Deriving the famous Euler’s formula through Taylor Series

Euler's formula

Euler’s formula is often coined the most remarkable formula in mathematics. It combines the seemingly unrelated exponential functions, imaginary numbers, and trigonometric functions into a single aesthetically pleasing and beautiful equation. We see five numbers (e, i, π, 0, and 1) that we are familiar with as well as three simple operations (exponentiation, multiplication, and …

Reduce the number of Colors of an image using K-Means Clustering

This article presents a method for reducing the number of colors in an image using K-means clustering. This is a continuation of my previously posted color quantization using Uniform Quantization and Median Cut Quantization. K-Means is one of the simplest unsupervised clustering algorithm used to cluster data into K clusters. The algorithm iteratively assigns the …

Basics of Image Convolution

Convolution is a process used for applying general-purpose filter effects like blurring, sharpening, embossing, edge detection, and more. To understand convolutions we must first understand what a convolution matrix is, also referred to as kernel. Take for example the blurring filter. In blur filter, we set each pixel to the mean of its neighbouring pixels. …