1. 240-373: Chapter 7: Two Dimensional Image Transformation
Image Processing
Montri Karnjanadecha
: Chapter 7: Two Dimensional Image Transformation

2. Two Dimensional Image Transformation
Chapter 7
Two Dimensional Image Transformation
: Chapter 7: Two Dimensional Image Transformation

3. Two-Dimensional Geometric Transformations
Scaling by sx in the x direction and by sy in the y direction (zooming in/zooming out)
: Chapter 7: Two Dimensional Image Transformation

4. Two-Dimensional Geometric Transformations
Translating by tx in the x direction and by ty in the y direction
: Chapter 7: Two Dimensional Image Transformation

5. Two-Dimensional Geometric Transformations
Rotating by a radian clockwise
: Chapter 7: Two Dimensional Image Transformation

6. Inverse transformations
Scaling by sx in the x direction and by sy in the y direction (zooming in/zooming out)
: Chapter 7: Two Dimensional Image Transformation

7. Inverse transformations
Translating by tx in the x direction and by ty in the y direction
: Chapter 7: Two Dimensional Image Transformation

8. Inverse transformations
Rotating by a radian clockwise
: Chapter 7: Two Dimensional Image Transformation

9. Combination of transformations
The three transformations can be combined by multiplying all transformation matrices.
For example, if an image is to be zoomed-in (2x), rotated clockwise for 45 degree about it origin and then shifted 20 old pixels to the right, evaluate the following expression:
: Chapter 7: Two Dimensional Image Transformation

10. Combination of transformations
giving
: Chapter 7: Two Dimensional Image Transformation

11. Combination of transformations
For new pixel position (8,10)
new pixel will be at (26,1)
: Chapter 7: Two Dimensional Image Transformation

12. 240-373: Chapter 7: Two Dimensional Image Transformation
Technique 8: Two-dimensional geometric transformations
USE: To turn an image around, zoom in or pan across it
OPERATION: Determine the matrix which maps every new pixel onto either an old pixel (if in range) or zero otherwise. That is:
: Chapter 7: Two Dimensional Image Transformation

13. 240-373: Chapter 7: Two Dimensional Image Transformation
Starting a pixel (0,0), plotting left to right, calculate
atx = cx; aty = cy
and make
Increment x and
atx = atx + ax; aty = aty + ay
: Chapter 7: Two Dimensional Image Transformation

14. 240-373: Chapter 7: Two Dimensional Image Transformation
and repeat Inew allocation. Repeat for each x in the row. For the next row, set starting values to
atx = bx*y + cx; aty = by*y + cy
: Chapter 7: Two Dimensional Image Transformation