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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<HTML>
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<HEAD>
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<TITLE>GOCR-documentation</TITLE>
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<META NAME="description" CONTENT="GOCR-documentation">
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<META NAME="keywords" CONTENT="ocr">
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<META NAME="resource-type" CONTENT="document">
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<META NAME="distribution" CONTENT="global">
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<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1">
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<META NAME="Generator" CONTENT="Joerg">
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</HEAD>
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<BODY >
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<H1 ALIGN="CENTER">GOCR-documentation</H1>
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<P ALIGN="CENTER"><STRONG>Jörg Schulenburg</STRONG></P>
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<P ALIGN="CENTER"><STRONG>Magdeburg, June 3, 2002</STRONG></P>
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<H3>Abstract:</H3>
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<DIV>
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In this documentation I describe some ideas for my OCR-program.
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It contains algorithms and examples and gives you
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an impression of what the program can (or could) do.
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</DIV>
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<P>
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<P>
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<BR><HR>
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<!--Table of Child-Links-->
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<A NAME="CHILD_LINKS"></A>
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<UL>
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<LI><A HREF="#SEC1">Introduction</A>
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<LI><A HREF="#SEC2">Segmentation of textual regions / Layout analysis</A>
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<LI><A HREF="#SEC3">Line detection</A>
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<LI><A HREF="#SEC4">Cluster detection</A>
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<LI><A HREF="#SEC5">Engines</A>
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<LI><A HREF="#SEC6">Remove pixels</A>
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<LI><A HREF="#SEC7">Add pixels</A>
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<LI><A HREF="#SEC8">Similarity analyzer</A>
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<LI><A HREF="#SEC9">Overlapping characters</A>
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<LI><A HREF="#SEC10">Black/White, Gray and Colors</A>
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<LI><A HREF="#SEC11">Pictures on scanned pages</A>
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<LI><A HREF="#SEC12">Tools</A>
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<LI><A HREF="#SEC13">glossary</A>
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<LI><A HREF="#SEC14">More information?</A>
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<LI><A HREF="#SEC15">About this document</A>
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</UL>
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<!--End of Table of Child-Links-->
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<H1><A NAME="SEC1"> Introduction</A>
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</H1>
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First I have to say that I am not a expert in pattern recognition
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or similar things. My knowledge is based mostly on experiments with my
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program.
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Therefore do not worry about stupid algorithms I put in this document.
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In this documentation I describe some ideas for my OCR-program.
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The examples give you an impression of how the program handles
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your images.
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If you have comments regarding contents or spelling please
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write to the author.
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<H1><A NAME="SEC2">Segmentation of textual regions / Layout analysis</A></H1>
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This is implemented as a recursive division in two parts.
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<UL>
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<LI>look for the thickest horizontal or vertical gap through the box</LI>
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<LI>if the gap is less than five times longer than thick do not divide </LI>
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<LI>do the same with the two new parts</LI>
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</UL>
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I know that this algorithm is not as good as you wish,
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but I do not know a better one.
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<P>
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It would be very helpful to know about a function which is able to
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decide whether the box represents a single text line or a more complex object.
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<H1><A NAME="SEC3">Line detection</A></H1>
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<P>
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Line detection is very importand for good recognition.
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For example it is difficult to distinguish between lowercase letter <B>p</B>
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and uppercase letter <B>P</B> without having a baseline (same total height).
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The lowercase version of <B>p</B> has a depht (the lower end is below the
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baseline) and therefore its easy to distinguish from the uppercase version
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if the baseline is known. The line detection is responsible for finding the
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baseline of every text line.
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<P>
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Lines of characters are detected by looking for interline spaces.
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These are characterized by a large number of non-black pixels in a
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row. Image rotation (skewing) presents a problem, therefore the program
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first looks only at the left half of the image. When a line is
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found, the left half of the right side is scanned, because lines
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are often short. The variation in height gives an indication of
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the rotation angle. Using this angle, a second run detects lines
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more accurately. Line detection may fail if there is dust on the
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image.
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<P>
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In version v0.2.3 this behaviour is slightly changed.
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To detect the rotation angle, the line through the most
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characters is detected.
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<H1><A NAME="SEC4">Cluster detection</A></H1>
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A cluster is a group of pixels which are connected with each other.
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The simplest way to detect a cluster is to look for a pixel.
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If you find one, look to the neighbouring pixels. This can be done recursively.
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<P>
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This method needs a lot of stack space if a cluster is very large,
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and can cause problems with the memory.
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<P>
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Do you remember the algorithm for leaving a maze?
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Go along the right (or left) wall. This seems to be a good approach
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for detecting clusters without recursion.
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The following picture shows a trace of the maze algorithm.
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<P>
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<TABLE WIDTH="680">
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<TR><TD>
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<PRE>
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first 35 steps next 36 steps
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..@@@@@..@@@@<.. ..v<<<<..v<<<@.. * = starting point
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..@@@@@@@@@.@^<. ..>>v@^<<<@.@@@. >^<v = go right,up,left,down
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....@@@@@...@@^. ....v@@@@...@@@. @ = black pixel
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....@@@@....@@^. ....v@@@....@@@.
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....@@@.....@@^. ....v@@.....@@@.
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....@@@.....@@^. ....v@@.....@@@.
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...@@@@.....@@^. ...v<@@.....@@@.
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...@@@......@@^. ...v@@......@@@.
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...@@@......@@^. ...v@@......@@@.
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...@@@.....@@@^. ...v@@.....@@@@.
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...@@@.....@@>^. ...v@@.....@@@@.
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...@@@.....@@^.. ...v@@.....@@@..
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..@@@@.....@@^.. ..v<@@.....@@@..
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..@@@@....@@@^.. ..v@@@....@@@@..
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*>>>>>>>>>>>>^<< @@@@@@@@@@@@@@@@
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</PRE></TD></TR>
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</TABLE>
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<P>
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The minimum and maximum coordinates can be used to create a box around the
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cluster. But does this algorithm work with diagonally connected pixels?
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<H1><A NAME="SEC5">Engines</A></H1>
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GOCR is able to work with different recognition engines.
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Since version 0.37 engines have to return a probability value together
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with the recognized character or a table of values to a table of characters.
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If the probability value is 100, the engine is 100% sure to have found the
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right character otherwise the value is less. This gives GOCR the possibility
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to compare results of different engines or in case of a not recognized character
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to inform the user or another
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application (spell checker) which characters probably could be there.
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<H2>Base-Engine</H2>
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The base engine (src/ocrX.c) is the original engine used in the first implementation
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of GOCR by Jörg. The idea was to get a fast and acceptable result
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without learning theoretical background. Later it should be replaced or completed
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by a better engine.
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The base engine is a rule based engine.
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The engine was written without theoretical
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background and is improved by try and error method but is is still far from
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perfect. The algorithm is very tolerant to size and form af characters
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(omnifont).
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How does the engine identify a character? For the explanation look at the
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following pattern.
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<P>
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<TABLE WIDTH="680">
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<TR><TD>
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<PRE>
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vvvv vv- white regions
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......@@...... <- crossing one line
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......@@......
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.....@@@@.....
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.....@@@@.....
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.....@@@@.....
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....@..@@@.... <- white hole / crossing two lines
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....@..@@@.... <- crossing two lines
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....@..@@@....
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...@....@@@...
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...@....@@@...
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...@....@@@...
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..@@@@@@@@@@.. <- horizontal line near center
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..@......@@@..
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..@......@@@..
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.@........@@@. v- increasing width of pattern
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.@........@@@. v
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.@........@@@. v
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@@@......@@@@@
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^^^-- gap
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</PRE></TD></TR>
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</TABLE>
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<P>
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In the future the program
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should detect edges, vertices, gaps, angles and so on.
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This is called feature extraction (as far as I know).
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With such data the engine could make a cluster analysis.
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But this is a difficult task, if the scanned image is noisy.
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<H2>Database-Engine</H2>
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The database engine (src/database.c) was the second engine added to GOCR.
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It was primary written to give users a simple tool to recognize
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special language-specific characters. The program generates a list
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(text file db.lst of image filenames and character codes)
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and image samples (pnm-files) in a database path (./db/).
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The database can be created by hand or extern programs or by GOCR itself
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using option (-m 130). In the last case GOCR prompts the user
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for not recognized characters. If he enters the character the pattern
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is saved in the database path as pnm-file and its file name is added
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to the database list (db.lst) together with the text string the pattern
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should be replaced by.
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For recognition GOCR first loads the database into memory (option -m 2).
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The main algorithm compares not recognized characters with stored images
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and calculates a distance value. If the distance value is small enough,
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the character is treated as recognized.
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<H1><A NAME="SEC6">Remove pixels</A></H1>
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The following picture shows an <I>n</I> which has additional pixels at the
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bottom. Therefore it can not be detected as <I>n</I>. What can be done?
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<UL>
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<LI>classify horizontal (<TT>=</TT>) and vertical (<TT>I</TT>) pixels by
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comparing the distance between the next vertical and next horizontal white
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pixels (.)
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</LI>
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<LI>measure mean thickness of vertical and horizontal clusters
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</LI>
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<LI>erase unusually thin horizontal pixels at the bottom line
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</LI>
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</UL>
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<P>
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<TABLE WIDTH="680">
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<TR><TD>
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<PRE>
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..@@@@@..@@@@@.. ..==III..===II.. dx=16 dy=15
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..@@@@@@@@@.@@@. ..==III====.III. thickness 2 to 3
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....@@@@@...@@@. ....III==...III.
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....@@@@....@@@. ....III=....III.
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....@@@.....@@@. ....III.....III.
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....@@@.....@@@. ....III.....III.
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...@@@@.....@@@. ...IIII.....III.
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...@@@......@@@. ...III......III.
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...@@@......@@@. ...III......III.
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...@@@.....@@@@. ...III.....IIII.
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...@@@.....@@@@. ...III.....IIII.
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...@@@.....@@@.. ...III.....III..
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..@@@@.....@@@.. ..IIII.....III..
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..@@@@....@@@@.. ..IIII....IIII..
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@@@@@@@@@@@@@@@@ ================
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^^^
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this causes the problem
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</PRE></TD></TR>
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</TABLE>
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<P>
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A better way is to find serifs (horizontal lines glued on the lower end
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of vertical lines) which touch together (v0.2.5).
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<P>
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The next picture shows blind pixels which are caused by dust on the paper.
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The upper right dots are not connected with the rest of the character.
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This can be detected via fill-algorithms. Currently the program
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assumes that dots near the upper end of a character are ``i''-dots
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or diaereses (umlaut dots).
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<P>
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<TABLE WIDTH="680">
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<TR><TD>
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<PRE>
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..........................O... ..........................O...
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..........................O... ..........................O...
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.............................. ..............................
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.............................. ..............................
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..........@@@.......@@@@...... ..........@@@.......@@@@......
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..@@@@..@@@@@@@...@@@@@@@..... ..@@@@..@@@@@@@...@@@@@@@.....
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@@@@@@@@@@@@@@@@.@@@@@@@@@.... @@@@@@@@@@@@@@@@.@@@@@@@@@....
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..@@@@@@....@@@@@@.....@@@@... ..@@@@@@....@@@@@@.....@@@@...
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..@@@@.......@@@@......@@@@... ..@@@@.......@@@@......@@@@...
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..@@@@.......@@@.......@@@@... ..@@@@.......@@@.......@@@@...
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..@@@@.......@@@.......@@@@... ..@@@@.......@@@.......@@@@...
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..@@@@.......@@@.......@@@@... ..@@@@.......@@@.......@@@@...
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..@@@@.......@@@@......@@@@... ..@@@@.......@@@@......@@@@...
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..@@@@.......@@@.......@@@@... ..@@@@.......@@@.......@@@@...
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..@@@@.......@@@@......@@@@... ..@@@@.......@@@@......@@@@...
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..@@@@.......@@@.......@@@@... ..@@@@.......@@@.......@@@@...
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..@@@@.......@@@.......@@@@... ..@@@@.......@@@.......@@@@...
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..@@@@.......@@@.......@@@@... ..@@@@.......@@@.......@@@@...
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..@@@@.......@@@.......@@@@... ..@@@@.......@@@.......@@@@...
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..@@@@.......@@@.......@@@@... ..@@@@.......@@@.......@@@@...
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..@@@@.......@@@@......@@@@... ..@@@@.......@@@@......@@@@...
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..@@@@......@@@@@......@@@@@.. ..@@@@......@@@@@......@@@@@..
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@@@@@@@@..@@@@@@@@@..@@@@@@@@@ @@@@@@@@..@@@@@@@@@..@@@@@@@@@
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</PRE></TD></TR>
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</TABLE>
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<H1><A NAME="SEC7">
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Add pixels</A>
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</H1>
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The following picture shows an <I>m</I>. The legs are only barely connected.
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How do we handle this?
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<UL>
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<LI>if the engine has failed, a filter is switched on and the engine
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starts over
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</LI>
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<LI>the 2x2 filter sets pixels to (<I>O</I>) near barely connected pixels
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</LI>
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</UL>
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<P>
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<TABLE WIDTH="680">
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<TR><TD>
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<PRE>
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vv vv
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@@@.@@@..@@@... @@@.@@@..@@@...
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.@@.@@@@.@@@@..< .@@O@@@@O@@@@.. filter: .@ => O@ @. => @O
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.@@@..@@@..@@..< .@@@..@@@..@@.. @. => @. .@ => .@
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.@@@..@@@..@@@. .@@@..@@@..@@@.
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.@@@..@@@..@@@. .@@@..@@@..@@@.
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.@@@..@@@..@@@. .@@@..@@@..@@@.
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.@@@..@@@..@@@. .@@@..@@@..@@@.
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.@@@..@@@..@@@. .@@@..@@@..@@@.
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.@@@..@@@..@@@. .@@@..@@@..@@@.
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.@@@..@@@..@@@. .@@@..@@@..@@@.
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.@@@..@@@..@@@. .@@@..@@@..@@@.
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.@@@..@@@..@@@. .@@@..@@@..@@@.
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.@@@..@@@..@@@. .@@@..@@@..@@@.
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@@@@@.@@@@.@@@@ @@@@@.@@@@.@@@@
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</PRE></TD></TR>
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</TABLE>
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<H1><A NAME="SEC8">
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Similarity analyzer</A>
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</H1>
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Some characters are a little bit noisy. These characters can be identified by
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comparison with other, already recognized characters. This can be done
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via a good distance function. May be
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the distance function in the actual version of GOCR is not very good.
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Feel free to send me your ideas, but be sure it does not waste my time.
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<H1><A NAME="SEC9">
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Overlapping characters</A>
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</H1>
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The following picture shows an overlapping <I>ru</I>.
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How do we handle this?
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<UL>
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<LI>look for 3 weak connections (sum over y is small, start in the middle)
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</LI>
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<LI>test if the right and left part can be detected by the engine
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</LI>
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<LI>correction of surrounding box
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</LI>
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</UL>
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<P>
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<TABLE WIDTH="680">
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<TR><TD>
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<PRE>
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....@@...@@@@@@@@@@....@@@@@@@.. ....@@...@@@@@@@@@@....@@@@@@@..
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..@@@@..@@@@@..@@@@......@@@@@.. ..@@@@..@@@@@..@@@@......@@@@@..
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@@@@@@@@@@@@@.,.@@@.......@@@@.. @@@@@@@@@@@@@...@@@.......@@@@..
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..@@@@@@..@@@...@@@.......@@@@.. ..@@@@@@..@@@...@@@.......@@@@..
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...@@@@.......,.@@@@......@@@@.. ...@@@@.........@@@@......@@@@..
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...@@@@.........@@@@......@@@@.. ...@@@@.........@@@@......@@@@..
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...@@@@.......,.@@@.......@@@@.. ...@@@@.........@@@.......@@@@..
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...@@@@.........@@@.......@@@@.. ...@@@@.........@@@.......@@@@..
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...@@@........,.@@@@......@@@@.. ...@@@..........@@@@......@@@@..
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...@@@..........@@@@......@@@@.. ...@@@..........@@@@......@@@@..
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...@@@........,.@@@@......@@@@.. ...@@@..........@@@@......@@@@..
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...@@@..........@@@.......@@@@.. ...@@@..........@@@.......@@@@..
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...@@@........,.@@@@......@@@@.. ...@@@..........@@@@......@@@@..
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...@@@..........@@@@......@@@@.. ...@@@..........@@@@......@@@@..
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...@@@........,.@@@@......@@@@.. ...@@@..........@@@@......@@@@..
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...@@@..........@@@@@...@@@@@@@. ...@@@..........@@@@@...@@@@@@@.
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..@@@@@.......,..@@@@@@@@@.@@@@@ ..@@@@@..........@@@@@@@@@.@@@@@
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@@@@@@@@@.........@@@@@@@..@@@.. @@@@@@@@@.........@@@@@@@..@@@..
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..............,....@@@.......... ...................@@@..........
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^^^
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213 weak vertical lines
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</PRE></TD></TR>
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</TABLE>
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<P>
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Of course the situation is more difficult with slanted characters.
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<P>
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The following example shows, how to deal with larger clusters.
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To get a fast program a first test should select the possible positions of
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division. That can be done by following upper and lower bows to a crease or a break. Than try to break on all detected creases, start at most
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important one (not implemented yet v0.2.4).
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<P>
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<TABLE WIDTH="766">
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<TR><TD>
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<PRE>
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>>>>vvv<<<<< >>vv<<<< >>>vvv<<<<
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......@@@@@@@..................@@.........@@@@@@@..........@@@@@@@.....
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....@@@@@@@@@@@...............@@@.......@@@@@@@@@@@......@@@@@@@@@@@...
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...@@@@@@@@@@@@@.............@@@@......@@@@@@@@@@@@@....@@@@@@@@@@@@@..
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..@@@@.......@@@@...........@@@@@.....@@@@.......@@@@..@@@@.......@@@@.
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..@@@........@@@@..........@@@@@@@....@@@........@@@@@@@@@........@@@@.
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.@@@@..........@@.........@@@@@@@@...@@@@..........@@@@@@@.........@@@@
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.@@@.....................@@@@.@@@@...@@@..............@@...........@@@@
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.@@@....................@@@@@.@@@@...@@@...........................@@@@
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@@@...@@@@@@@...........@@@@..@@@...@@@...@@@@@@...................@@@.
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@@@@.@@@@@@@@@@........@@@@...@@@@..@@@@.@@@@@@@@@@...............@@@@.
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@@@@@@@@@@@@@@@.......@@@@....@@@@..@@@@@@@@@@@@@@@...............@@@..
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@@@@@@@.....@@@@@.....@@@.....@@@@..@@@@@@......@@@@@............@@@@..
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@@@@.........@@@@...@@@@......@@@@..@@@@@........@@@@...........@@@....
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@@@@..........@@@@.@@@@.......@@@@..@@@@..........@@@..........@@@@....
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@@@@..........@@@@@@@@@.......@@@@.@@@@@..........@@@.........@@@@.....
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@@@@..........@@@@@@@@@@@@@@@@@@@@@@@@@@..........@@@@.......@@@@......
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@@@@..........@@@@@@@@@@@@@@@@@@@@@@@@@@..........@@@@......@@@........
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.@@@..........@@@@@@@@@@@@@@@@@@@@@@.@@@..........@@@@....@@@@@........
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.@@@@........@@@@.............@@@@...@@@@........@@@@....@@@@..........
|
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..@@@@.......@@@@.............@@@@....@@@@.......@@@@...@@@@...........
|
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..@@@@@....@@@@@..............@@@@.....@@@@....@@@@@...@@@@@@..........
|
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....@@@@@@@@@@@...............@@@@......@@@@@@@@@@@...@@@@@@@@@@@@@@@@@
|
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.....@@@@@@@@@................@@@@........@@@@@@@@....@@@@@@@@@@@@@@@@@
|
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........@@@@...................@@..........@@@@@........@@@@@@@..@.@@@.
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>>>>^ ^<<>>^ ^<<<<< >>>^<<< ^^ ^
|
|
|
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>,< show the path of the detection algorithm
|
|
</PRE></TD></TR>
|
|
</TABLE>
|
|
|
|
<P>
|
|
The latest version of GOCR may use different algorithms.
|
|
You have to look at the sources learn more.
|
|
|
|
<H1><A NAME="SEC10">
|
|
Black/White, Gray and Colors</A>
|
|
</H1>
|
|
For simplicity colored images are converted to gray internally.
|
|
That means a red text on green background will not be detected.
|
|
You should use your own filter for this purpose.
|
|
|
|
<P>
|
|
If the original image is gray, a critical value is calculated to
|
|
extract characters from the background. This can fail, if images are
|
|
on the scanned page or tha scan is bad (dark edges or borders).
|
|
It is difficult to overcome this problem because graylevels are mostly
|
|
restricted to the 8 bit limit (16 bit would help to overcome this problem).
|
|
|
|
<P>
|
|
Black/White images are internally converted to gray with two levels (0 and
|
|
255).
|
|
|
|
<P>
|
|
The lowest 4 bits are not used, because they are used by internal functions
|
|
(this can be changed in future).
|
|
|
|
<P>
|
|
After calculation of the threshold value (otsu.c) the brightness of
|
|
every pixel is recalculated to a new internal threshold value
|
|
of 160 (128+32).
|
|
This is a bit above the middle of the 8 bit range. The idea is to
|
|
make the live easier for the other routines. Pixels which does not sure
|
|
belong to the white or black ones get a value near the threshold value.
|
|
Some routines can use this bit of more information to ignore outriders.
|
|
Second point is, that this is necessary for using lowest for bits
|
|
without destroying image informations.
|
|
|
|
<H1><A NAME="SEC11">Pictures on scanned pages</A>
|
|
</H1>
|
|
At first all objects on the scanned page are detected.
|
|
Objects are clusters of black pixels.
|
|
Pictures are detected if they are larger than 4 times the mean size of
|
|
all objects. This rule is very simple and can fail some times.
|
|
But it works fast and mostly the result is ok.
|
|
|
|
<H1><A NAME="SEC12">Tools</A></H1>
|
|
|
|
<P>
|
|
<DL COMPACT>
|
|
<DT>pbmclean:</DT>
|
|
<DD>This program is written by Angus Duggan and Jef Poskanzer.
|
|
It cleans up ``snow'' on bitmap images.
|
|
</DD>
|
|
<DT>pnmtools:</DT>
|
|
<DD>This tools are used to convert different image-formats to
|
|
easy readable PNM (PBM,PGM,PPM) format.
|
|
GOCR uses the popen-routine to call this programs if the
|
|
suffix of the filename matches to a list in pnm.c.
|
|
This will fail if pnmtools are missing.
|
|
</DD>
|
|
</DL>
|
|
|
|
<H1><A NAME="SEC12b">related projects (to learn from)</A></H1>
|
|
|
|
<P>
|
|
<DL COMPACT>
|
|
<DT>unpaper:</DT> <!-- Dec05 JS -->
|
|
<DD> <a href="http://unpaper.berlios.de/">unpaper</a> -
|
|
post-processing scanned and photocopied book pages,
|
|
written by Jens Gulden 2005, GPL
|
|
</DD>
|
|
</DL>
|
|
|
|
<H1><A NAME="SEC13">glossary</A> </H1> <DL COMPACT>
|
|
<DT>font series:</DT> <DD>bold, condensed</DD>
|
|
<DT>font shape: </DT> <DD>normal, italic, slanted, sc... </DD>
|
|
<DT>points:</DT>
|
|
<DD>length unit used for font size, 1/72 inch,
|
|
but I do not know its exact relation to the font size (height?
|
|
totalheight? width? 10pt and 300dpi results in 40 pixel heigh font?)
|
|
</DD>
|
|
<DT>sans serif:</DT>
|
|
<DD>font without the (often thin) lines on the ends
|
|
of the character
|
|
</DD>
|
|
<DT>descewing:</DT>
|
|
<DD>compensation of (slightly) rotated text
|
|
</DD>
|
|
</DL>
|
|
|
|
<H1><A NAME="SEC14"> More information?</A> </H1>
|
|
<DL COMPACT>
|
|
<DT>·</DT>
|
|
<DD>see "/usr/share/doc/package/tetex/texmf/.../fntguide.dvi"
|
|
in the documentation of the tetex package
|
|
|
|
</DD>
|
|
<DT>·</DT>
|
|
<DD>the fonts-HOWTO file is helpfully too
|
|
("www.faqs.org/faqs/fonts-faq/")
|
|
|
|
</DD>
|
|
<DT>RTF:</DT>
|
|
<DD> RichTextFormat - does someone have a good documontation?
|
|
</DD>
|
|
</DL>
|
|
|
|
<H1><A NAME="SEC15"> About this document</A> </H1>
|
|
This Document was originaly written in LaTeX.
|
|
In May 2002 Joerg has convertet it to HTML. The reason is, that
|
|
you can read it now directly and you does not need to have LaTeX and
|
|
Ghostscript installed on your computer to read it.
|
|
As a side effect you do not need tetex package to build the gocr.rpm-package.
|
|
A good viewer to read this document is lynx, links or w3m.
|
|
|
|
<BR>
|
|
<HR>
|
|
<ADDRESS> jNOschulen-at-gSmPAMx.de (remove NO+S+PAM) </ADDRESS>
|
|
</BODY>
|
|
</HTML>
|
|
<!---
|
|
%
|
|
% -----------------------------------------------------------------
|
|
% # v
|
|
% # v mark connected points via fifo-stack
|
|
% ### *<< and 3bit direction code per pixel,
|
|
% # # ^ ^ should be better for overlapping letters
|
|
% ### ^<<
|
|
% --------------------- point connections ----------------------
|
|
% searching next nearest point
|
|
% /----\
|
|
% | |
|
|
% ^ | ## |
|
|
% | | ## |
|
|
% | | | |
|
|
% | \--/ |
|
|
% \------/
|
|
%-------------------------------------------------------------
|
|
%
|
|
|
|
---> |