I. Change of Basis
Change of basis is a technique for converting objects (vector, matrices etc) from one coordinate system to another.
Harris Corner Detection
A corner is a point for which there are two dominant and different edge directions in a local neighbourhood of that point. These points (corners) are important features which is termed as intrest points which are invariant to translation, rotation and illumination. One method to detect these points are using Harris corner detection which introduces an detection operator used to extract corners in a image.
The section I to VI below are ordered in way for the reader to grasp the pre-requistes before needing it in a topic. However, the reader is expected to know what a vector is, how to compute a determinant, what a basis set is and what does span mean in context of linear algebra. Then, in calculus the reader must know what a derivative is and how to compute them. Finally, if you find I have made any mistakes or can suggest any improvements feel free to reach out to me regarding it on LinkedIn.
Harris-Corner Detection Series
II. Eigen Values and Eigen Vectors
In this section we look at what eigen values and eigen vectors are. How to calculate them and get a geometeric intution behind them.
III. Eigen Decomposition (Diagonalization)
Eigen decomposition is a process of representing a matrix into it's eigen values and eigen basis.
IV. Eigen Application: Ellipse
One of the application of eigen vectors and eigen values are finding the equation of the ellipse given an +ve definite quadratic equation.
V. Taylor Expansion
To approximate the function or understand the function around an aribitary value we use taylor series.
VI. Harris Corner Detection (Theory)
This section uses all the concepts from the previous sections to derive the equation for harris corner detection.
VII. Harris Corner Detection (Pratical)
We use an OpenCV's API to compute the Harris corners in an image using a sample image.