Median Filter If the objective is to achieve noise reduction rather than blurring, an alternative approach is to use median filters. That is, the gray level of each pixel is replaced by the median of the gray levels in a neighbourhood of that pixel, instead of by the average.

This method is particularly effective when the noise pattern consists of strong, spike-like components and the characteristic to be preserved is edge sharpness. The median m of a set of values is such that half the values in the set are less than m and half are greater than m. In order to perform median filtering in a neighbourhood of a pixel, we first sort the values of the pixel and its neighbours, determine the median, and assign this value to the pixel.

For example, in a 3 X 3 neighbourhood the median is the 5th largest value, in a 5 x 5 neighbourhood the 13th largest value, and so on. When several values in a neighbourhood are the same, all equal values have to be grouped. For example, suppose that a 3 X 3 neighbourhood has values (10, 20, 20, 20, 15, 20, 20, 25,100). These values are sorted as (10, 15, 20, 20, 20, 20, 20, 25, 100), which results in a median of 20.

Thus the principal function of median filtering is to force points with distinct intensities to be more like their neighbours, actually eliminating intensity spikes that appear isolated in the area of the filter mask.

(b)(c)(a) Fig.7.28 Noise suppression. (a) Original image corrupted by 5% impulse noise (b) Result of 3 x 3 mean filtering (c) Result of 3 x 3 median filtering.

Fig.7.29 A 3 x 3 neighbourhood within a portion of the image in Fig.7.28(a)

The new value obtained for this pixel using a 3 x 3 mean filter is ( )/9=128 So mean filtering has not removed the noise completely. To apply a median filter, we place the grey levels from the neighbourhood in a list, {64,64,64,64,255,255,64,64,255}, and sort the list into ascending order {64,64,64,64,64,64,255,255,255}.

The median from this set of values is 64. The noisy values have migrated to the end of the list. Clearly, median filtering can eliminate the impulse noise only if the noisy pixels occupy less than half the area of the neighbourhood.

Edge detection One of the major applications for convolution is in edge detection. Edges can be defined loosely as locations in an image where there is a sudden variation in the grey level of pixels. The contours of solid objects, surface markings, shadows, etc. all generate intensity or colour edges.

The most common method in edge detection is based on the estimation of grey level gradient at a pixel. The gradient is used frequently in industrial application, either to aid humans in the detection of defects or, as a preprocessing step in automated inspection.

Fig (a) A 3 x 3 region of an image (the z’s are grey level values); (b) Prewitt masks; (c) Sobel masks used to compute the gradient at point labelled z 5. z1z1 z2z2 z3z3 z4z4 z5z5 z6z6 z7z7 z8z8 z9z9 (a)

(b) Prewitt operator

(c) Sobel operator

For Prewitte operator, the gradient magnitude g is given by g ≈ |(z 7 + z 8 + z 9 ) - (z 1 + z 2 + z 3 )| + |(z 3 + z 6 + z 9 ) - (z 1 + z 4 + z 7 )| For Sobel operator, g is given by g ≈ |(z 7 + 2z 8 + z 9 ) - (z 1 + 2z 2 + z 3 )| + |(z 3 + 2z 6 + z 9 ) - (z 1 + 2z 4 + z 7 )|

Fig Optical image of contact lens (note defects on the boundary at 4 and 5 o’clock). (a) original image (b) result of Sobel gradient (a)(b)