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00 -- 11
2007 Texas Instruments Inc,
Content developed in partnership with
Tel-Aviv University
From MATLAB and Simulink toReal Time with TI DSPs
Detecting Shapes in Images usingthe Hough Transform
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SlideSlide 22 20072007 Texas Instruments Inc,Texas Instruments Inc,
Outline
Detecting Straight Lines
Detecting Straight Lanes
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SlideSlide 44 20072007 Texas Instruments Inc,Texas Instruments Inc,
Multiple Lines over a single point
Each pair (m,b) defines a distinct straight line containing
the point (x,y)
(x,y)
y=m1x+b1
y=m2x+b2
y=m3x+b3
y=m4x+b4
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SlideSlide 66 2007 Texas Instruments Inc,2007 Texas Instruments Inc,
Dealing with digital pictures
A line formed by M (N) pixels in the image space will be mapped to theintersection point of M (N) lines in the parameters space, where eachline corresponds to a pixel in the image space.
The number of lines intersecting in a single point in the parameterspace represents the length of the original line in the image space.
N lines
M lines
Image Plane Parameter Plane
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SlideSlide 77 2007 Texas Instruments Inc,2007 Texas Instruments Inc,
The Accumulator Concept
The (m.b) space (parameterplane) is subdivided in cells.
Each pixel (x,y) in the originalimage vote in the (m,b) space
for each line passing throughit.
The votes are summed in anAccumulator
bbmax
m
bmin
mmin mmax
b1
m1
N
Correspondstoastraightline
y=m1x+b1ofN pixelslength
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SlideSlide 88 2007 Texas Instruments Inc,2007 Texas Instruments Inc,
Using Polar Coordinates
(x1,y1)
(x2,y2)
r
UU
UU
UU
sincos
sincos
sincos
22
11
yxr
yxr
yxr
!
!
!
For each point (x,y) in theline the following equationapplies:
In particular:
UU sicos yxr !
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SlideSlide 99 20072007 Texas Instruments Inc,Texas Instruments Inc,
The Motivation for Polar Coordinates
rx
rrx
!
! 00 sicos
x = r
r
Vertical lines cannot be mapped to the(m,b) space, since:
Vertical lines can be described usingpolar coordinates :
?!
g!
b
m
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SlideSlide 1010 2007 Texas Instruments Inc,2007 Texas Instruments Inc,
Hough Transform - The (r,) Space
(x1,y1)
(x2,y2)
(x3,y3)
r=x2cos+y2sin
r=x1cos+y1sin
r=x3cos+y3sin
(x4,y4)
r=x4cos+y4sin
Hough Transform - Each point in the (x,y) space is mapped to asinusoid in the (r,) space.
Sinusoids corresponding to collinear points in the (x,y) spaceintersect at a common point in the (r,) space.
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SlideSlide 1111 20072007 Texas Instruments Inc,Texas Instruments Inc,
Accumulators in the (r,) Plane
max
r
min
rmin rmax
1
r1
N
Correspondstothestraightline
r1=xcos1+xsin1ofN pixelslength
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SlideSlide 1212 2007 Texas Instruments Inc,2007 Texas Instruments Inc,
The Region of Interest (ROI)
The ROI is the area in the original image, where lines need to bedetected. The ROI for the picture above is:
xmaxxmin
ymax
ymin
ree
ee!
ee
ee
3600
022
U
max
minmaxminmaxmax
maxmin
maxminrr
yyxxryyy
xxx
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SlideSlide 1313 20072007 Texas Instruments Inc,Texas Instruments Inc,
Longest Line Detection
Edge
Detection
Hough
TransfomDraw Line
Input
Image
Output
Image
Binary
Image
LongestLine
(rm,m)
+FindMax.
AccumulatorArray
HoughAlgorithm
Thelineisreconstructedusing
theequation:
rm=xcosm+ysinm(Calculatedforthe values of
(x,y)that votedforthe
accumulatorcell (rm, m).
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SlideSlide 1414 2007 Texas Instruments Inc,2007 Texas Instruments Inc,
Line Detection Model
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SlideSlide 1515 20072007 Texas Instruments Inc,Texas Instruments Inc,
The Hough Algorithm
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SlideSlide 1616 2007 Texas Instruments Inc,2007 Texas Instruments Inc,
Line Drawing & Image Construction
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SlideSlide 1717 20072007 Texas Instruments Inc,Texas Instruments Inc,
Line Detection - Hands-On
Simulation
Implementation using the DSK6416
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SlideSlide 1818 2007 Texas Instruments Inc,2007 Texas Instruments Inc,
Simulation
Image File
MATLAB Display
Line
Detection
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SlideSlide 1919 20072007 Texas Instruments Inc,Texas Instruments Inc,
DSK6416
ImageFile
MATLABDisplay
Line
Detection
Script
RGB
to
Grayscale
RTDXRTDX
Real Time Implementation
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SlideSlide 2020 2007 Texas Instruments Inc,2007 Texas Instruments Inc,
From Line to Lane
1. Find two longest lines in thepicture
2. Draw Polygon
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SlideSlide 2121 20072007 Texas Instruments Inc,Texas Instruments Inc,
Lane Detection
HoughTransfom
DrawLane
Input
Image
Output
Image
Binary
Image
+Find2 Max.
Accumulator
Array
HoughAlgorithm
EnhancedEdge
Detection
(r,)Correction
DetermineROI
Two Longest Lines
(rm,m) / (rn,n)
Twolinesarereconstructedusing the
equation:
rm=xcosm+ysinm(Calculatedforthe values of (x,y)that
votedforthetwomaximum valuesin
theaccumulatorcell.
Apolygon is constructed connecting
thoselines
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SlideSlide 2222 2007 Texas Instruments Inc,2007 Texas Instruments Inc,
Enhanced Edge Detection
An histogram-basedthresholdingedgedetection methodenablestheidentificationofareaswherepixels changefromlighttodarkordarktolight, whichmightindicate
laneedges.
Edge
Detection
HistogramBased
Threshold
ROILogical
ANDBinary
Image
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SlideSlide 2323 20072007 Texas Instruments Inc,Texas Instruments Inc,
Edge Detection Only
Edge Detection with HistogramBased Thresholding
Why Enhanced Edge Detection?
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SlideSlide 2424 2007 Texas Instruments Inc,2007 Texas Instruments Inc,
NoCorrection
(r,)Correction
The Need for (r,) Correction
Misdetection ofthe
longestlines
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SlideSlide 2525 20072007 Texas Instruments Inc,Texas Instruments Inc,
(r,) Correction
If the lane position given by the Hough Transform blockchanges abruptly with respect to its values in the previousframe, the Rho Theta Correction subsystem discards thecurrent position and keeps the previous position. Maximumallowable variation in E and F with respect to previous values
are:
degreesor
pixelsrr
previouscurrent
previouscurrent
10
30
e
e
UU
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SlideSlide 2626 2007 Texas Instruments Inc,2007 Texas Instruments Inc,
Lane Detection Model
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SlideSlide 2727 20072007 Texas Instruments Inc,Texas Instruments Inc,
Enhanced Edge Detection
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SlideSlide 2828 2007 Texas Instruments Inc,2007 Texas Instruments Inc,
The Hough Algorithm
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SlideSlide 2929 20072007 Texas Instruments Inc,Texas Instruments Inc,
Lane Drawing
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SlideSlide 3030 2007 Texas Instruments Inc,2007 Texas Instruments Inc,
Lane Detection - Hands-On
Simulation
Implementation using the DM6437 DVDP