Augmenting the Generalized Hough Transform to Enable the Mining of Petroglyphs

1
Augmenting theGeneralized Hough Transform to
Enable the Mining of Petroglyphs

• Qiang Zhu, Xiaoyue Wang, Eamonn Keogh, 1Sang-Hee
  Lee
• Dept. Of Computer Science Eng., 1Dept. of
  Anthropology
• University of California, Riverside

2
Outline

• Motivation
• Approach
• Evaluation
• Conclusion

3
Motivation(1) -applications

• Petroglyphs are one of the earliest expressions
  of abstract thinking.
• Providing a rich source of information
• climate change
• existence of a certain species
• patterns of humans migrations and interactions

4
Motivation(2) -difficulties

• Progress in petroglyph research has been
  frustratingly slow.
• due to their extraordinarily diverse and complex
  structure
• most matching algorithms can not capture the
  similarity of petroglyphs
• for those that can, even in limited cases, do not
  scale to large collections

5
Approach

• How to preprocess the raw data?
• How to define the distance measure?
• How to speed up?

6
Preprocessing(1)

• With rare exceptions, petroglyphs do not lend
  themselves to automatic extraction with
  segmentation algorithms.

The border of this rock may be recognized as the
edge of this petroglyph
7
PetroAnnotator
Load the raw image into our human computation tool
8
PetroAnnotator (cont.)
Draw an approximate boundary around object, and
then trace the shape
9
Preprocessing(2) -downsampling
A

• Two overlaid skeleton traces (340 by 250) of the
  same image of a Bighorn sheep. Less than 3.5 of
  the pixels from each image overlap.
• (B) The same two images after downsampling (30 by
  23).
• 75.6 of the pixels (denoted by black) are
  common to both.

10
Distance Measure -why GHT?

• essentially makes no assumption about the data
• open/closed boundaries
• connected/disconnected shapes
• correctly captures the similarity
• subjective/objective similarity on
  unlabeled/labeled datasets
• tightly lower bound the distance
• allowing for very efficient searches in large
  datasets

11
Classic GHT

• GHT is a useful method for two dimensional
  arbitrary shape detection.

12
(1) Find the star-pattern
13
(2) Superimpose Accumulate
14
(3) Find the peak
Q
R
R
0
1
1
1
0
A
0
0
1
0
0
1
2
3
2
1
0
1
1
1
0
15
A Basic Distance Measure

• Classic GHT doesnt explicitly encode a
  similarity measure
• We can simply define a GHT-based distance
• minimal unmatched edge points (MUE)
• number of edge points in Q maximal matched
  edge points
• 4 3 1 (for our toy example)

16
A New Cell Incrementation Strategy

• When can we obtain the value of a particular cell
  in the accumulator?
• In the classic GHT, until the end of all
  incrementation
• Is it possible to obtain the value one by one?
• Need to check all positions that are possible to
  increase the cell value

?
17
Lower Bound
?
Q
C
?
?
?
?
?
?
?
?
In this column Q needs 2 pixels in C, and has 3
In this column Q needs 2 pixels in C, and has 2
In this column Q needs 4 pixels in C, and has
only 2
In this column Q needs 2 pixels in C, and has 2
In this column Q needs 2 pixels in C, and has 3
Minimal missed points
2
0
0
2
0
0
18
Time Complexity

• Classic GHT
• O(NQNCS2)
• superimpose all query vectors to all edge points
  in the candidate image
• Lower bound GHT
• O(S2)
• compare one-dimensional signatures
• further reduced by early abandon and shifting
  order
• one to two orders of magnitude speed-up

19
Variants on the Basic Distance Measure

• Query-by-Content
• Clustering
• Finding Motifs

20
Evaluation

• We performed three sets of experiments
• Evaluation of Utility
• -on unlabeled data
• Evaluation of Accuracy
• -on labeled data
• Evaluation of Scalability
• -on synthetic data

21
Evaluation of Utility (1)

1. Our GHT-based distance measure correctly groups
   all seven pairs
2. The higher level structure of the dendrogram also
   correctly groups similar petroglyphs

Atlatls
Anthropomorphs
Bighorn Sheep
A clustering of typical Southwestern USA
petroglyphs
22
Evaluation of Utility (2)
23
(No Transcript)
24
Evaluation of Utility (3)

• Whether our distance measure can find meaningful
  motifs?
• 2,852 real petroglyphs
• 4,065,526 possible pairs
• 52 top motifs (0.00128) by motif cutoff

Motif Cutoff
25
Evaluation of Accuracy -datasets

• NicIcon dataset
• 24,441 images
• 14 categories
• 33 volunteers
• 234234 pixels
• WD/WI tests

• Farsi digits dataset
• From 11,942 registration forms
• 60,000 digits for training
• 20,000 digits for testing
• 5464 pixels (largest MBR)

26
(1) Test the Downsampling Size
30
20
Error Rate ()
WD
In both datasets, the error rate of
one-nearest-neighbor test varies little once the
resolution is greater than 1010
10
WI
0

10
20
30
40
50
60
70
80
5
Resolution (RR) of Downsampled Images (NicIcon)

16
12
Error Rate ()
8
4
2
5
10
20
30
Resolution (RR) of Downsampled Images (Farsi)
27
(2) Competitive accuracy

• NicIcon dataset
• Error rate for WD 4.78
• 8.46 for WI
• The dataset creators tested on the online data
  using three classifiers.
• Only one of them (DTWB) is better, however,
  slower

• Farsi digits dataset
• Error rate 4.54
• Borji et al. performed extensive empirical tests
  on this dataset
• Of the twenty reported error rates, the mean was
  8.69
• Only four beat our approach, but need to set at
  least six parameters

28
Evaluation of Scalability -datasets

• We made 8 synthetic petroglyph datasets
• Based on 22 classic petroglyphs
• Duplicated by 10 volunteers on a tablet
• Applied a Random Polynomial Transformation
• Containing up to 1,280,000 objects

29
(1) Querying by Content

• Leave-one-out one-nearest-neighbor test.
• Repeated the test for 10 times on each dataset.

30
(2) Finding Motifs

• A brute force algorithm requires time quadratic
  in the size of dataset.
• By using the triangular inequality of our
  distance measure, we only need to calculate a
  tiny fraction of the exact distance.
• Even for the smallest dataset
• -our algorithm is 712 times faster
• -we can prune 99.84 of the calculations

31
Conclusion

• In this work we considered, for the first time,
  the problem of mining large collections of rock
  art.
• Introduced a novel distance measure
• Found an efficiently computable tight lower bound
  to this measure
• Enabled mining large data archives effectively

32
All datasets and the code can be downloaded
from http//www.cs.ucr.edu/qzhu/petro.html
Thanks for your listening ! ?