Lecture #19 - Case Western Reserve Universityengr.case.edu/merat_francis/eecs490f07/Lectures/Lecture19.pdf · Lecture #19 • Shading and texture analysis using morphology • Gray

EECS490: Digital Image Processing

Lecture #19

• Shading and texture analysis using

morphology

• Gray scale reconstruction

• Basic image segmentation: edges v. regions

• Point and line locators, edge types and noise

• Edge operators: LoG, DoG, Canny


Gray Scale Morphology

© 2002 R. C. Gonzalez & R. E. Woods

original “top-hat”

h = f f b( )

A top-hat transformationsubtracts an opening fromthe image.

Enhances detail inthe presence ofshading



Gray-Scale Morphology


Chapter 9Morphological Image Processing




Algorithm for locatingtexture boundaries1. Repeatedly close theinput image with a SEsmaller than the largecircles. This willeventually remove allthe smaller objects.2. Now do a singleopening with a SElarger than theseparation betweenright hand circles3. Use a morphologicalgradient to computethe boundary



Gray-Scale MorphologySmooth to eliminatewood grain

Open withr=10 disk

Open withr=20 disk

Open with r=25 disk

Open withr=30 disk

Summing the surface area (light intensity) and subtracting to determinethe change as a function of r gives the particle size distribution




This shows that the image is basically composedof images of r=19 and r=27 particles


Gray Scale Morphology


Granulometry — how to determine size distributions1. Open with structuring elements which increase in size with eachiteration2. Compute differences between original and each opening3. Normalize these differences to give the size distribution




Original image

Opening by reconstructionusing 71 pixel horizontal line

Opening using 71 pixelhorizontal line

Top-hat byreconstruction 71pixel horizontal line

Top-hat

Opening byreconstructionusing 11 pixelvertical line

Dilation byreconstructionusing 21 pixelvertical line

MINFinal reconstruction

Thisillustratesmorphologicalreconstruction to eliminatevertical andhorizontallines andshadows in animage.


Chap. 10 Image Segmentation


Image Segmentation

• Segmentation partitions image R intosubregions R1, R2, …, Rn such that:– R1 R2 … Rn=R

– Each Ri is a connected set– Ri Rj=0 for all i,j where i

– Q(Ri)=TRUE for every i

– Q(Ri Rj)=FALSE for any two adjacent regions


Image Segmentation


Original images

Boundariesobtained fromderivatives orsimilartechniques

Segmented image.Ri are orthogonaland havedifferentintensity.

Edge-basedsegmentation

Region-basedsegmentation

Segmented imagebased uponstandarddeviation of theintensity in 4x4regions


Line Detection


Edge basedsegmentationrequires findinggood edges —typically using afirst or secondderivative spatialoperator.

There are multiple typesof edges such as rampand step giving differentresponses.

First derivativeoperators typically givethicker edge responses;second derivativeoperators respond tofiner detail, includingnoise

Second derivatesproduce a double edgeresponse for ramp andstep edges


Line Detection


While we typically regarded a mask such as the 3x3 shown aboveas a spatial operator it can also be thought of as a correlationmask.


Line (and point) Detection


Single black pixelwe want to find

Regard thisas acorrelationmask for ablack pixel,i.e., a pointlocator

Response R tocorrelationmask

Threshold atT=90 of maxpixel intensity

R = wizii=1

9


Line Detection


Original image Laplacian processedimage. Intensitytransformed so 50%gray is zero. Double lineeffect is clearly visible.

Absolute value ofthe Laplacian giveswide lines

Using only positive valuesof the Laplacian givesnarrower lines.


Line Detection


These can be regarded as line detector masks for lines withspecific orientations.


Line Detection


Original image Response using +45˚line detector

Zoom of topleft response

Zoom of bottomright response

Response withall negativevalues set tozero

Select onlymaximum valuesfrom (e)


Line Detection


Step edge andits intensityprofile.

Ramp edge andits intensityprofile.

Roof edge andits intensityprofile.


Line Detection


Real intensity image showing multiple typesof edges


Line Detection


Observations:1. Magnitude of the firstderivative can be used to detectthe presence of an edge at apoint2. Sign of second derivativeindicates which side of the edgethe pixel is on3. Zero crossings of the secondderivative can be used to locatethe centers of thick edges


Line Detection


Ramp edgecorrupted bysteadilyincreasingamounts ofadditiveGaussian noise

Firstderivative

Secondderivative

Fundamental steps inedge detection:1. Smoothing — fornoise reduction2. Detection — of allpotential edgecandidates3. Localization — selectthe real edge points


Line Detection


Strength and direction of an edge can bedetermined using the gradient

f =

f

xf

y

=gxgy

Strength (magnitude)

Direction

M x, y( ) = mag f( ) = gx2+ gy

2

x, y( ) = Tan 1 gxgy


Line Detection


f =

f

xf

y

=1

1

Gray=0, white=1

The gradientvector isperpendicular tothe actual edge.


Image Segmentation


The Prewittand Sobel arethe mostcommonlyused gradientmasks

The Sobel has betternoise characteristicsthan the Prewitt


Image Segmentation


ModifiedPrewitt andSobel masks fordetectingdiagonal edges

-45˚ +45˚


Image Segmentation


1200x1600original image

|Gx| using 3x3Sobel

|Gy| using 3x3Sobel

|Gx|+|Gy|gradientapproximation


Image Segmentation


Gradient angle plotted as an intensity. Areas of constant intensity havethe same gradient vector (perpendicular to the edge). Black means thegradient vector is at 0˚ so the actual edge is vertical (at -90˚)


Image Segmentation


1200x1600original imagesmoothed with a5x5 averagingfilter

|Gx| using 3x3Sobel

|Gy| using 3x3Sobel

|Gx|+|Gy|gradientapproximation

Averagingcauses theedges to beweaker butcleaner. Noteloss of brickedges


Image Segmentation


-45˚ Sobel +45˚ Sobel

Note that both can detect a horizontal or verticaledge, but with a weaker response than ahorizontal or vertical operator


Image Segmentation


Thresholded gradientimage w/o smoothing

Thresholded gradientimage w/smoothing

Threshold = 1/3 max_value


Image Segmentation


The LoG is sometimescalled the Mexican hatoperator

The Laplacian isNEVER used directlybecause of its strongnoise sensitivity

Combining theLaplacian with aGaussian gives the LoG

2h r( ) =r2 2

4e

r2

2 2


Image Segmentation

Marr-Hildereth algorithm:– Filter image with a nxn Gaussian low-pass filter

– Compute the Laplacian of the filtered image using anappropriate mask

– Find the zero crossings of this image

This operator is based upon a 2nd derivative operator and canbe scaled using the parameter to fit a particular image orapplication, i.e., small operators for sharp detail and largeoperators for blurry edges

G x, y( ) = ex2 + y2

2 2

Documents

Lecture #19 - Case Western Reserve Universityengr.case.edu/merat_francis/eecs490f07/Lectures/Lecture19.pdf · Lecture #19 • Shading and texture analysis using morphology • Gray