Vector-Valued Image Regularization with PDEs

This project implements vector-valued image regularization technique using PDE's as described in the paper - Vector-Valued Image Regularization with PDEs: A Common Framework for Different Applications by David Tschumperle and Rachid Deriche

A detailed report on methods and results can be found as report.pdf. It was made as the final project for CS 663 - Digital Image Processing course in Autumn 2018 at Indian Institute of Technology (IIT) Bombay, India.

Getting Started

These instructions will get you a copy of the project up and running on your local machine for development and testing purposes.

1. Run /src/inpainting.m file for image inpainting, /src/denoising.m file for image denoising and /src/flowVisualisation.m file for flow visualisation.
2. Replace the arguments of the functions with respective input image paths and set the hyperparameters you wish to use to generate the output images.
3. The tuned hyperparameters for our output images can be found in /src/main.m file.

Results

Image Inpainting

                Figure 1: Inpainting with 21x21 neighbourhood, t=5 and 10 iterations

                Figure 2: Inpainting with 10x10 neighbourhood, t=2 and 20 iterations

                Figure 3: Inpainting with 20x20 neighbourhood, t=3 and 20 iterations

Image Denoising

Figure 4: From L to R : Noisy image, image filtered with gaussian smoothing with 5x5 kernel, image 
filtered with PDE regularisation with t=3, 3x3 neighbourhood and 5 iterations - better performance 
and lower noise especially on left and top parts of the image

Figure 5: From L to R :Noisy image, image filtered with PDE with t=3, 3x3 neighbourhood, 5 iterations

Image Magnification

Figure 6: From L to R : Original Image. This image was downsampled by 4 to serve as input for the two
algorithms. Magnified image using bi-linear interpolation, magnified image using PDE regularisation
with t=3, 3x3 neighbourhood and 10 iterations.

Flow Visualisation

Original Image	Flow	Flow Visualisation

Figure 7: Input images, flow vectors and output images, with dt = 0.01, 100 iterations and sobel 
gradient vectors for Hessian Matrix. Paralallised code, runs much faster compared to others.

Image Restoration

Figure 8: From L to R : Input Image, image with 50 % pixels removed in 2x2 granularity, output 
image with SSIM of 0.995, better than results with median filter. Also, median filter will 
become less accurate on increasing the box sizes.

Image with pixels missing	Restored Image

Figure 9: from L to R : image with 50 % pixels removed and SSIM = 0.23, restored image with t=4, 
10 iterations with 3x3 neighbourhood, SSIM = 0.966 with original image.

Authors

• Saiteja Talluri - saiteja-talluri
• Shreyas Pimpalgaonkar - shreyas-7
• Meet Kathiriya

License

This project is licensed under the MIT License - see the LICENSE file for details.