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Image Restoration using Partial Differential Equations


An image restoration program which uses partial differential equations to predict missing information, made in Python.


Equations originating from physics have recently found their way to other areas. One possibly surprising application is that of restoring art or images. To understand how Partial Differential Equations (PDEs) from physics can help with image restoration, consider a greyscale image of your own choice. Due to some unwarranted graffiti, let us assume that a piece is missing (black region). Can we fill in this missing region without any information as to what is missing? This may seem like a hopeless task, but PDEs are here to help!

PDE-based methods for image restoration are based on propagating the information (typically, colour-specific intensity values and gradients) at the boundaries of the missing region inwards. The propagation is performed by solving a partial differential equation for the missing regions’ given boundary conditions.


I really enjoyed collaborating on this project, where I created the initial code logic, and later took responsibility for handling user inputs and finding innovative ways of improving the algorithms results through a new technique. This new technique consisted of breaking the regions to be solved into individual sections; The border colours of which were then averaged over to create an appropriate initial fill colour for each section. This was found to both speed up solving and greatly improve results for large pieces of graffiti. Though we just touched the tip of the iceberg in terms of image restoration techniques, the project demonstrated how useful physics-based equations can be in novel applications, such as graphical programming.