0.25
Voting weight αm = 1.12
Total error = 0
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Final Strong Classifier
AdaBoost: Step-By-Step
Total error = 0!
(rarely met in practice)
Colored back-ground dots in figure is test set.
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Misclassified samples receive higher weight. The higher the weight the "more attention" a training sample gets
Algorithm generates weak classifier by training the next learner on the mistakes of the previous one
Now we also understand the name: adaptive Boosting → AdaBoost
Once training is done, AdaBoost is a voting method
Large impact on ML community and beyond
AdaBoost: Wrap Up
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Contents
Motivation
AdaBoost
Boosting Features for People Detection
Boosting Features for Place Labeling
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Problem and Approach
Can we find robust features for people, legs and groups of people in 2D range data?
What are the best features for people detection?
Can we find people that do not move?
Approach:
Classifying groups of adjacent beams
Computing a set of simple (scalar) features on these groups
Boosting the features
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Related Work
People Tracking [Fod et al. 2002] [Kleinhagenbrock et al. 2002] [Schulz et al. 2003] [Scheutz et al. 2004] [Topp et al. 2005] [Cui et al. 2005] [Schulz 2006] [Mucientes et al. 2006]
SLAM in dyn. env.
[Montemerlo et al. 2002] [Hähnel et al. 2003] [Wang et al. 2003] ...
People detection done with very simple classifiers: manual feature selection, heuristic thresholds
Typically: narrow local-minima blobs that move
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Segmentation
Divide the scan into segments
"Range image segmentation"
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Segmentation
Feature profiles
Segmented scan Raw scan
Method: Jump distance condition See [Premebida et al. 2005] for survey
Size filter: rejection of too small segments
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Segmentation
Feature profiles
Segmented scan Raw scan
Method: Jump distance condition See [Premebida et al. 2005] for survey
Size filter: rejection of too small segments
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Segmentation
Feature profiles
Segmented scan Raw scan
Method: Jump distance condition See [Premebida et al. 2005] for survey
Size filter: rejection of too small segments
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Features
Segment
1. Number of points
2. Standard Deviation
3. Mean avg. deviation from median
4. Jump dist. to preceding segment
5. Jump dist. to succeeding segment
6. Width
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Features
Segment
7. Linearity
8. Circularity
9. Radius
rc
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Features
Segment
10. Boundary Length
11. Boundary Regularity
12. Mean curvature
13. Mean angular difference
14. Mean speed
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Features
Resulting feature signature for each segment
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Training: Data Labeling
Mark segments that correspond to people
Either manually or automatically
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Training: Data Labeling
Automatic labeling: obvious approach, define area of interest
Here: discrimination from clutter is interesting. Features include spatial relation between fore- and background. Thus: labeling is done by hand
4 m
3 m
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Training
Resulting Training Set
Segments corresponding to people
(foreground segments)
Segments corresponding to other objects
(background segments)
+1 -1
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Each binary weak classifier hj(x) is created using a single-valued feature fj in the form:
Where θj is a threshold and pj ∈ {-1, 1} indicates the direction of the inequality
Weak classifier must be better than random
AdaBoost: Weak Classifiers
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example1 . . . exampleN
Boosting
f#1 . . . f#14
w1 h1
wT hT
Σ
Weighted majority vote classifier
{-1,1} . . .
Strong Binary Classifier
Vocabulary of features
AdaBoost: Final Strong Classifier
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Experiments
Env. 1: Corridor, no clutter
Env. 2: Office, very cluttered
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Experiments
Env. 1 & 2: Corridor and Office
Env. 1→2: Cross-evaluation Trained in corridor, applied in office
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Experiments
Adding motion feature (mean speed, f#14)
→ Motion feature has no contribution
Experimental setup:
Robot Herbert
SICK LMS 200 laser range finder, 1 deg angular resolution
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Experiments
Comparison with hand-tuned classifier
Jump distance θδ = 30 cm
Width θw,m = 5 cm, θw,M = 50 cm
Number of points θn = 4
Standard deviation θσ = 50 cm
Motion of points θv = 2 cm
People are often not detected
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Experiments
Five best features:
1: Radius of LSQ-fitted circle, robust size measure (#9)
2: Mean angular difference Convexity measure (#13)
3/4: Jump distances Local minima measure (#4 and #5)
5: Mad from median Robust compactness measure (#3)
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Result: Classification T F
T
F
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Summary
People detection phrased as a classification problem of groups of neighboring beams
AdaBoost allows for a systematic approach to perform this task
One-shot/single-frame people detection with over 90% accuracy
Learned classifier clear superior to hand-tuned classifier
No background knowledge such as an a priori map is needed (e.g. to perform background substraction)
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Contents
Motivation
AdaBoost
Boosting Features for People Detection
Boosting Features for Place Labeling
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Place Labeling: Motivation
A map is a metric and topological model of the environment
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Place Labeling: Motivation
Room
Corridor Doorway
Wanted: semantic information about places
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Scenario Example
I am in the corridor
Albert, where are you?
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Scenario Example 2
Semantic mapping
Human-Robot Interaction of type: "Robot, get out of my room, go into the corridor!"
Room Corridor
Doorway
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Problem Statement
Classification of the position of the robot using a single observation: a 360° laser range scan
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Observations
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Observations
Room Room
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Observations
Room Room
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Observations
Room Room Doorway Doorway
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Observations
Room Room Doorway Doorway
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Observations
Room Room Corridor Corridor Doorway Doorway
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Similar Observations
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Similar Observations
Corridor Doorway
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Classification Problem
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Classification Problem
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Classification Problem
Room Room Corridor Corridor Doorway Doorway
?
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Representing the Observations
How we represent the 360 laser beams for our classification task?
As a list of beams Problem: which beam is the first beam?
Not invariant to rotation!
!=
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Representing the Observations
A list of scalar geometrical features of the scan
The features are all invariant to rotation
=
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Simple Features
• Gap = d > θ • f = # Gaps
Minimum
• f =Area • f =Perimeter • f = d
d di d
• f = d •
d
Σ di
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Simple Features
Features of the raw beams
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Simple Features
Features of the closed polynom P(z) made up by the beams
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Multiple Classes
Room Room Corridor Corridor Doorway Doorway 1 3 2
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Multiple Classes
Room Room Corridor Corridor Doorway Doorway 1 3 2
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Multiple Classes
Sequence of binary classifiers in a decision list
Order matters as accuracy differs Order according to error rate Generalizes to sequential AdaBoost for K classes
Corridor Classifier
Room Classifier
H(x)=–1 H(x)=–1
H(x)=1 H(x)=1
Corridor Corridor Room Room
Doorway Doorway
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Experiments Training (top) # examples:
16045
Test (bottom) # examples:
18726 classification: 93.94%
Building 079 Uni. Freiburg
Room Room Corridor Corridor Doorway Doorway
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Training (left) # examples:
13906
Test (right) # examples:
10445 classification: 89.52%
Building 101 Uni. Freiburg
Room Room Corridor Corridor Doorway Doorway Hallway Hallway
Experiments
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Application to New Environment
Training map
Intel Research Lab in Seattle
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Application to New Environment
Training map
Intel Research Lab in Seattle
Room Room Corridor Corridor Doorway Doorway
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Training
Learn a strong classifier from a set of previously labeled observations
AdaBoost
Multi-class Classifier
Room Room Corridor Corridor Doorway Doorway
features features features features features features