MARR_HILDRETH_ED_CVIP

marr_hildreth_ed_cvip() -performs a Marr Hildreth edge detection on the image.

SYNTAX
DESCRIPTION
REFERENCE
EXAMPLE
CREDITS

SYNTAX

out = marr_hildreth_ed_cvip( input_image, sigma, threshold )

Input Parameters include :

input_image - Input image can be gray image or rgb image of MxN size.

sigma - The Gaussian variance.

threshold - The threshold tested against the absolute value of the difference between the two pixels that have the sign changes.

Output Parameter include :

out_img - The output image after edge detection. An image with the same size as the input image.

DESCRIPTION

Marr-Hildreth algorithm is one of the advanced edge detection algorithms which have multiple steps. First the image is convolved with a Gaussian smoothing filter. Then the result is convolved by a Laplacian mask. And finally the zero crossings are found which will create the output image.

Convolving with a Gaussiang and then a Laplacian can be shortened to one step which is convolving with an LoG mask. The formula to determine the size of the filter based on the Gaussian variance is as follow:

$n = 2.ceil(3.35 \sigma + 0.33) + 1$

and the LoG filter in that window is computed by the following formula. The center of the window corresponds to r=c=0:

$LoG = (\frac{2 \sigma^2 - r^2 - c^2}{\sigma^4})e^{- \frac{r^2 + c^2}{2 \sigma^2}}$

After filtering, zero crossings in the results are found and iterpreted as the edges in the output image.

REFERENCE

1. Scott E Umbaugh. DIGITAL IMAGE PROCESSING AND ANALYSIS: Applications with MATLAB and CVIPtools, 3rd Edition.

EXAMPLE

% Read images

 input_image = imread('cam.bmp');

% sigma

 sigma = 5;

% Threshold

 threshold =.2;

% Calling function

 out = marr_hildreth_ed_cvip( input_image, sigma, threshold );

% Display input image

 figure;imshow(input_image);title('Input Image');

% Display output image

 figure; imshow(remap_cvip(out));title('Output image');

MARR_HILDRETH_ED_CVIP

Contents

SYNTAX

DESCRIPTION

REFERENCE

EXAMPLE

CREDITS