Lines, Curves and Surfaces in 3D
Lines, Curves and Surfaces in 3D
Lines, Curves and Surfaces in 3D
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Least Squares Fit of a L<strong>in</strong>e (Cont.)<br />
Now<br />
∂χ 2<br />
∂m = −2 ∑ (y i − mx i − c)x i = 0<br />
∂χ 2<br />
= −2 ∑ (y i − mx i − c) = 0<br />
∂c<br />
which leads to<br />
∑<br />
yi − m ∑ x i − nc = 0<br />
CM0268<br />
MATLAB<br />
DSP<br />
GRAPHICS<br />
556<br />
∑<br />
xi y i − m ∑ x 2 i − c ∑ x i = 0<br />
which can be solved for m <strong>and</strong> c to give:<br />
1<br />
m = n ∑ x i y i − ∑ ∑<br />
x i yi<br />
n ∑ x 2 i − ( ∑ x i )<br />
∑ ∑ 2<br />
yi x<br />
2<br />
c =<br />
i − ∑ ∑<br />
x i xi y i<br />
n ∑ x 2 i − ( ∑ x i ) 2<br />
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