simple-homography/index.ts

Calculates a homography matrix using exact point correspondences

import * as Math from 'mathjs'
import { Matrix } from 'mathjs'

//See https://math.stackexchange.com/a/2619023
export function calculateHomography(a1: number[], b1: number[], a2: number[], b2: number[], a3: number[], b3: number[], a4: number[],  b4: number[]): Matrix {
    
    let points = Math.matrix([
        [-a1[0] , -a1[1] , -1   , 0     , 0     , 0     , a1[0]*b1[0]   , a1[1]*b1[0]   , b1[0]],
        [0      , 0      , 0    , -a1[0], -a1[1], -1    , a1[0]*b1[1]   , a1[1]*b1[1]   , b1[1]],
        [-a2[0] , -a2[1] , -1   , 0     , 0     , 0     , a2[0]*b2[0]   , a2[1]*b2[0]   , b2[0]],
        [0      , 0      , 0    , -a2[0], -a2[1], -1    , a2[0]*b2[1]   , a2[1]*b2[1]   , b2[1]],
        [-a3[0] , -a3[1] , -1   , 0     , 0     , 0     , a3[0]*b3[0]   , a3[1]*b3[0]   , b3[0]],
        [0      , 0      , 0    , -a3[0], -a3[1], -1    , a3[0]*b3[1]   , a3[1]*b3[1]   , b3[1]],
        [-a4[0] , -a4[1] , -1   , 0     , 0     , 0     , a4[0]*b4[0]   , a4[1]*b4[0]   , b4[0]],
        [0      , 0      , 0    , -a4[0], -a4[1], -1    , a4[0]*b4[1]   , a4[1]*b4[1]   , b4[1]],
        [0      , 0      , 0    , 0     , 0     , 0     , 0             , 0             , 1     ]
    ])

    let pointsInv = Math.inv(points) as Matrix

    let hnum = (Math.multiply(pointsInv, [0,0,0,0,0,0,0,0,1])) as Matrix

    return Math.reshape(hnum, [3,3]) as Matrix
}