GEOG4110/5100AdvancedRemoteSensing

Lecture8

1GEOG4110/5100

• GeometricEnhancement:Richards5.1- 5.8• GeometricProperties5.10

Review• Histogrammatching• DensitySlicing• GeometricEnhancement

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Image-to-ImageContrastMatching

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XValuesSource

CEqual.

yMod.Values

Neary

0 0 0 0

1 0 0 0

2 0 0 0

3 0 0 0

4 0 0 0

5 1 1 1

6 3 1.8 2

7 5 2.6 3

8 6 3 3

9 7 4 4

10 8 8 5

11 8 8 5

LUTforcontrastmatching

HistogramMatching

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Landsat MSSscenesofnorthernsuburbsofSydneyAustralia(fromRichardsandJia,2006)

Autumn Summer

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HistogramMatchingAutumnaftermatchingto

summerhistogram Summer

Landsat MSSscenesofnorthernsuburbsofSydneyAustralia(fromRichardsandJia,2006)

DensitySlicing

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• Maprangesofbrightnesstoparticularshadesofgrayorcolor– Losesdetail– Reducesnoise

• Thisisasimpleone-dimensionalparallel-pipedclassifier(Ch.8)

• Sevengraylevels(below)orsixdistinctcolors(right).Couldbemoreorlessineithercase

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Contouringinwaterdetailtodefinebathymetryusingdensityslicing.Upperleft:Landsat MSScompositeimageofbands5and7smoothedtoreducelinestripinglowerleft:blackandwhitedensityslicing;lowerright:colordensityslicing

GeometricEnhancement• Enhancesgeometricdetailinanimage,asopposedto

radiometricdetail.• Changesinpixelbrightnessaredrivenbygeometric

considerations,andthusaredirectlyinfluencedbythecharacterofothersurroundingpixels.– Spatialinterdependenceofpixelvaluesleadstovariationsinthe

perceivedimagegeometricdetail– Operationsoccuroverneighborhoods

• Ourcurrentfocuswillbeintheimagedomainasopposedtothespatialfrequencydomain.– Imagedomain:operationsconsiderthecharacteristicsoftheimage

itself– Spatialfrequency:operationsconsiderrateatwhichimageintensity

valuesarechangingintheimagedomain

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Convolution

(ConvolutionFilter)

Convolution:Applicationofafunctiontoasignalthatmodifiesthesignal

h(t) y(t)f(t)

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Convolution

(ConvolutionFilter)

Convolution:Applicationofafunctiontoasignalthatmodifiesthesignal

h(t) y(t)f(t)

https://en.wikipedia.org/wiki/Convolution

Convolution:A functionderivedfromtwogivenfunctionsbyintegrationthatexpresseshowtheshapeofoneismodifiedbytheother.

• Convolutionfilterproducesoutputimageinwhichthebrightnessvalueatagivenpixelisafunctionofthebrightnessvaluesoftheneighboringpixels.

• Convolutionfiltersinclude:LowPass,HighPass,Median,Sobel,Roberts,etc…

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Convolution

ConvolutionFilter),(),( nmtnm ),( jir

Convolution:Applicationofafunctiontoasignalthatmodifiesthesignal• Imageprocessing:convolutionseekstoachieveanintendedoutcome• Sensingsystems:producesanunavoidableoutcomeforwhichwemay

seektocompensate

f

GeometricEnhancement

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Convolutionofatemplate(kernel)

GeometricEnhancementTemplate

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ForanyMx Npixelsizedtemplate,theresponseforimagepixeli,j is:

Where:

f(m,n)isthepixelbrightnessvalueaddressedaccordingtothetemplateposition,and

t(m,n)isthetemplateentryatthatlocation(canbesimilartoaweighting)

= =

=M

m

N

nnmtnmjir

1 1),(),(),( ∑∑f

ImageSmoothing(LowPassFiltering)• Reduceshigh-variabilityvalues(suchasnoise)inanimageby

“sliding”asmoothingtemplateacrosstheimage– Example:MeanValueSmoothing

– Pixelr(i,j)isassignedtheaverageofallvalueswithinthetemplate

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r(i, j) =1MN

(m,n)n=1

N

m=1

M

∑∑f

MeanSmoothingFilters

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OriginalImage 3x3meansmoothingfilterapplied

5x5meansmoothingfilterapplied3x1meansmoothingfilterapplied

Originaltimeseries

Smoothedtimeseriesusinginterval3 Smoothedtimeseriesusinginterval5GEOG4110/5100 16

TimeSeriesSmoothingUsingMovingAverage

0

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60

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100

120

140

160

0 20 40 60 80 100

Precip.(mm)

Day

0

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140

0 20 40 60 80 100

Precip.(mm)

Day

0

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0 20 40 60 80 100

Precip.(mm)

Day

ImageSmoothing(LowPassFiltering)

• Meansmoothingwillbluredgeswithinanimage.Toavoidthis,wecanapplyathresholdtothefilter

– TheThresholdfilterleaveslargegradientslargelyunchanged

– Usuallypre-specifiedbasedonaprioriknowledgeofimageproperties

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(i, j) =1MN

(m,n)n=1

N

m=1

M

r(i,j)=r(i,j)if|f(i,j)– r(i,j)| <T

r(i,j)=f(i,j)if|f(i,j)– r(i,j)| ≥T

∑∑fr

MedianFiltering• Ratherthanassign

themeanofvalueswithinthetemplatetothecenter(i,j)pixel,themedianisassigned.– Avoidsaveragingin

sporadicnoisydata

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OriginalImage

OriginalPlusnoise

MedianFilteredImage

EdgeDetectionImageEnhancement• EdgeEnhancementincreasesgeometricdetailinanimage

– Edgesareverysharpgradientsinbrightnessindicatingboundariesoffeaturesinanimage

– Accomplishedbydetectingedgesandaddingthembacktotheoriginalimagetoincreasecontrastorbyusingsaturatedoverlays(blackorwhite)ontheoriginalimagetodefineborders.

– Whydowecareaboutedges???

• Threegeneralapproachestoedgedetection– Useofanedge-detectiontemplate– Subtractingasmoothedimagefromitsoriginal– Calculatingspatialderivatives(spatialgradients)– Firsttwoaredesignedtoexaggerateinterfaces,lastisdesignedto

quantifytransitions

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LinearEdgeDetectingTemplates-1 0 +1

-1 0 +1

-1 0 +1

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t(m,n) =Templatethatdetectsverticaledgesinanimageisgivenby

Centralvalueistheaccumulateddifferencehorizontallybetweenpixelsin3adjacentrows

2 2 2 2 8 8 8 8

2 2 2 2 8 8 8 8

2 2 2 2 8 8 8 8

2 2 2 2 8 8 8 8

2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2

� � � � � � � �

� 0 0 18 18 0 0 �

� 0 0 18 18 0 0 �

� 0 0 12 12 0 0 �

� 0 0 6 6 0 0 �

� 0 0 0 0 0 0 �

� 0 0 0 0 0 0 �

� � � � � � � �

LinearEdgeDetectingTemplates

+1 +1 0

+1 0 -1

0 -1 -1

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Vertical Horizontal Diagonal Diagonal

Centralvalueishorizontallyaccumulateddifference

-1 0 +1

-1 0 +1

-1 0 +1

-1 -1 -1

0 0 0

+1 +1 +1

0 +1 +1

-1 0 +1

-1 -1 0

NW/SEEdge NE/SWEdge

Centralvalueisverticallyaccumulateddifference

CentralvalueisaccumulateddifferenceacrossaNW/SEline

CentralvalueisaccumulateddifferenceacrossaNE/SWline

• Thetemplateisreferredtoasakernel• Thesystematicsequentialapplicationofthattemplateacrossthe

imageisreferredtoasconvolutionofthekernel• Otherconvolutionkernelsfordifferentapplicationsaregivenbelow

SpatialDerivativesTechniques:GradientOperators

• Consideracontinuousbrightnessfunctioninsteadofadiscretebrightness

• Wecandefinethespatialgradient()as:

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Discrete Continuousx

y

Where:f(x,y) isthebrightnessvalueatpixellocationx,y andiandjareunitvectorsinthex andy directionsrespectively

Δ

Δ

(x,y) =x(x,y)i +

y(x,y) jd

df d

dff

SpatialDerivativesTechniques:GradientOperators

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Discrete Continuousx

y

Thespatialgradientameasureofhowabruptachangeisinagivendirection.Itisdefinedasthevectorsumofchangewithrespecttothex directionandchangewithrespecttotheydirection,takeninthedirectionofmaximumgradient

Δ

(x,y) =x(x,y)i +

y(x,y) jd

df d

dff

SpatialDerivativesTechniques:GradientOperators

• Foredgedetection,wetypicallyfocusonthemagnitudeanddirectionofchangegivenrespectivelyby:

• Inotherwords,themagnitudeofthevectoristhevector(Pythagorean)sumofthegradientinthexdirectionandthegradientintheydirection

• Theaboveisforcontinuousgradients.Fordiscretegradients(i.e.acrosspixelsinimagery),wereplacethederivativeswithdifferences. Twodifference-basedspatialoperatorswewilldiscussaretheRobertsoperatorandtheSobeloperators(eachisafunctioninENVI)

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1 =x(x,y)

2 =y(x,y)

∇ = ∇1 +∇2

Where

2 2 =tan-1(/)Δ Δ Δ

2 1and

∇ ∇ddf d

df

TheRobertsOperatorDiscretecomponentsofthederivativeonthepreviouschartaregivenby

forthepointi+½,j+½

Inotherwords:weassessthegradientacrossthetwodiagonalsasameanstodeterminetheedges

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1 = (i, j) (i +1, j +1)

2 = (i +1, j) (i, j +1)

i+1

j j+1

(i+½,j+½)

Sincealocalgradientiscomputed,itisnecessarytospecifyathresholdvaluetodetermineedgegradientsandsuppressminorgradients

i

Detectshorizontal,verticalanddiagonaledgesandassignsthemtotheedgethatisinthedirectionofincreasingIandj,offsetbyhalfapixel.

∇ f - f ∇ f - f