Welcome Guest, you are in: Login

MUST Creative Engineering Laboratory



Technical Doc

Search the wiki

MUST Corp.

MUST Corp.


 Microsoft CERTIFIED Partner Software Development, Web Development, Data Platform

 Microsoft Small Business Specialist


Microsoft Certified IT Professional

Microsoft Certified Professional Developer

Laplacian of Gaussian (LoG)

Modified on 2010/05/05 00:54 by Administrator Categorized as Digital Image Processing
Laplacian of Gaussian (LoG)

As Laplace operator may detect edges as well as noise (isolated, out-of-range), it may be desirable to smooth the image first by convolution with a Gaussian kernel of width Image

to suppress the noise before using Laplace for edge detection:

The first equal sign is due to the fact that

So we can obtain the Laplacian of Gaussian Image first and then convolve it with the input image. To do so, first consider Image

and Image

Note that for simplicity we omitted the normalizing coefficient Image . Similarly we can get

Now we have LoG as an operator or convolution kernel defined as

The Gaussian Image and its first and second derivatives Image and Image are shown here:


This 2D LoG can be approximated by a 5 by 5 convolution kernel such as

The kernel of any other sizes can be obtained by approximating the continuous expression of LoG given above. However, make sure that the sum (or average) of all elements of the kernel has to be zero (similar to the Laplace kernel) so that the convolution result of a homogeneous regions is always zero.

The edges in the image can be obtained by these steps:

Applying LoG to the image Detection of zero-crossings in the image Threshold the zero-crossings to keep only those strong ones (large difference between the positive maximum and the negative minimum) The last step is needed to suppress the weak zero-crossings most likely caused by noise.


MUST Creative Engineering Laboratory

ImageImage Image Image

Image Image Image Image Image Image Image

Copyright © 2010 MUST Corp. All rights reserved. must@must.or.kr
This Program is released under the GNU General Public License v2. View the GNU General Public License v2 or visit the GNU website.