HMAX

M. Riesenhuber and T. Poggio,

"Hierarchical Models of Object Recognition in Cortex,"

Nature Neurosciece, Vol. 2, No. 11, November 1999. pp 1019-1025.

They say simple cells and complex cells and

complex cells are responsible for invariant properties.

Invariance can be implemented as a pooling mechanism

where there are view-invariant units and view-tuned units.

Hierarchical feedforward network is considered and

the network is based on MAX rather than linear summation (SUM).

MAX is proved to be more robust and invariant than SUM.

That is, Hierarchical MAX has view-invariant object recognition ability

and is supported by biological (physiological) facts.

Anyway, I say, this is a very similar concept to ISA, but a little more flexible.

But this paper doesn't say much of implementation such as

how to get the simple cells or complex cells,

and how to construct the network structure.

See [1] for a specific implementation and examples of HMAX.

In [1], interestingly, simple and complex cells are not learned from data

but designed by second derivative of Gaussians.

[1] T. Serre and M. Riesenhuber,

"Realistic Modeling of Simple and Complex Cell Tuning in the HMAX Model,

and Implications for Invariant Object Recognition in Cortex,"

AI Memo 2004-017, CBCL Memo 239, MIT, July 2004.

- H. Choi

Complex Cells and Object Recognition

S. Edelman, N. Intrator and T. Poggio, "Complex Cells and Object Recognition," NIPS97.

Note that this paper was published in 1997, which is 'long time ago.'
It says complex cells-like filter has invariant recognition. And, actually, it is really simple. Apply one filter for complex cells and check the correlation of the filter output to classify.

The problem is how to implement the complex cells-like filters. And we have one answer, which is independent subspace analysis (ISA) which is kind of a generalization of independent component analysis (ICA). BTW, ICA is a filter like simple cells.
The real problem is these theories are not like math theories. So the performance really depends on the situations such as noise or background or the shape of object.

Our brain is sooooo amazing... How does it do all these complicated stuffs?

- H. Choi