Assume f=l, r are known, for the i model point: Scalar Functions Let f: R-R be n function of n variables denoted by r, T? Let r=(rh,. In). We present first order and second order Taylor M=(,Y, Zi )is a guessed 3-D model point expansions of the function f(r), without providing convergence results Let a=(a1, ag.,,,)ER". The linear Taylor expansion of the funetion f(r) around the point a It f(x)≈f(a)+∑(r-a)(a (5.25) gn(1,M1) aX (x1-X) ag,(e, M) ag, (0, M (Z1-Z)--4a) Y Z v1-g,(61,M,)≈ g40,M(x-x)+31,) o(-分)+g(,M (21-21)-(4b) OX aZ combine(4a)and(4b), put them in a matrix form X.-Ⅹ l1 2 jM Y-Y 21 ag,(0,M)agn (0, M) ag, (0, M) X-X g(C.Dg(,M)图,M aX ar aZ aX ar aZ 3x1 Pose estimation vO.aContinue • Pose estimation V0.a 13 (5) ~ ~ ~ ) ~ ) ( , ~ ) ( , ~ ( , ) ~ ) ( , ~ ) ( , ~ ( , ~ ~ ~ ~ ~ combine (4a) and (4b), put them in a matrix form )--(4b) ~ ( ) ~ ( , ) ~ ( ) ~ ( , ) ~ ( ) ~ ( , ) ~ ( , )--(4a) ~ ( ) ~ ( , ) ~ ( ) ~ ( , ) ~ ( ) ~ ( , ) ~ ( , ~ is a guessed 3- D model point ~ ~ ~ ~ Assume are known, for the model point : 3 1 2 3 , , , , , 1,.., − − −       − − −                 =       − − − =      − − = −   − +   − +   −  −   − +   − +   −  − = =   =  i i i i i i v t v t v t u t u t u t i i i i i i M i i i i i i v t i i v t i i v t i t v i t t i i u t i i u t i i u t i t u t i i t i t i i i i th t Z Z Y Y X X Z g M Y g M X g M Z g M Y g M X g M Z Z Y Y X X j v v u u e Z Z Z g M Y Y Y g M X X X g M v g M Z Z Z g M Y Y Y g M X X X g M u g M u u M (X ,Y ,Z ) i               