Gaussian Pyramid - Expand and Reduce routines

This contains set of routines, for the 'expand' and 'reduce' operations of Gaussian Image Pyramids.

Description

This contains the code for the 'Expand' and 'Reduce' routines for Gaussian image pyramids, as discussed in the Paper - "
The Laplacian Pyramid as a Compact Image Code" - Burt and Adelson, 1983.

Important applications of the same include motion estimation.

• Acknowledgements: This submission has inspired the following:; Gaussian Pyramid - Expand and Reduce routines 1D, 2D and 3D
• Required Products: Image Processing Toolbox
• MATLAB release: MATLAB 6.1 (R12.1)

[Isabel Sargent]

Doesn't give information about required inputs. Can figure this out fairly easily from code. Code looks a little crude however, not really taking advantage of matrix functionality of Matlab. This was useful to help me understand the paper from which it was taken and I'm sure it works well.

[Izz S]

Having said the above, I can see how this method works better for larger data sets - sorry!

[KGD -]

As noted this is a very poor Matlab implementation (i.e., 3 NESTED loops). A far more efficient Matlab implementation can be had by utilizing Matlab's 2D convolution (conv2) with a separable filter lowpass filter (i.e., two 1D convolutions).

[simon rohl]

i can not iúnderstand input parameter Wt. some body please descibe it.

[nana nana]

i also can understand Wt?

[Abdella Gr]

w is what Burt refers to as the "generating kernel" (it's a filter, 5-tap in this case). What is really happening here is that rather than using a 2D kernel w(m,n) the code is using the a separable formulation of w(m,n) (i.e., filtering in each of the dimensions with a 1D filter). This reduces the computational cost of the filtering. Here is a common w = (1/16)*[1 4 6 4 1]. If you refer to some of Peter Burt's earlier papers he provides a set of constraints for building the weight.

[Kashif Riaz]

 

[Mikel Rodriguez]

I set Wt to [.05; .25 ;.4; .25;.05].

[P. S.]

Changing the line "A = [A, tmpval] ;" to "A = A + sum(tmpval);" highly increases speed because memory has not to be allocated in each loop.

[Deshan Yang]

There are an error with the 'expand' function.

The most inner loop should be as:

                if ( (floor(pixeli) == pixeli) & (floor(pixelj) == pixelj ) )
                    pixeli = pixeli + 2;
                    pixelj = pixelj + 2;
                    tmpval = I (pixeli, pixelj) * Wt(m + 3) * Wt(n + 3);
                    A = [A, tmpval] ;
                end

Otherwise, the expanded image will have 1 pixel shifting to right and down.

[Amirzeb Badshah]

it helped me a lot

[ss sharif]

i could not undrestant what does means ?

[Rachel]

Bad MATLAB implementation.