Foundation of Image Processing-Least Squares

Least 2 Multiplication

 

 

Least 2 multiplication linear fitting

When we study the relationship between two variables (x, y), we usually get a series of paired data (x1, Y1, X2, y2... XM, ym); plot the data in the x-y coordinate system (1). If you find these points near a straight line, you can make this linear equation (Formula 1-1 ).

 

Y = A0 + A1 X (type 1-1)
Where, A0 and A1 are arbitrary real numbers.
In order to establish this linear equation, we need to determine A0 and A1, and apply the principle of least square method to Yi and Utilization of the measured values (Formula 1-1) the sum of squares of the deviation (Yi-y) of the calculated values (y = A0 + A1 X) is the minimum value of [Σ (Yi-y) 2] as the "optimization criterion ".
Order: Phi = Σ (Yi-y) 2 (Formula 1-2)
Replace Formula 1-1 into Formula 1-2:
Phi = Σ (Yi-A0-A1 xi) 2 (Formula 1-3)
When the Σ (Yi-y) square is the least hour, the partial derivative of A0 and A1 can be obtained by using the function Phi, so that the two partial derivatives are equal to zero.

 

The least square method is used to fit two curves and apply the existing sampling time points to reproduce the changes of the two curves described by these points, that is, to obtain a quadratic curve equation Y = ax2 + bx + c (the main problem of this algorithm is how to calculate the equation coefficient ABC with the given data)

Foundation of Image Processing-Least Squares