I'm confused how the second term on the first line (with the $$\delta p$$) expands into the second term on the second line denoted by chain rule. Specifically, it seems that the denominator of the first partial derivative and the numerator of the second partial derivative do not match up, so I'm unsure how this is a use of the chain rule.
motoole2
The denominator of the first partial derivative and the numerator of the second partial derivative do in fact match up, because $x' = W(x;p)$. Note that the first partial derivative represents the derivative of a warped image (hence why we use $x'$ instead of $x$ here).
I'm confused how the second term on the first line (with the $$\delta p$$) expands into the second term on the second line denoted by chain rule. Specifically, it seems that the denominator of the first partial derivative and the numerator of the second partial derivative do not match up, so I'm unsure how this is a use of the chain rule.
The denominator of the first partial derivative and the numerator of the second partial derivative do in fact match up, because $x' = W(x;p)$. Note that the first partial derivative represents the derivative of a warped image (hence why we use $x'$ instead of $x$ here).