Noise Filtering & Edge Detection

Noise Filtering & Edge Detection Jeremy Wyatt

Filtering • Last time we saw that we could detect edges by calculating the intensity change (gradient) across the image • We saw that we could implement this using the idea of filtering

Linear filtering: the algorithm for i=2:image_height-1 for j=2:image_width-1 end end j+x x+2 j y+2 i i+y NB We count from the upper left,and in MATLAB we start at 1

Linear Filtering: the algorithm for i=2:image_height-1 for j=2:image_width-1 end end j+x j=2 x+2 y+2 i=2 i+y

Noise filtering • We can use convolution to remove noise as we mentioned, e.g. mean filter • This is a linear filter • The most widely used is Gaussian filtering

Effect of mean filtering Original 3x3 filter 5x5 filter

Horizontal Sobel operator Abs(Gx) Threshold=30 5x5 Mean Filter Horizontal Sobel operator Abs(Gx) Threshold=30

Effect of Gaussian filtering Original 5x5 filter Horizontal Sobel Operator Abs(Gx) Threshold = 30

Sequenced filters We can replace a 2d Gaussian filter with 2, 1d Gaussian filters in sequence

Gaussian edge detection • We can take the first derivative of the masks and then convolve with those • Then we can combine the resulting images using the formula for magnitude • However when thresholded we can see that this loses edge information • How can we keep this?

Second order operators • Thresholding the first derivative of the smoothed signal thickens the edges and also we lose some useful edges • One solution is therefore to take the second derivative instead • A basic second order mask is the Laplacian

Reading • RC Jain, Chapter 4

Noise Filtering & Edge Detection