🚀 go-pugleaf

singlis@waikato.ac.nz writes:

>Thanks to all who replied about FFT segmentation.

>A Fourier Transform in 1D is a breakdown into the waveform component
>sin/cos terms. This sin/cos waves when added approximate (v. closely) the
>original waveform.

>How is the 2D case explained? Is the 2D transform a sum of "planar" sin/cos
>"waves", or is it more of a breakdown of the horizontal groups of vertical
>transforms?

Due to the separability, you can do row and column transforms after each
other, but you can do it the other way round as well, so this would seem
to be missing the point some way.

Another possibility is to view the term (xu+yv) in the exponential as
a dot product (x,y).(u,v).
If you view (u,v) as a vector, you can interpret the
value at index (u,v) as a complex exponential wave crossing the picture
in direction (1/u,1/v) (or was that (v,u)?) with frequency |u,v|. A real-
valued interpretation (phase and amplitude) would have to take index
(-u,-v) into consideration as well.

In article <1992Aug27.215818.10407@waikato.ac.nz>, singlis@waikato.ac.nz writes:
|> Thanks to all who replied about FFT segmentation.
|> 
|> How is the 2D case explained? Is the 2D transform a sum of "planar" sin/cos
|> "waves", or is it more of a breakdown of the horizontal groups of vertical
|> transforms?

The two are equivalent, as you can see by looking at the equations.
E.g. define the relationship between the Fourier pair f(x,y), F(u,v) as

	F(u,v) = \int \int f(x,y) \exp (-2 \pi i (ux + vy) )  dx dy     (1)
	f(x,y) = \int \int F(u,v) \exp ( 2 \pi i (ux + vy) )  du dv     (2)

Reorder the integration in (1) to get

	F(u,v) = \int  [ \int f(x,y) \exp (-2\pi i vy) dy ]  \exp (-2\pi i ux) dx

which shows you can think of the 2D transform F(u,v) as the 1D "horizontal"
transform of the function that is the 1D "vertical" transform of f(x,y) for 
each x.

On the other hand, (2) shows that f(x,y) is the sum of functions of the
form \exp(2\pi i (ux + vy)), each weighted by F(u,v) du dv.  Each component is a 
plane complex exponential of frequency \sqrt(u^2 + v^2) and 
orientation \arctan (v/y).

	--Paul

Hello everyone,

	There are many commercial OCR engines on the market right now for
reading printed text. I am aware of products like the Kurzweil K-5000 and
Discover 7320 Model 5 (from Xerox), OmniPage (from Caere Corp.), SAIC (from
Differential Processing System) and NestorReader.

	I wonder if anybody has done independent evaluation of any OCR
products, since such information would be useful to potential users. 
Specifically, I need answers to the following questions:


(i) name of product and company which produces it  

(ii) fonts and point sizes handled by product

(iii) whether the OCR engine exhibits true multifont and "multisize"
      capability i.e. is able to recognize text without the user
      having to specify in advance its font type and point size.

      If so, what is the accuracy over a variety of fonts and point sizes?

      If not, what is the accuracy over common fonts like Courier, Times
      Roman and Helvetica and point sizes from 8 to 24 points? 

(iv) What are the commercial OCR products, if any, that can
     1. recognise a page of text containing a mixture of fonts and point
	sizes at greater than 98% accuracy?

     2. recognise a page of text containing a single known font and a
	range of point sizes at greater than 99% accuracy?

(v) Are there any commercial OCR systems that accept noisy input or 
    text on shaded background eg. carbon and photostated/fax copies and
    still maintain an acceptable accuracy (say greater than 95%)?
  

Further, if there are any evaluations of commercial handwritten OCR systems, 
I will also be interested to hear about them.

Please email all replies/references to kaykit@iti.gov.sg. If there are 
enough responses, I will summarise.

Thanks!




---
Kay-Kit CHAN    			| Internet: kaykit@iti.gov.sg
Knowledge Systems Lab			| Bitnet:   kaykit@itivax
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