Definition: The Fibonacci sequence is defined by the equation, where \(F(0) = 0 \), \(F(1) = 1 \) and \(F(n) = F(n-1) + F(n-2) \text{for } n \geq 2 \). This gives us the sequence 0,1,1,2,3,5,8,13 … called the Fibonacci Sequence. This post is about how fast we can find the nth number in the […]

### Understanding Graham scan algorithm for finding the Convex hull of a set of Points

Convex Hull is one of the fundamental algorithms in Computational geometry used in many computer vision applications like Collision avoidance in Self Driving Cars, Shape analysis and Hand Gesture-recognition, etc. By Definition, A Convex Hull is the smallest convex set that encloses a given set of points. For Example, Given a set of points P […]

### Find clusters of collinear points from a given set of data points

A set of 3 or more points are said to be collinear if they all lie on a straight line as shown in the image below. One common way of checking if three points are collinear is by finding the area of the triangle formed by the points. The area will be zero if the […]

### Deriving the famous Euler’s formula through Taylor Series

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 […]

### Function to get the preceding odd number (y) for any given number (x)

For any function, We want, for every value of x, return the corresponding odd number. If x is odd then return it as it is, else return the next number. This can easily be done using a computer program by checking if the number is odd or even. But if you had to find a […]

### Using the law of cosines and vector dot product formula to find the angle between three points

For any 3 points A, B, and C on a cartesian plane. If we have to find the angle between these points, there are many ways we can do that. In this article I will talk about the two frequently used methods: The Law of Cosines formula Vector Dot product formula Law of Cosines For […]

### Algorithm for detecting and extracting number plates from images of cars

Abstract This article presents a method for automatic detection and extraction of number plates from the images of cars. There are usually three steps in an Automatic Number Plate Recognition (ANPR) system. The first one is to binarize the image and separate the background from the foreground. The Foreground contains the numbers of the number […]

### 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 […]

### Reducing the number of colors of an image using Median Cut algorithm

In my previous post, I talked about the Uniform Quantization algorithm, which was a simple way of reducing the colors in the image. Though it’s easy to implement, it doesn’t always yield good results when there are many colors belonging to the same region. Also, a lot of color regions will not have any colors […]

### Reduce the number of colors of an image using Uniform Quantization

Reducing the number of colors in an image is also called Color quantization. It’s commonly used for generating GIF images which currently supports only 256 colors. The general idea is, group similar colors in an image into regions, replace them with the color which closely resembles or represents the region. This color is also called […]