Shape Detection

8/7/2019 Shape Detection

1/30

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


2/30

SlideSlide 22 20072007 Texas Instruments Inc,Texas Instruments Inc,

Outline

Detecting Straight Lines

Detecting Straight Lanes


3/30


4/30


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


5/30


6/30

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


7/30


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


8/30


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 !


9/30


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


10/30


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.


11/30


Accumulators in the (r,) Plane

max

r

min

rmin rmax

1

r1

N

Correspondstothestraightline

r1=xcos1+xsin1ofN pixelslength


12/30


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


13/30


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).


14/30


Line Detection Model


15/30


The Hough Algorithm


16/30


Line Drawing & Image Construction


17/30


Line Detection - Hands-On

Simulation

Implementation using the DSK6416


18/30


Simulation

Image File

MATLAB Display

Line

Detection


19/30


DSK6416

ImageFile

MATLABDisplay

Line

Detection

Script

RGB

to

Grayscale

RTDXRTDX

Real Time Implementation


20/30


From Line to Lane

1. Find two longest lines in thepicture

2. Draw Polygon


21/30


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


22/30


Enhanced Edge Detection

An histogram-basedthresholdingedgedetection methodenablestheidentificationofareaswherepixels changefromlighttodarkordarktolight, whichmightindicate

laneedges.

Edge

Detection

HistogramBased

Threshold

ROILogical

ANDBinary

Image


23/30


Edge Detection Only

Edge Detection with HistogramBased Thresholding

Why Enhanced Edge Detection?


24/30


NoCorrection

(r,)Correction

The Need for (r,) Correction

Misdetection ofthe

longestlines


25/30


(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


26/30


Lane Detection Model


27/30


Enhanced Edge Detection


28/30


The Hough Algorithm


29/30


Lane Drawing


30/30


Lane Detection - Hands-On

Simulation

Implementation using the DM6437 DVDP

Documents

Shape Detection