During this lab, I learned about transformation matrices and their role in changing the position, orientation, and shape of images. We practiced several types of matrix transformations, including:
- Rotation
- Scaling
- Shearing
- Translating
- Reflection
- Perspective shift
We also discussed how the values and shape of the transformation matrix affect the resulting image, and how different combinations of transformations can lead to different outcomes.
- A transformation matrix is a matrix that changes a vector from its initial position to another position with the help of matrix multiplication.
- The shape of a typical transformation matrix is 2 × 3, with the third column used for translation. The values in the matrix determine the positions of pixels in the resulting image and can affect its shape.
- Composition of transformations refers to consecutive operations performed on a given vector, and the order of these operations can change the outcome. For example, the composition of two reflections across intersecting lines results in the same transformation as rotation by 180 degrees.
- Perspective shift transformation is used to project a 3D object onto a 2D plane, and involves manipulating parallel projections of the 3D space onto the 2D plane. It is described mathematically by a transformation matrix and involves a distance from the point of view to the point in 3D space.
Overall, this lab provided a good introduction to transformation matrices and their use in image processing. By practicing different types of transformations and exploring their effects on images, we gained a better understanding of how to manipulate images using linear algebra.