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150 Chapter 4

4. BINARY IMAGE ROTATION USING
TRANSFORMATION MATRIX

Figure 4-8. Vector basis for Binary Image Rotation

T
T
Consider the vector space spanned by the basis [1 0] and [0 1] .
Transformation of the vector [1 0] is the vector [0.7071 0.7071] that is in
the same space. Transformed vector is represented as the linear
T
T
combination of the basis [1 0] and [0 1] with vector co-efficient 0.7071
T
and 0.7071 respectively. Similarly the transformation of the vector [0 1] is
the vector [-0.7071 0.7071] that is in the same space.
The transformed vector [-0.7071 0.7071] is represented as the linear
T
T
combination of the basis [1 0] and [0 1] with co-efficient –0.7071 and
0.7071 respectively.
The transformation described above rotates the vector counter clockwise
0
by 45 as mentioned in the figure 4-7.
Thus the transformation matrix used to rotate the vector counter
0
clockwise by 45 is computed using the method described in the chapter 3 is
given below.

0.7071 0.7071
0.7071 -0.7071