David Bisaccia

ObjectivesHistory and ApplicationGray Scale vs. ColorConvolution MaskGradient ImagePeaksDouble Threshold and Final PeaksOutput

HistoryDeveloped by John Canny in 1986

ApplicationUsed to find edges in imagesCan be used for defense, security, and much

moreFace Detection or Human Detection

ObjectivesHistory and ApplicationGray Scale vs. ColorConvolution MaskGradient ImagePeaksDouble Threshold and Final PeaksOutput

Gray Scale vs. ColorColor typically isn’t need when looking for

edgesLess Computation in gray scale, no R,B,G,A

ObjectivesHistory and ApplicationGray Scale vs. ColorConvolution MaskGradient ImagePeaksDouble Threshold and Final PeaksOutput

Loud Noises!Images can have noise in them

Heat wavesDustSmokeAcquisition Noise

Solution: Convolution MaskSuppresses NoiseAverages a pixel with surrounding pixelsSimple mask below

Scan the convolution mask below across the target image (dot product)

Ignore the edges, usually don’t matter

1/4 1/4

1/4 1/4

Dot Product Applied23

45

12

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90

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23

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66

67

36

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87

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1

3 45

6 7 88

1/4 1/4

1/4 1/4* = 35

Before Convolution:

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73

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6 7 88

After Convolution: Table

Current Pixel

Overlapped pixel’s with Mask (needed for dot product)

Gaussian MaskUses Gaussian Mask Sigma is a value chosen by youX and Y are the distances away

from target pixelRange from positive to negative

Mask RadiusMask Radius = 3 * Sigma

22 2/ xe

Gaussian Mask: Pseudo Codeint Maskx[][], Masky[][];Sigma = 3;int MaskRadius = Sigma * 3;

For P = -MaskRadius to +MaskRadiusFor Q = -MaskRadius to +MaskRadius

Maskx[P+MaskRadius][Q+MaskRadius] =-Q*e^(-(P*P + Q*Q)/(2*Sigma));

Masky[P+MaskRadius][Q+MaskRadius] =-P*e^(-(P*P + Q*Q)/(2*Sigma));

222 2/)( yxex

Applying the Gaussian MaskNeed to convolve the target picture with the

Gaussian MaskNeed to do it for the X and Y directionsYields a output convolved X and output

convolved Y matrix (outConvX, outConvY)

Applying the Mask: Pseudo CodeFor i = MaskRadius to Picture Max Row –

MaskRadius For j =MaskRadius to Picture Max Column

MaskRadius -Convolve the current pixel, Pic[i][j], with the maskX -Save result in outConvX[][] -Convolve the current pixel, Pic[i][j], with the maskY -Save result in outConvY[][]

ObjectivesHistory and ApplicationGray Scale vs. ColorConvolution MaskGradient ImagePeaksDouble Threshold and Final PeaksOutput

Gradient ImageAchieved by obtaining the magnitude for

each pixel from the outConvX[][] and the outConvY[][]

Saved in a matrix named Magnitude[][]Iterate through each pixel i and j

Magnitude[i][j] =)][j]outConvY[i ][j]outConvX[i 22

Getting the SlopeSlope = Δy/ ΔxSlope =The slope for each pixel will determine what

neighboring pixels will be compared with the current pixel

vX[][])][]/outCon(outConvY[tan -1

Getting the Slope (cont.)If slope -22.5 to 22.5

If slope 22.5 to 67.5

If slope -67.5 to -22.5

Else

TableRelevant Neighbor Pixel

Current Pixel

Example SlopeThe slope for each pixel will determine what

neighboring pixels will be compared with the current pixel

Compare the Red Neighbors with Current Pixel Value(Green)A slope of 10 degrees

A slope of 85 degrees

TableRelevant Neighbor Pixel

Current Pixel

ObjectivesHistory and ApplicationGray Scale vs. ColorConvolution MaskGradient ImagePeaksDouble Threshold and Final PeaksOutput

PeaksPeaks is represented as a boolean matrix for

each pixel of the image, peak[][]If it is true, then that pixel is considered a

possible peakIf false, then that pixel is not a peak

Getting PeaksFor each pixel use the relevant neighbor pixel

magnitudes and compare with the current pixel’s magnitude

If current pixel’s Magnitude[i][j] > relevant pixel’s Magnitude[i][j]

Then peak[i][j] = trueElse peak[i][j] = false

Example of PeaksThe matrix is represented with values

of the pictures Magnitude[][]Since current pixel’s Magnitude[i][j] > relevant

pixel’s Magnitude[i][j]peak[i][j] = true

Since current pixel’s Magnitude[i][j] < relevant pixel’s Magnitude[i][j]

peak[i][j] = false

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ObjectivesHistory and ApplicationGray Scale vs. ColorConvolution MaskGradient ImagePeaksDouble Threshold and Final PeaksOutput

Double ThresholdFinal[] is another boolean matrix that represents

peak values that are accepted by the double threshold

High ThresholdValues is selected by the programmerIf the Magnitude[] > High Threshold and peak[] ==

true then that pixel is a peak in Final[] Low Threshold

Value is selected by the programmerIf the Magnitude[] > Low Threshold and peak[] ==

trueand that pixel has a neighboring pixel that is connected to a pixel with a high threshold

Getting the High ThresholdFor i = 0 to Row length

For j = 0 to column lengthif(peak[i][j] == true && magnitude[i][j] >

High)peak[i][j] = falsefinal[i][j] = true

else if(peak[i][j] == false && magnitude[i][j] < Lo)

peak[i][j] == falsefinal[i][j] == false

Example High Threshold

7 77

43

32

21

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81

1 91

1 1

34

43

65

67

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2

1 1 91

1 1 1

91

1 1 1 92

1

1 83

82

82

3 2

Magnitude Table Peak Table Final Table

TableTrue Peak True Final

False Peak False Final

Threshold: 80

Getting The Low ThresholdMoreToDo = OnWhile(MoreToDo == On)

For i = 0 to Row lengthFor j = 0 to column length

if(Final[i][j] == true) For p = -1 to 1

For q = -1 to 1 if(peak[i+p][j+q] == true) Final[i+p][j+q] == true

peak[i+p][j+q] = falseMoreToDo = On

Example Low ThresholdGeneral Peaks Table with High and Low:

Final Table:

TableLow Peak

High Peak True Final

False Peak False Final

ObjectivesHistory and ApplicationGray Scale vs. ColorConvolution MaskGradient ImagePeaksDouble Threshold and Final PeaksOutput

OutputFor i = 0 to Row length

For j = 0 to column lengthif(Final[i][j] == true)

print white pixelelse

print black pixel

Example Inputs and OutputsInput Magnitude Peaks

Output:

Home WorkIs this a peak?

12

34

23

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90

30

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90

SourcesMachine Vision : Theory, Algorithms,

Practicalities. E.R. DaviesWikipedia for pictures