2. Outline
• Motivation and Problem Statement (2 min)
• Past Progress (8 min)
• New Work (30 min)
– Key elements
– Illustrative results/plots
– New insights
– Key questions still to be answered
• Lit Review (14 min)
– give more detailed overview of only one paper (10min)
– list out four others (1 min each)
• Discussion and Feedback (2 hrs!)
2
3. Motivation and Problem Statement
• How do you effectively produce a 3D map when
sensor measurements are:
– Sparse
– Noisy
• The map will be:
– Complete, info is well exploited
– Compact: representation is small
• Metrics:
– Map Quality
– Extra Voxels
– Storage
3
4. Past Progress
• Utilize patches defined within a cell, with variable
length
• Defined association as product of:
– Prob of belonging to cell
‣ Integral of in-plane distribution of meas within cell
– Prob of belonging to patch, given it belongs to cell
‣ P = 1 – chi2cdf(x,1), where x = (elevation distance to
patch)^2/variance
• Created additional elevation-only variance on
measurement, SigU, as tunning parameter
– Determine way of picking SigU as function of noise/cell-size
ratio
4
5. Past Progress
• Pro:
– Produced better performance than previous work
• Con:
– Limited to information sparsity
‣ Prevented single-patch simpler representation
– Seriously limited by cell-representation
‣ 10x10 cell floor produces at least 10x10 patches!!! Should be
ONE!
5
6. New Work
• Utilize GP
– To fill in information such as probability of space between
patches being occupied -> patch fusion! -> more compact
representation
• SuperPatch (Spatch) Definition:
– Patch that is not contained within a cell, but is defined to
contain more than one cell!
• Questions:
– How do we create and update Spatches?
– How do we simplify patches into Spatches (patch fusion)?
– How do we break Spatches if necessary?
– How do we assign measurements to Spatches?
– How do we utilize GP to influence assignment accordingly?
‣ Define P_GP that is not patch-size dependent!
6
7. New Work
• Utilize GP
– To fill in information such as probability of space between
patches being occupied -> patch fusion! -> more compact
representation
• SuperPatch (Spatch) Definition:
– Patch that is not contained within a cell, but is defined to
contain more than one cell!
• Questions:
– How do we create and update Spatches?
– How do we simplify patches into Spatches (patch fusion)?
– How do we break Spatches if necessary?
– How do we assign measurements to Spatches?
– How do we utilize GP to influence assignment accordingly?
‣ Define P_GP that is not patch-size dependent!
7
8. New Work: Answers to questions – Patch
Fusion
• How do we create and update Spatches?
– Spatches are created via horizontal patch fusion
• How do we fuse patches into Spatches (patch fusion)?
– Determine which patches are enclosing similar vertical
spaces in near cell-vicinity, and calculate if average prob of
occupied space is large enough.
8
9. New Work: Answers to questions – Prob
Assign
• How do we assign measurements to Spatches?
– P_assign = P_belongs * P_space_between_occupied
‣ P_belong = distance measure using chi2 dist
‣ P_space = prob space between Spatch and meas is occupied as
Spatch & meas
9
10. New Work: Example raw data…
• 8 scans
scans • 20 (+)
meas
(-) meas Pocc
• 12 (-)
meas
• Assume in-
cell
assignmen
t known
• Elevation
(+) meas
uncertain
10
21. New Work: Example processing …
• Patch
Patch too low, fusion
p_occ is high finally
around it!
Spatch (-) gains
enough
evidence
that space
between (-)
patches is
empty, so
fuses two
of them
into Spatch
21
22. New Work: Example processing …
• Continue
processing
meas …
creates
two new
patches
22
23. New Work: Example processing …
• Patch
fusion
(horizontall
y) creates
another
Spatch
23
24. New Work: Example processing …
• Next (+)
meas are
assigned
to Spatch
(cell 4 & 5)
and patch
(cell 6)
24
25. New Work: Example processing …
• Patch
fusion
(horizontall
y) does not
create any
more
fusion!
25
26. New Work: Example comparison
• PML* (left) :
– 10 patches
– Unsure about cell 2 space
• Proposed change (right):
– 5 patches
– 2 Spatch+, 1 Spatch-
– 1 patch+, 1patch-
– Deems cell 2 space
occupied
26
27. New Work: Example processing …
• PML* (left) :
– 10 patches
– Unsure about cell 2 space
• Proposed change (right):
– 5 patches
– 2 Spatch+, 1 Spatch-
– 1 patch+, 1patch-
– Deems cell 2 space
occupied
27
28. New Work: Unanswered Questions – P_space
• P_space is dependent on size of space
– Cons: wall with small hole example…
Pave sum(P ) +
= sum(P )
Pave num( largenum(
can be
)+
)
even when the hole
is certainly empty!
If Spatch+ is created, can
still maintain Spatch-
overlapping it!
28
29. New Work: Unanswered Questions – patch
break
• How do we break Spatches if necessary?
– Still need to determine???
Challenging Easier
29
30. Literature Review
• Contextual Occupancy Maps Incorporating Sensor
and Location Uncertainty – ICRA’10, O’Callaghan
ACFR
– Uses GP to fill in information between measurements
‣ GP over distributions instead of points!
– Produces framework covariance for noisy inputs
‣ Uses Gauss-Hermite Quadrature to approximate in close form
30
32. Literature Review (cont.)
• Building Occupancy Maps with a Mixture of Gaussian
Processes – ICRA’12, Kim Australian National
University
– Build local GP’s with cluster of ‘similar’ LIDAR rays
– Combine with mixture of experts
– Faster results, more accurate
32
33. Literature Review (cont.)
• Continuous Occupancy Mapping with Integral Kernels
– ICRA’11, O’Callaghan ACFR
– Create 2/3D occupancy maps using GPs
– Integral Kernel for continuous line ‘empty’ measurements
‣ Closed-form for SQExp Covariance
– General framework for covariance kernels with fewer
sampling points
‣ Use quadrature to approximate integral
‣ Use quadrature to select sampling points
34. Literature Review (cont.)
• Gaussian Process Moderling of Large Scale Terrain –
ICRA’09, Vasudevan ACFR
– Create terrain maps using GPs
‣ SQExp kernel and neural network kernel
– Uses KD-tree to obtain training data
– Offline processing of data
35. Literature Review (cont.)
• Adaptive Non-Stationary Kernel Regression for Terrain
Modeling – RSS’07, Lang University of Freiburg
– Non-stationary Gaussian Kernel
– Iteratively adapt kernel matrix with local elevation
gradient
36. Discussion and Feedback
• Implementing:
– Integral kernel for patches!
– Integral kernel for inferring occupancy state of fuse space
– KD-Tree to find ‘NN’ patches for potential fusion
– Explore other kernels (non-stationary)
• Time-goals:
– Paper 1st draft (early oct)
– Paper final (late oct)
– Thesis building (early nov)
– Defense (late nov)
36
