Re: Defect detection

aruzinsky <aruzinsky@xxxxxxxxxxxxxxxxxxxx> wrote in
news:1193160468.387448.94960@xxxxxxxxxxxxxxxxxxxxxxxxxxx:

On Oct 23, 9:31 am, agpx...@xxxxxxxx wrote:
On 22 Ott, 18:16, aruzinsky <aruzin...@xxxxxxxxxxxxxxxxxxxx> wrote:





On Oct 22, 12:34 am, agpx...@xxxxxxxx wrote:

...
In reality, the surface isn't
smooth as you can see from the picture (there is some noise).
To filter out that noise I use a rational smoothing filter (that
try to preserve edges). Look at the result:

http://img143.imageshack.us/img143/4972/filteredyl3.png
...

Looks like texture that can be modeled as colored noise. I would
try using a 2D autoregressive (AR) model to turn it into white
noise of a much smaller variance.

To simplify my explanation, consider the general 1D AR model.

Xt = a1*Xt-1 + a2*Xt-2 + ... + an*Xt-n + Et

where { Et } is white noise of zero mean.

1. Estimate AR parameters { ai } by a least squares fit.

2. Using estimated { ai } calculate { Et }.

3. Anomalies such as defects will be evident among the { Et }.

You will have to google for information about 2D AR models. I am
not an expert on 2D AR models, but I have used them for texture
synthesis.

Hi, thanks for the reply. This sound quite interesting. I'll give a
try with 1D AR (using a single row). Also I'm going to search about
2D AR models (but at first look seems that is quite hard to found 2D
AR documentation on Internet). Anyway, thanks to all for your
replies.- Hide quoted text -

- Show quoted text -

It has to be a 2D AR model. Just to give you an intuitive idea of how
well this model fits your background, I took your first image and
replaced the center defect with texture synthesized using a 2D AR
model with 15x15 parameters here:

http://www.general-cathexis.com/originalln9TextureSynthesis.jpg



I agree, it's 2D AR for sure, otherwise you would have random pixels only along one direction (the
other would look more or less shifts of one fixed pattern). The size of the 2D convolution kernel for an
equivalent FIR (MA) model is roughly the size (in pixels) of the largest visual object in this texture, an
equivalent IIR (AR) model is usually much smaller but more unstable in terms of jumping around
between large extremes. MA models are easy to formulate (weighted averages), AR require more
careful design and usually a specialized tool (e.g. Matlab).


--
Harris
.

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