BillyDoesDev / fast-image-rotation

Fast Parallel Image Rotation Algorithm

Abstract
yes.

Setup and building

• Install OpenCV (this is only temporary, since we'll use this to read and write images only for now, and later on will switch to Halide)

  # the following instructions are for arch
  # packages and procedures may vary
  sudo pacman -Sy glew fmt vtk hdf5 opencv
  
  # optionally install `zlib` for Halide in case your system doesn't already have it

• Clone this repo, download and extract the binary release of Halide for your system and place it in the current working directory.

  Note: You may have to modify the CMakeLists.txt file accordingly.

  # Add include directories for Halide
  include_directories(${PROJECT_SOURCE_DIR}/Halide-17.0.1-x86-64-linux/include)

  Also, make sure you have the zlib and OpenCV binaries in your path.

• Build the thing

  mkdir build
  cd build
  cmake ..
  make

How it works

Stage 1: The naive rotation matrix approach

• First, we calculate the new dimensions of the image to fit the rotation.
  
  the figure above represents the new size of the image after rotation by an angle $\theta$

• Next, we decide on a centre for rotation (in this case, the centre of the image $(cx, xy)$), and apply the rotation matrix for each pixel coordinate, $(x, y)$ of the image $$\begin{bmatrix} x'\ y' \end{bmatrix} = \begin{bmatrix} x - cx\ y - cy \end{bmatrix} * \begin{bmatrix} cos(\theta) & -sin(\theta)\ sin(\theta) & cos(\theta) \end{bmatrix}$$

  Assuming the centre of rotation of the new image is $(cx', cy')$, the final new coordinates are: $$\begin{bmatrix} x'\ y' \end{bmatrix} = \begin{bmatrix} x' + cx'\ y' + cy' \end{bmatrix}$$

• Finally, we do pixel_val_at(x', y') = pixel_val_at(x, y)

Issues:

A lot, but mostly, for now, anti-aliasing. This means, we'll most likely be looking into a multi-pass program.