Spatial filtering

Filter

Filter

Removes undesirable impurities such as noise

Convolution

Given pixel (i, j), the center of the filter/mask is lined up, and the filters in the sub image are multiplied with the corresponding coefficients in the filter. This yields a matrix which is then simplified to a single value which replaces the center pixel

Padding

Creating new values for pixels outside of the image boundary. Assumed to be 0, NN, or mirrored

Mean filter

Coefficients are all 1, the whole image is divided by the number of pixels in the filter (3×3 is divided by 9)

Weighted mean filter

Coefficients aren’t all 1’s and the image is divided by the total weight for normalization

Median filter

Non-linear filter type, a sliding window is chosen and is placed on the image at position (i, j). All pixel values under the filter are collected, median is computed and given to (i, j). Commonly used for salt and pepper noise

Max/min filter

Takes the max/min from filter space and replaces the center pixel with that. Max is used for lightening and min is used for darkening

Edges

Set of points in an image where there is a change of intensity

First derivative edge detection

Has a peak at the edge which decreases afterwards

Second derivative edge detection

Positive before the edge and is then negative afterwards. 0 at the edge

Zero-crossing

The second derivative changing sign when crossing the edge

Sobel filter

First derivative filter, used to find horizontal and vertical edges. Sum of the coefficients is 0

Prewitt filter

First derivative filter, doesn’t reduce noise, sum is 0

Canny filter

First derivative filter, 3 parameters to detect edges (standard deviation, threshold values t1, and t2)

Laplacian filter

Second derivative filter, adds noise

Laplacian of Gaussian filter

Second derivative filter, offsets the noise of the laplacian

Frangi filter

Shape detecting filter, used to detect vessel like objects. Uses eigen values on second derivative