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Re: How to downsample a image matrix using left and right

• To: mathgroup at smc.vnet.net
• Subject: [mg100913] Re: [mg100864] How to downsample a image matrix using left and right
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Thu, 18 Jun 2009 04:52:11 -0400 (EDT)
• References: <200906170153.VAA25945@smc.vnet.net>

tenveer wrote:
> HI all
> 
> i am just stuck with a unique problem ...
> 
> What i want is to downsample a matrix (image matrix) using two left
> and right matrices....
> e.g if i have a 100 by 100 image matrix X what i want is to downsample
> X to 25 by 25 matrix Y using two downsampling matrices U and V which
> are on left and right respectively i.e Y=U*X*V
> 
> than what will the contents of the U and V matrices.
> 
> Any help will be appreciated

I'm not sure if this answers your question, but you can approximate the 
image using the singular value decomposition. This is not really the 
same as downsampling, but, viewed as a matrix decomposition, it does 
have the form that you indicate.

Here is an example from another recent MathGroup thread.

tt = Table[Cos[x*y], {x, -3., 3., .05}, {y, -3., 3., .05}];

The dimension is 121x121. We use the 25 largest singular values (in this 
example, six seems adequate)

ttsvd = SingularValueDecomposition[tt, 25];

Then the approximated image is reconstructed as

tt2 = ttsvd[[1]].ttsvd[[2]].Transpose[ttsvd[[3]]];

One can compare

ListContourPlot[tt]

to

ListContourPlot[tt2]

to get an idea of the quality.

Daniel Lichtblau
Wolfram Research

• References:
  • How to downsample a image matrix using left and right downsampling
    • From: tenveer <ten.veer@gmail.com>