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# Parallel Linear Transformations on Two-Dimensional Binary Images

IP.com Disclosure Number: IPCOM000074268D
Original Publication Date: 1971-Apr-01
Included in the Prior Art Database: 2005-Feb-23
Document File: 3 page(s) / 38K

IBM

## Related People

Casey, RG: AUTHOR [+2]

## Abstract

This is a method for performing a fast transformation of axes on two dimensional binary images. The method is used in the normalization of hand printed characters or in other applications where it is desired to perform a positional or rotational transformation of a binary image.

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Parallel Linear Transformations on Two-Dimensional Binary Images

This is a method for performing a fast transformation of axes on two dimensional binary images. The method is used in the normalization of hand printed characters or in other applications where it is desired to perform a positional or rotational transformation of a binary image.

In a normalization transformation, it is generally required to change scale, orientation, and shear of a binary image. Under such a transformation, a point x,y would be transformed to x' = Ax + By and y' = Cx + Dy. The following algorithm enables the transformation to take place without the need to process the image on a point-by point basis. Considering, for example, a clockwise rotation of a single point, x' and y' would take the form as shown in Fig. A.

Now referring to Figs. B and C, there is shown a 30 degree transformation of the character A. The character is assumed to be placed in storage as a binary image representing raster lines across the image of the character. The algorithm to perform the transformation consists of the following six steps which correspond to Fig. B:

1) First perform a shear in the x direction by using shift instructions on all x values. x' = x + py

y' = y

2)Modify all y positions (vertical) by using move instructions on all y values. x" = x'

y"= qy

3) Perform a transposition of the axes.

x'''= y"

y'''= x"

4) Perform a shear in the x direction by using shift instructions on all x values. x/iv/ =...