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

passive reflective markers on the skin for localization but mainly implemented in
tracking whole body or limbs using multiple camera [4]. It is still under active research
for its implementation with out gloves in hand articulation like grasping for its high
degree of freedom, marker slip due of skin stretch and cross occlusion. In our approach,
we apply a subset of this work, and leverage these results for the purpose of behavioural
biometrics during palmer grasp from an image. Since for a particular pose two views are
to be captured simultaneously, during dynamic palmer grasp operation, we have used
two cameras but the relevant information have been extracted from single image i.e
abduction –adduction (ab/ad) information from palmer view and flexion–extension (f/e)
information from lateral view.
3. JOINT MOTION PARAMETERS
The defined joint parameters are four degrees of freedom (DOF) for each finger, two for
Z
X
metacarpophalangeal joint (MCP) f/e ( θ MCP ) and ab/ad ( θ MCP ), two for the proximal
interphalangeal (PIP) and distal interphalangeal (DIP) joints f/e, Z
θ PIP and Z
θ DIP
respectively (Fig.1). The thumb was modeled by five DOF with the assumption of
orthogonal intersecting axis, two for
f/e and ab/ad of the carpometacarpal
Z
X
(CMC) joint ( θ CMC and θ CMC ),
another two for thumb rotation and
Z
f/e of the MCP joint( θ MP and X
θ MP )
and one for f/e of the interphalangeal
Z
(IP) joint ( θ IP ). l1, l2 and l3are joint
offsets (~phalange lengths) for index
finger, lT1, lT2 and l T3
are joints
Fig. 1 Joint motion parameters for hand articulation
offsets for the thumb [5].
4. MATHEMATICAL FRAMEWORK
Points on one image plane π can be mapped to another plane π ' by plane to plane
homography matrix P, assuming central projection model. It is a bijective mapping and
P is 3x 3 non singular [1,2]. In this
approach XYZ has been defined as an
affine coordinate system whose origin lies
on the reference plane (π), X and Y are the
axis that spans the plane and Z is the
reference direction which is any direction
not parallel to the plane. We want to take
measurement in the plane π ' which may
not be parallelπ in the image plane
(Fig. 2). If X is an point in space which is
projected in the affine image plane the
relation can be written as
x = PX = [ p 1 p 2 p 3 p]X, 4 where X and x
are homogeneous vectors in the form x =
(x,y,w) T and X=(X,Y,Z,W) T Fig. 2 Measuring the distance of a plane π '
along Z, parallel to the plane π in the world.
and equality means ‘equality up to the scale’ and pi are the