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Line Segment Maps:
Fast and Deterministic Line Detection on the GPU
(Dr-Ing. Gernot Ziegler)

May 2016
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FastLineSegmentDetection
Business Background
 Algorithmic consulting and training
in general purpose GPU computing.
 Main focus on computer vision and
visual computing, e.g. GPU-based
camera calibration or lightfield
acquisition/rendering.
 Spatial computing in HPC as well,
e.g. volume compression or
tomography reconstruction.

geofront e.U., privately owned, was founded in January 2016.

June 2016
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Open Investigations: Purpose
 Create new algorithms and technologies
as part of geofront's algorithmic portfolio.
 Real-time game graphics techniques
(on GPU, e.g. shadow mapping, Z buffer, data parallelism)
 Computer vision knowledge on multi-view acq. vision
(Image Based Reconstruction and Rendering)
 Client-Server and Mobile Rendering / Vision
(WebGL, Android, but also Tegra X1)

May 2016
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Line Detection in WebGL
https://www.geofront.eu/demos/lines
 Line segments derived from
local edge filter results (line angle bins)
 Data-parallel Segmented Scan
?connects“ local edges
 2D line segment maps, one per line angle bin
 Interactive run times on mobile GPUs
 Novel for WebGL, through
Data Compaction algoritm which produces lists
of line segments above certain length

May 2016
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Task Setting
 Reliable Real-time Line Detection in images and video
(a basic component for medium-level vision, e.g. in cars)
 Lines can be at any angle. Line start/end is important, too.
 Example input in automotive computer vision:
http://www.gmroadmarkings.co.uk/images/gm-road-markings-header.jpghttp://www.pringlesurfacing.co.uk/wp-content/uploads/road-markings-6.jpg

June 2016
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Line Hypotheses
 Line hypotheses are ?laid“ at all aftersought angles
 Best to maintain input image resolution (avoid undersampling)
 Also parts of the hypothesis can be true

May 2016
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Line Atoms, or: What is a ?line“?
 ?Line segment hypotheses“ verified by edge detection
(central difference thresholding)
 Condition 1: No edge along line hypothesis (yellow)
 Condition 2: Edge present orthogonal to line hypothesis
 Line atom:
One local verification,
both conditions met.

May 2016
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FastLineDetection
Line Segment Map
 We create a 2D map over all line atom tests (0:s and 1:s)
 Layers represent the angle bins (e.g. Layer 0: Angle 0-22.5
deg) Layer 0: -12.5° to 12.5°
Layer 5: 60° to 80°
0 0 0 0 0 0 ....
0 0 0 0 0 0 ....
0 0 0 0 1 1 1 0 ....
0 0 0 0 0 0 ....
0 0 0 1 1 1 1 1 0 ....
0 0 0 1 1 1 1 1 0 ....
....

June 2016
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Challenges
 Massive memory bandwidth needed:
Edge detection has to read pixel values repeatedly to evaluate
line hypotheses at all angles.
 Edge detection at non-trivial angles
requires bilinear interpolation of input pixels.
 On GPU: Texture cache and shared memory alleviates this!
 (On CPU: Must often resort to stochastic evaluation – but
makes line detection is non-deterministic .... )

June 2016
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Inference of Line Segments

Now that we have found line support through edge detection, how to infer
line segments? CPU approaches use Edge Tracking, but that is serial.

We use segmented scan:
From 2 and 2 connected
elements, we can infer that
all 3 are connected, etc.

CUDA, OpenGL Compute:
Shared memory

OpenGL ES 2.0, WebGL:
Repeated shader calls

May 2016
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FastLineDetection
Line Segment Map to Line List
 Inference stores lengths in Line Segment Map
 Create Line list (*) via
?Values above Threshold T, preceded by a Zero“
Layer 0: -12.5° to 12.5° Layer 5: 60° to 80°
0 0 0 0 0 0 ....
0 0 0 0 0 0 ....
0 0 0 0 3 2 1 0 ....
0 0 0 0 0 0 ....
0 0 0 5 4 3 2 1 0 ....
0 0 0 5 4 3 2 1 0 ....
....L0: (4,2), l=3 L5: (3,1), l=5 L5: (3,2), l=5

(*) OpenGL or CUDA : Atomics
(OpenGL ES, WebGL:
Data Compaction,postponed)

May 2016
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FastLineDetection
Result
 Line List can now be rendered or used in further processing
....L0: (4,2), l=3 L5: (3,1), l=5 L5: (3,2), l=5
 (Line Segment Map is still useful, showing later)

May 2016
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Musings on detection guarantuees

How can we make sure that every line direction angle is detected? (And only falls
into one angle bin?)

Look at Bresenham algo:
(rasterizes lines based
on their slope angle):

Insight:
For short line segments,
close line angles cannot be told apart

(they have identical Bresenham images).

June 2016
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Musings on detection guarantuees
 How many angle bins needed to catch all angle?
(Without proof: Number of required angle bins is outer rim cells of Bresenham window:
here, 16 angle bins (easy to count), or 8 if 180 degrees symmetric.
 Larger Bresenham window : Narrower angle range

Gerneal:
The longer found
line segments are,
the more we can tell about their angle!
 Optimization : Use multi-stage to catch all angles;
Then you can subdivide angle bins recursively to narrow down.

June 2016
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Angle identification in real images

Reality has smaller image gradients than those from black-on-white
Bresenham lines:


But: Central difference cross for any pixel pattern
responds highest on ?its“ matching angle bin ->
Proper detection threshold can be determined
(unless crosstalking is desired for ambious cases).

May 2016
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FastLineDetection
Imperfection tolerance
 Segmented scan expects line atoms at every sample position of line hypothesis.
 But lines in input image might be imperfect (e.g. withered road marking).
 Fill-in step before seg-scan starts.
 E.g. allow for one missing line atoms: insert 1 iff 1 before and after.
0 0 1 1 1 0 1 1 0 0 -> 0 0 1 1 1 1 1 1 0 0
 BUT: How long defects do we want to tolerate?
-> We might connect line segments that should not. Use dep. on application.

(Note: stochastic approach might ignore imperfection -
but that is not deterministic!)

June 2016
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Primitive Detection

Complex symbols are needed by high level AI
(e.g. traffic signs or road markings)

Searching through whole image is prohibitively expensive
(esp. considering symbol?s possible rotation angles and scales)
 How can we reduce bandwidth and computation requirements?

May 2016
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FastLineDetection
Primitive Detection
 Look first for components of the higher level primitives: Lines!
 Only ?deeper“ investigation where lines have been found:
 Line list -> Massively reduced computation & bandwidth

May 2016
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FastLineDetection
Example: Quadrangle Detection

We want to look for quadrangles of a side length min. 50 pixels,
made up of (approx.) orthogonal lines (angle 70-110 degrees)

First, we create a list for all lines at 50 pixel min length in the
image (side result: Line segment map)

Start a thread for every line

For every thread: use line origin coordinate to look up in line
segment map if there are other lines originating at same position
(tolerance window,e.g. +/- 3 pixels in x and y).

Effect: Maintain spatial correlation of lines via line segment map,
but benefit from reduced parallelism of line list to detect quads.

May 2016
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Primitives from Line Detection
(OpenGL, coming in WebGL)
 Higher level primitives (e.g. parallel lines, quadrilaterals,
vector symbols, ...) usually too complex to search for in
whole image (scale, rotation, ...)
 Data compaction reduces candidates to line segments of
required length (as parts of above primitives)
 Side results of 2D line segment maps (one per line angle bin)
still provides spatial neighbourhood info
 Correlation only done in relevant spots (with tolerances)
 Augmented Reality Marker Tracking in
WebGL browser, mobile and desktop, without .exe
 Computer Vision tasks on limited OpenGL ES 2.0 hardware
(e.g. automotive, robotics, … )

May 2016
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FastLineDetection
Primitive detection in HPC signal processing

This can be generalized, detecting complex shapes that are comprised of
subshapes of similar ?atoms“. Atom and sub-shape identification limits
complexity of shape search to promising locations. Shapes can be built in
multiple stages that limit complexity every stage.

Example from astronomy:
Stars as atoms
Constellations as Symbols.

Multi-stage
Detect atoms (stars),
then two subshapes of
“The Great Bear“, then see if
the candidates comprise final.

N-dimension as well!

June 2016
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Other Projects

May 2016
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Projects ?WebGL Computer Vision?
 HTML5 enables real-time video input
 WebGL enables GPU access from Javascript
 Limited (only OpenGL ES level), but 2008
algos for data compaction apply!
-> can extract sparse feature lists, build
quadtrees, octrees, geometry shader, etc.
 Line detection, Object tracking, …
 Contact me if you are curious and I give
you a short intro!

May 2016
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Bounding Box Tracking in WebGL
https://www.geofront.eu/webgl/bboxpyramid

Quick tracking of largest pixel group of certain color

Threshold pixels, assume small bounding boxes

Data Parallel Reduction:
Merge bounding boxes (if adjacent) OR
Choose largest one (if competing)

Interactive run times on mobile GPUs

Doesn?t have to be color (e.g.group local motion
vectors)

May 2016
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Photogrammetry

Reflective materials and their lighting
are hard to reproduce in 3D rendering

3D Reproduction with light fields,
i.e. dense view acquisition.
(2D Video Compression for elimination of redundancy –
later depth maps with proj. texture mapping for compression a
and view angle interpolation)
http://www.geofront.eu/demos/360rotate

May 2016
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FastLineDetection
Other data-parallel research
 HistoPyramids have been extended to create quadtrees and
octrees through bottom-up analysis:
www.geofront.eu/thesis.pdf

Summed Area Ripmaps fix precision issues of
Summed Area Tables / Integral Images:
http://on-demand.gputechconf.com/gtc/2012/presentations/S0096-Summed-Area-Ripmaps.pdf
(Note for implementation: US patent filed!)

Connected Components using full GPU parallelism:
http://on-demand.gputechconf.com/gtc/2013/presentations/S3193-Connected-Components-Kepler.pdf

Thank you.
Questions? http://www.geofront.eu

May 2016
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FastLineDetection
Data Compaction
(the ?postponed“
algorithm explanation
from Line List generation)

May 2016
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FastLineDetection
Line Segment Map to Line List
 Inference stores lengths in Line Segment Map
 Create Line list (*) via
?Values above Threshold T, preceded by a Zero“
Layer 0: -12.5° to 12.5° Layer 5: 60° to 80°
0 0 0 0 0 0 ....
0 0 0 0 0 0 ....
0 0 0 0 3 2 1 0 ....
0 0 0 0 0 0 ....
0 0 0 5 4 3 2 1 0 ....
0 0 0 5 4 3 2 1 0 ....
....L0: (4,2), l=3 L0: (3,1), l=5 L0: (3,2), l=5

(*) OpenGL or CUDA : Atomics
(OpenGL ES, WebGL:
Data Compaction,postponed)

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Data-Parallel Challenges: Data Compaction
? Our task: Select elements from a larger array, write into a list
? Example from Computer Vision: List of all black pixels in an image
? Step 1: Detect black pixels:
? Step 2: Create a list of detected pixels

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Data Compaction: Problem task in 1D
? Keep number of elements from input, based on a
Classifier:
? Implementation is trivial on CPU, single-thread.
? On GPU: Need to parallelize into 10k threads!
? First count number of output elements
using data-parallel reduction!

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Data Compaction via HistoPyramid:Buildup
? First, count number of output elements,
e.g. 4:1 data-parallel reduction
? (Note the reduction pyramid, it is retained - HistoPyramid)
? Can now allocate compact output, no spill.
? But how are output elements generated?
Histogram pyramid /
HistoPyramid

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Data Compaction via HistoPyramid: Traversal
? Output generate: Start one thread per output element
? Each output thread traverses reduction pyramid (read-only)
? No read/write hazards = Data-parallel output writing!
? As many threads as output elements

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HistoPyramid: 2D Data Compaction
? 1D was tutorial, actual webGL implementation is 2D !
? Dataflow diagram:

May 2016
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FastLineDetection
Other Projects

May 2016
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GeoCast & GeoScene
https://www.geofront.eu/blog/geoscene-and-geocast-formats.html
 Data Exchange between Computer Vision and Computer
Graphics requires exact viewing ray mapping, also for
depth maps
 GeoCast provides common data format using OpenGL!
 Useful for virtual simulation testing of computer vision
algorithms (e.g. AIT has started using Blender for this)
 Multi-view scene reconstruction requires complete camera
paths as well.
 Generate arbitrary testing scenarios, and ground truth.

May 2016
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GeoCast & GeoScene
Top view and more using proxy geometry

With proxy geometry such as a quad describing the street level, the GPU can reconstruct car viewpoints or help
debug vision and decision making of car AI.

https://www.geofront.eu/demos/20160318_street_camviews_on_proxy/

May 2016
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GeoCast & GeoScene
?Depth map projection“

GeoCast faciliates data exchange with data sources such as depth cameras, laser scanners, 3d modelling

GPU helps reconstructs novel views
from partial depth surfaces using Z-buffer

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