1 / 14

Understanding Two-Dimensional Image Transformations: Scaling, Translation, and Rotation

This chapter delves into the fundamentals of two-dimensional image transformations, covering key geometric transformations such as scaling, translation, and rotation. You will learn how to zoom in and out by adjusting scaling factors, shift images using translation values, and manipulate images through rotation by radians. Moreover, we will explore inverse transformations to revert these changes and understand how to combine multiple transformations into a single matrix operation. This knowledge is essential for effective image processing and manipulation.

penn
Download Presentation

Understanding Two-Dimensional Image Transformations: Scaling, Translation, and Rotation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 240-373 Image Processing Montri Karnjanadecha montri@coe.psu.ac.th http://fivedots.coe.psu.ac.th/~montri 240-373: Chapter 7: Two Dimensional Image Transformation

  2. Chapter 7 Two Dimensional Image Transformation 240-373: 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) 240-373: 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 240-373: Chapter 7: Two Dimensional Image Transformation

  5. Two-Dimensional Geometric Transformations • Rotating by a radian clockwise 240-373: 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) 240-373: Chapter 7: Two Dimensional Image Transformation

  7. Inverse transformations • Translating by tx in the x direction and by ty in the y direction 240-373: Chapter 7: Two Dimensional Image Transformation

  8. Inverse transformations • Rotating by a radian clockwise 240-373: 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: 240-373: Chapter 7: Two Dimensional Image Transformation

  10. Combination of transformations • giving 240-373: Chapter 7: Two Dimensional Image Transformation

  11. Combination of transformations • For new pixel position (8,10) new pixel will be at (26,1) 240-373: Chapter 7: Two Dimensional Image Transformation

  12. 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: 240-373: Chapter 7: Two Dimensional Image Transformation

  13. 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 240-373: Chapter 7: Two Dimensional Image Transformation

  14. 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 240-373: Chapter 7: Two Dimensional Image Transformation

More Related