Jesus Malo, July 5, 2001
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As you know,the divisive normalization model along with
the Barlow hypothesis accounts for a number of experimental
results in visual and auditory perception.
Also, this (simple) nonlinearity has very appealing statistical
properties that cannot be achieved with linear transforms.
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The inversion of the transform could have a number of
applications in diverse fields:
- Design of accurate stimuli for vision research.
- Texture synthesis.
- Image compression.
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However, the straightforward inversion of the normalization
is very hard!:
While the interaction among coefficients in the DIRECT
normalization is LOCAL (sparse, convolution-like interaction
matrix), the interaction between the normalized coefficients
in the INVERSE is GLOBAL, (dense, complex-structure interaction
matrix).
The dense matrix of the inverse becomes hard to handle even
with moderate size images.
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In the next lab meeting I will present a fast inversion method
that doesnot involve dense matrices. This method is based on
the (finite) expansion of the inverse of a matrix.
I will discuss the convergence of the method. Also, I will
show some application results.