Browse Prior Art Database

Algorithm for Transforming Two-Dimensional Quadrilateral Areas

IP.com Disclosure Number: IPCOM000113662D
Original Publication Date: 1994-Sep-01
Included in the Prior Art Database: 2005-Mar-27
Document File: 4 page(s) / 50K

Publishing Venue

IBM

Related People

Miyata, K: AUTHOR [+3]

Abstract

Disclosed is an algorithm for transforming two-dimensional quadrilateral areas, such as image areas. As a result of a split in its transforming procedure, performance of the disclosed algorithm in calculating transformation matrices is superior in several respects to that of existing algorithm.

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Algorithm for Transforming Two-Dimensional Quadrilateral Areas

      Disclosed is an algorithm for transforming two-dimensional
quadrilateral areas, such as image areas.  As a result of a split in
its transforming procedure, performance of the disclosed algorithm in
calculating transformation matrices is superior in several respects
to that of existing algorithm.

Fig. 1 shows an example of a source (pre-transformation) area and a
target (post-transformation) area.

The transformation procedure is split into the following two steps
(Fig. 2):
  1.  Transform the source area into the unit square whose origin is
      (0, 0).
  2.  Transform the unit square into the target area.

The transformation matrices, M1 and M2, are shown in Fig. 3.

      The computation cost of this algorithm is smaller than that of
direct calculation or the Gauss-Seidel method.  When the target or
source area is changed, only one side of the transformation matrix,
M1 or M2, must be recalculated, and the matrices then multiplied.
Therefore, this algorithm is effective when the target area is
changed frequently, as in the case of interactive photo-retouching
software.