first order differentiation

timer Asked: Dec 18th, 2018

Question description

I would appreciate if you could have a look at the attached file that

contains the formula for two distances, d(a,B_H) and d(b, A_H). The

final result, D is the maximum of the two distances.

In this question, the first order derivative of D is needed (differentiated with respect to A_H).
I would like to ask if a full solution will be presented, step-by-step, for the first order differentiation?

Consider two 2D images of the same spatial size, AH and BH . Both images can be represented as point sets, AH = {a1 , ..., aNa } and BH = {b1 , ..., bNb }, respectively, where AH , BH ⊂ Rn such that |AH | , |BH | < ∞. From here, the distance between a point a and set of points, BH , is defined as:   s X d(a, BH ) = min  (a − b)2  b∈BH (1) b∈BH and similarly, the distance between a point b and set of points, AH , is defined as:   s X d(b, AH ) = min  (b − a)2  a∈AH (2) a∈AH D, can be described as: ( D = max ) 1 X 1 X d(a, BH ), d(b, AH ) |AH | |BH | a∈AH b∈BH (3)

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