The project focused on methods of aligning images and understanding techniques that are fundamental to image processing such as application of gaussian and lapalcian stacks and image pyramids.
Image alignment is an important topic in computer vision, and arises in many problems such as image transformation, stitching, and registration.
Filters are effective tools for edge detection and separating frequencies. They are powerful because they line up closely with how people process visual data. In convoluting a filter with an image, we are essentially finding points in the image where the filter matches the image, a form of template matching. Our brains essentially does the same process, and contains neurons dedicated to detecting certain features in an image, such as an oriented edge/pattern.
In this project, I explore using filters to separate frequencies between images to do cool things such as blending.
Filters act on the pixels of an image, but we can also consider transformations on the positions of these pixels. If we think of images as a function from \(I: \mathbb{R}^{2} \rightarrow \mathbb{R}\), where the position of a pixel is mapped to a value, there there is a class of transformations \(T\) that augment the pixel locations.\begin{equation*} I(T(x)) = y \end{equation*}This project explores these transformations, specifically affine transformations, and their use in mapping triangles to triangles for face morphing.
The previous project looks at a euclidean mapping (rotation followed by displacement), but if we want to account for shifts in perspective, this is not enough. This is where homographies come in, which allows us to map quadrilaterals to quadrilaterals.
With this, we can create panoramas by taking multiple pictures, processing with a perspective warp, and stitching them together. This project also explores automatic image alignment to make the stitching process easier.
Many image processing techniques for removing noise are not effective. We can use linear/nonlinear filters to get different results depending on the input image, but these are not flexible when dealing with a lot of noise.
Training a denoiser helps us with this complex task of denoising and also offers an interesting way to generate new images. We can start with pure noise and iteratively denoise this to obtain a clean image that looks realistic. Combined with several other techniques, we can obtain a wide range of images.
By establishing the correspondences between points in the image with those in 3D space, we can map arbitrary points from 3D space into the image.
Using homographies, we and reconstruct the 3d scene of the image.