A GPU based Real-Time Line Detector using a Cascaded 2D Line Space

A GPU based Real-Time Line Detector using a

Cascaded 2D Line Space Jochen Hunz, Anna Katharina Hebborn, Stefan Müller

University of Koblenz - LandauInstitut für Computervisualistik

Germany

[email protected]

Line Detection

• Task: Find lines in an image (often: Canny image)

• Most common technique: Hough Transform

Jochen Hunz ([email protected]) University of Koblenz-Landau

2

Input Image Canny Image

Hough Transform

For an image point the lines though this

point are the pairs with

Accumulate pairs in the Hough Accumulator.


3

),( ii yx

),( d

sincos 00 yxd

),0[

Hough Transform: Discretization

How to discretize ?

4

x

y

is to small is appropriate

Line Space - Idea• Linear instead of angular parametization

• Number border edges from 0 to 4n-1

• Consider (rasterize) all Lines from Border to Border, identified by a tuple (start, end)


5

0

1

2

3

11

10

9

8

4 5 6 7

15 14 13 12

Line Tuple (1,8)

Rasterization

• Rasterize every line using DDA (DigitialDifferential Analyzer) for example

• Count pixels not equal to zero

• Store result in two dimensional space (LS) ofsize 4n x 4n at position (start,end)

Rasterize every line in parallel on the GPU!


6


7

0

1

2

3

11

10

9

8

4 5 6 7

15 14 13 12 s

e

0

5

10 150 5

10

15

Canny Image Line Space

16 n² Lines

LS Properties


8

s

e

0

5

10 150 5

10

15

• LS(s,e) = LS(e,s)

• CollinearityLines betweencollinear edges aredegenerated

CLS: The Cascaded Line Space

• Line Space: 16n² lines to rasterize

• Using DDA, lines have max. length of n

– We rasterize many long lines!

• Performance for image of size 512x512: 34.13 ms

• Idea: Divide Canny image in Cascades of size k*k


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Cascades (k=4)


10

0

4

12

8

1516 282420 31

32

36

40

44

47

4852566063

0

1 2 30

1

2

3

Cascaded Line Space


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Observation

• Still 16n² lines to rasterize• But much shorter lines (max length: k)• Merging to global LS necessary• Performance for image of size 512x512:

0.91 ms. (Versus 34.13 ms for global LS)


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Merging


13

Merging


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• Determine (or precompute)intersection points for eachcascade• Perform look ups in the CLS:

(2,5) or (5,2) (12,13) or (13,12) (1,6) or (6,1)

• Accumulate CLS values and• Store in next higher hierarchy.

Here at position (2,14)

0

16

16 31

31

Merging

• Repeat merging times

• Performance for image of size 512x512: 7.45 ms.


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)/( knld

k = n = 16Global LS

k = 4 k = 8Canny

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Input Image Canny Image

Line SpaceResult

Canny Operator

Maxima Detection

P = 13.5 %

Performance


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n

(degree)

P

(%)

Hough

CPU

(ms)

Hough

GPU

(ms)

Line

Space

(ms)

Cascaded Line Space

(ms)

Initial

CascadesMerge Total

64 0.45115.3

16.3

2.14

2.37

2.11

1.560.11 0.02 0.06 0.08

128 0.22613.4

15.1

23.30

26.97

1.56

1.570.60 0.07 0.30 0.37

256 0.1129.8

14.4

147.89

207.79

2.70

4.564.43 0.24 1.49 1.73

512 0.066.7

13.5

780.57

1576.35

8.50

13.2334.13 0.91 7.45 8.36

1024 0.0284.5

10.6

5040.72

12952.30

30.62

59.52247.53 3.31 36.46 39.77

Discussion

• LS captures all potential Lines with noredundancy

• Our brute force CLS implementation cancompete with CUDA Hough

• Merge phase has to be optimized

• LS has high potential


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The Future: Line Segment Detection

• We are working on Line Segment Detectionusing the CLS

• CLS provides already line segments of size k in 3ms @1024² images

• Line Segments need to get merged

• For each line exit point in one cascade, thestarting point in the next cascade is well defined


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Line Segment Detection: Merge


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0

1

2

3

4 5 6 7

15 14 13 12

10

9

8

4 5 6 7

15 14 13 12

s

e

0

5

10 150 5

10

15

s

e

0

5

10 150 5

10

15

Recruiting & HR

A GPU based Real-Time Line Detector using a Cascaded 2D Line Space