Canny’s Algorithm for Edge Detection

Canny’s Algorithm for Edge Detection David Bisaccia

Objectives • History and Application • Gray Scale vs. Color • Convolution Mask • Gradient Image • Peaks • Double Threshold and Final Peaks • Output

History • Developed by John Canny in 1986

Application • Used to find edges in images • Can be used for defense, security, and much more • Face Detection or Human Detection

Gray Scale vs. Color • Color typically isn’t need when looking for edges • Less Computation in gray scale, no R,B,G,A

Loud Noises! • Images can have noise in them • Heat waves • Dust • Smoke • Acquisition Noise

Solution: Convolution Mask • Suppresses Noise • Averages a pixel with surrounding pixels • Simple mask below • Scan the convolution mask below across the target image (dot product) • Ignore the edges, usually don’t matter

Dot Product Applied Before Convolution: * = 35 After Convolution: Table Current Pixel Overlapped pixel’s with Mask (needed for dot product)

Gaussian Mask • Uses Gaussian Mask • Sigma is a value chosen by you • X and Y are the distances away from target pixel • Range from positive to negativeMask Radius • Mask Radius = 3 * Sigma

Gaussian Mask: Pseudo Code intMaskx[][], Masky[][]; Sigma = 3; intMaskRadius = Sigma * 3; For P = -MaskRadius to +MaskRadius For 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));

Applying the Gaussian Mask • Need to convolve the target picture with the Gaussian Mask • Need to do it for the X and Y directions • Yields a output convolved X and output convolved Y matrix (outConvX, outConvY)

Applying the Mask: Pseudo Code For 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[][]

Gradient Image • Achieved 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] =

Getting the Slope • Slope = Δy/ Δx • Slope = • The slope for each pixel will determine what neighboring pixels will be compared with the current pixel

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 Table Relevant Neighbor Pixel Current Pixel

Example Slope • The 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 Table Relevant Neighbor Pixel Current Pixel

Peaks • Peaks is represented as a boolean matrix for each pixel of the image, peak[][] • If it is true, then that pixel is considered a possible peak • If false, then that pixel is not a peak

Getting Peaks • For 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] = true • Else peak[i][j] = false

Example of Peaks • The matrix is represented with valuesof 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

Double Threshold • Final[] is another boolean matrix that represents peak values that are accepted by the double threshold • High Threshold • Values is selected by the programmer • If the Magnitude[] > High Threshold and peak[] == true then that pixel is a peak in Final[] • Low Threshold • Value is selected by the programmer • If 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 Threshold For i = 0 to Row length For j = 0 to column length if(peak[i][j] == true && magnitude[i][j] > High) peak[i][j] = false final[i][j] = true else if(peak[i][j] == false && magnitude[i][j] < Lo) peak[i][j] == false final[i][j] == false

Example High Threshold Threshold: 80 Peak Table Final Table Magnitude Table Table True Peak True Final False Peak False Final

Getting The Low Threshold MoreToDo = On While(MoreToDo == On) For i = 0 to Row length For 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] = false MoreToDo = On

Example Low Threshold General Peaks Table with High and Low: Final Table: Table Low Peak High Peak True Final False Peak False Final

Output For i = 0 to Row length For j = 0 to column length if(Final[i][j] == true) print white pixel else print black pixel

Example Inputs and Outputs Input Magnitude Peaks Output:

Home Work Is this a peak?

Sources • Machine Vision : Theory, Algorithms, Practicalities. E.R. Davies • Wikipedia for pictures

Canny’s Algorithm for Edge Detection