Hi Enrick,
To compute PCA for skew correction using corner points in MATLAB, you can follow these textual steps:
- Prepare your data by collecting the corner points of the skewed object. Each point should have its x and y coordinates, and you should place them in a matrix where each row represents a point.
- Compute the mean of the corner points across each dimension (x and y). Then, subtract this mean from all the points to center your data around the origin. This step is crucial for PCA because it ensures that the first principal component describes the direction of maximum variance.
- With the centered data, calculate the covariance matrix. The covariance matrix captures the variance and the relationship between the x and y dimensions of your data.
- Use MATLAB's eig function to calculate the eigenvalues and eigenvectors of the covariance matrix. The eigenvectors represent the principal components, and the eigenvalues indicate the amount of variance captured by each principal component.
- Sort the eigenvalues in descending order and reorder the eigenvectors accordingly. The first eigenvector corresponds to the direction of greatest variance, and for skew correction, this is typically the direction you want to align with the x-axis or y-axis.
- Calculate the angle of the first principal component relative to the x-axis. This angle represents the skew of your data.
- Rotate the data points by the negative of the skew angle to correct for the skew. If you're working with an image, you would apply an image rotation by this angle.
- If necessary, translate the rotated points back by adding the mean you subtracted earlier, so they return to their original position in the coordinate space.
Once you've completed these steps, your corner points should be corrected for skew, and you can use them for further processing or analysis. If you're correcting an image, you'll have an angle that you can use to rotate the image and correct the skew visually.
