ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

up1 = ( u1x, u1y,1)
and up2 = ( u2x, u2y,1)
in the reference grid so that u1 = up1× up2.
u1, u2... u n are the vanishing lines in X direction , v1, v2... v n are the vanishing lines in Y
direction and w1, w2... w n are the vanishing lines in Z direction.
The best fit vanishing point u in X direction is computed by considering the
eigenvector associated with the smallest Eigen value of the second moment matrix (M)
1
of the set of vanishing lines u1, u2... u n , obtained by
1
n
T
M = ∑ uu i i . Similarly for v and
n i=
w along Y and Z directions [7]. The principal point pp has been estimated from the
vanishing point triplet ( uvwalong , , ) the orthogonal reference planes.
The planar offset of the measurement plane ' OBy Z = (264mm) in the palmar view
π is 1
Fig. 4 User selected points of interest in palmer and lateral
views, used for extracting joint parameters.
and 2 OBy Z = (616mm) in the
lateral view. The reference
distance TyBy (528mm) is used
along with planar offset OBy for
determining the affine parameter
α y spanning the vanishing points
[ uv , ] , by selecting the points Ty
and By in the image. The
reference distance txbx (528mm,
by selecting the points tx and bx)
α
is used along with planar offset OBy for determining the affine parameter and x
spanning the vanishing points [ uw , ] in (1). Once α x and α y has been determined in
the initial setup, it can be used for determining the distance (Z) for the remaining frames
as long as the camera is not moved. l1= By× u and l2= By× v are the rays lies on π '
and passes through u and v respectively. Tx = l 1 × (tx×w) and Bx = l 1 × (bx×w) are the
projection of reference lengths in π ' . Hence l 1 and 2
l are new base references for any
measurement along vanishing point v and u respectively. If tm = P( x′ , y′
) is user
selected point set (Fig. 4) in π ' , the vanishing line through tm and v is lvtm = ( tm× v)
,
corresponding bottom point is bm = ( lvtm × l1)
. Now given the affine factor α y , and the
vanishing line l 1,
dy can be estimated from (1) , where
x tm, x ' bm, l l1 , and w v
α andl 2 , dx can be estimated from
= = = = . Similarly given x
(1), where x = tm, x ' = bm, l = l2 , and w = u . Hence for any point P i selected in the
plane π ' , the corresponding metric rectified set Pri = ( dx, dy)
. Once the coordinates of
these points are estimated in the Euclidian space, the next step of calculating the joint
jangles and joint offset length is trivial. Feature detection and extraction, whether
manual or automatic (using an edge detector), can only be achieved to a finite accuracy.
The summary of steps involved estimation of uncertainty are mentioned below [1,2].
Repeat k times ( k= 20)
[i] Select the center of marked points A-L and N-U , input variables x i . [ii]
Compute mean x i , std. deviation i
σ x and covariance i Λ x . [iii] Generate the