grey=(r+g+b)/3	grey=sqrt((r*r+g*g+b*b))/3	grey=0.229*r+g*0.587+b*0.114

mask : 3x3 sigma : 0.7	mask : 3x3 sigma : 0.9	mask : 3x3 sigma : 1.2
mask : 5x5 sigma : 0.7	mask : 5x5 sigma : 1	mask : 5x5 sigma : 1.2
mask : 7x 7 sigma : 0.7	mask : 7x 7 sigma : 1	mask :7x 7 sigma : 2

EXPLANATION:

The progression of images from top to bottom along the same vertical colummn shows the effect of truncation error. These images have been calculated with the same smoothening factor sigma but using different mask size. The progression of the images from left to right shows the effect of increasing the smoothening factor sigma. These images have been calculated using the same mask size but increasing sigma. One can see the effect of increasing the smoothing is reduced noise but it also suffers from lost edges.This is Evident in the 3rd image of the 1st row where the  distinctive vertical edge on the left is missed. The effect of truncation is the introduction of a lot of spurious edges.This because of neglecting nonzero contribution from the neighbouring pixels as a result the gradient estimates are erroneous.

EXPLANATION:
The histogram of the pixel  values can be used  to find a suitable value of the threshold.The number of pixels will reduce as  the  threashold is increased. A low threshold leads to  an image with a lot of spurious edges while  a high threshold will lead to missed edges. Thus one needs to trade off   these  two effects. At a threshold value of  0 all the pixels will be considered edge pixels as one raises the treshold value spurious edges will drop of.It  is expected that  near the true value of the threshold  only the correct edge pixels will be selected .Thus the cumulative frequrency plot will flatten out at those points.Thus one can set the threshold; to a value; where the slope of the Cumulative frequency becomes zero or nbsp; minimum. Note however that such a point may not be unique.As in this case where we see that  the distribution of the pixel values are trimodal .Thus it has 2 zones where the slope of cumulative frequency is near zero. This shows that the image has some strong and moderate edges.

mask :3x3 sigma : 0.7	mask : 3x3 sigma : 0.9	mask : 3x3 sigma : 1.1
mask : 5x5 sigma : 0.7	mask : 5x5 sigma : 1.0	mask : 5x5 sigma : 1.2
mask : 7x 7 sigma  :0.7	mask : 7x 7 sigma : 1.0	mask : 7x 7 sigma : 1.2

mask : 3x3 sigma : 0.7 threshold : 110	mask : 3x3 sigma : 0.9 threshold : 110	mask : 3x3 sigma : 1.1 threshold : 110
mask : 5x5 sigma : 0.7 threshold : 120	mask : 5x5 sigma : 1.0 threshold : 110	mask 5x5 sigma1.1 threshlold : 110
mask : 7x 7 sigma : 0.7 threshold : 122	mask :7x 7 sigma : 1 threshold : 120	mask :7x 7 sigma : 2 threshold : 115