ImageToFourierSeries

Draw images as Fourier series

How it works

Application first extracts edges from image. For this step it uses Canny edge detector implemented from scratch. Then it transforms image with extracted edges to the list of points to sort these points, so they create a path. Path is then passed to discrete_fourier_transform function to transform this path to the set of epicycles. Then all it has to do is draw epicycles and track position of the last epicycle. For visualizing this process I use pygame and pygameZoom (It gives ability to zoom into pygame figures without quality loss and has a feature to track any point on canvas with specified zoom). All algorithms are written in Cython which is much faster then pure python.

Useful links so you can better understand this algorithm:

Canny edge detector:

• https://en.wikipedia.org/wiki/Canny_edge_detector
• https://towardsdatascience.com/canny-edge-detection-step-by-step-in-python-computer-vision-b49c3a2d8123

Discrete fourier transform:

• https://www.youtube.com/watch?v=7_vKzcgpfvU
• https://en.wikipedia.org/wiki/Discrete_Fourier_transform

Example

If you feed this image to program,

You will get this:

Usage

Install requirements:

pip3 install -r requirements.txt

Setup cython functions:

python3 setup.py build_ext --inplace

Run main.py

python3 main.py img_path=path/to/image

Modify output with flags

• Use --static_path if you want path to not lose color over time

• Use --reset_path if you want path to reset every cycle.

• Use --image_visibility=VISIBLE if you want to see image as the background.

• Use --image_visibility=NOT_VISIBLE (default) if you don't want image to be visible in the background

Video options

Important note

When using --save_as_video flag window will pop up anyway because this option records screen. You can do other things on your computer while this program is running. Video will be recorded properly even if popup window will be covered by other windows. For images with a lot of details generating video could take a while but when the video is recorded it will be much faster (one cycle will last for 30seconds , unless --cycle_duration option is used). Recording stops when you close the window or after one full cycle, unless --custom_recording flag is used, then video ends only when you close the window.

• Use --save_as_video if you want to save result to MP4 file. It will save in current directory with name ImageToFourierSeries-1629031103830.mp4. This long number represents current timestamp.

• Use --custom_recording if you want to decide when the video ends by simply closing window. By default, it will end when one full cycle is completed.

• Use --cycle_duration=duration where duration is a number to specify duration of one cycle (in seconds). It can be useful when you want to slow down animation (visible only on video). Default is 30 seconds, so anything greater than 30 will slow down animation and anything lower will speed it up.