Edge detection by Marr and Hildreth's Method (continued)

If an edge is present in only one edge map one reason may be that two independent physical phenomena are operating to produce intensity changes in same region of the image. From the smoothed images, edges can be detected by using the edge det algorithm discussed earlier.Depending on which method is used the LP filtering operation in equ (1) and the partial derivative operation used for edge detection may be combined.

For eg. noting and convolution "*" are linear we obtain.

i.e

Marr and Hildreth chose to detect edges by looking for zero crossing points of . Bandlimiting tends to reduce noise thus reducing the noise sensitivity problem associated with detecting zero crossing points.

Clearly is equivalent to Band pass filtering where is a parameter that controls the BW of BPF.

For a sequence simply replace x by and .

Problem : Try out Marr and Hildreth method by blurring an original image with h(x 1 ,x 2 ) for =4, 8, 32 and obtain the edge maps by detecting the zero crossings of with for