Image-Processing

This project explores different methods to alter and process images. These include convolution (blurring), grayscaling, mirroring.

Grayscale

Grayscales is a range of gray shades from white to black, all these color share that red = green = blue. There are several methods to convert colored images to grayscale, two of them are:

Average Method

In the average method, the RGB-value is calculated as the average of green, red and blue, that is: $$\text{Grayscale Value} = \frac{R + G + B}{3}$$

Weighted Method / Luminosity Method

Human eyes react differently to RGB, eyes are most sensitive to green light, less to red and least to blue light. Therefore the weighted method weighs red, green and blue according to their wavelenghts. The updated formula then becomes: $$\text{Grayscale Value} = 0.299 R + 0.587 G + 0.144 B$$

Convolution

In the module Convolution.js different methods for convolutions are implemented. Convolution of pictures is done by multiplying the image ($I$) with a kernel ($H$) to recieve a blurred image ($B$). $$I * H = B$$ These are

Gaussian blur

Gausssian blur uses a Gaussian function for convoluting a picture. The Gaussian function in two dimensions is: $$G(x, y)=\frac{1}{2 \pi \sigma^2} e^{-\frac{x^2+y^2}{2 \sigma^2}}$$ where $x$ is the horizontal distance, $y$ the vertical distance and $\sigma$ the standard deviation of the Gausssian distribution.

Deconvolution

The task of unblurring images is much more difficult and can be done using Fourier Transforms. The convolution equation ($I*H=B$) becomes $$FT(I)FT(H)=FT(B)$$ using Fuorier Transform. Solving for the original picture $I$ yields: $$FT(I)=\frac{FT(B)}{FT(H)}$$

Sources:

Kumar, Shashank (2022) (https://towardsdatascience.com/how-to-de-blur-images-without-training-neural-networks-72f8597c0014)