A COMPARISON AND EVALUATION OF MOTION INDEXING ...

of feature functions is helpful on focusing on certain aspects of motion which are
required by the application.
A generic relational feature is constructed such that it encodes certain joint
constellations in 3-D space and time. This generic feature depends on a set of joint
variables, denoted by j1, j2, · · · , js as well as on a variable θ for a threshold value
or a threshold range, where s is the number of joints used in the feature. Feature
functions are classified as follows:
1. Feature functions describing a plane.
This category of generic functions are plane-based. The equation of the plane
is defined by the 3-D coordinates of the joints j1, j2, · · · , js. A plane function
uses four joints to calculate its boolean value Fplane = Fθ,plane (j1, j2, j3; j4). The
three plane-based generic functions which are used in the algorithm are defined
as follows:
• The plane is defined such that it passes through the joints j1, j2, j3 and the
function checks if the joint j4 is on or infront of the oriented plane. It has
value 1 if the joint j4 is lying on the plane or infront of the plane and its
value is 0 when joint j4 is behind the plane.
• The plane is defined such that it passes through the joints j1, j2, j3 and
the function checks if the joint j4 has a signed distance greater than θ ∈ ℜ
from the oriented plane. It has value 1 if the signed distance is greter than
θ, else its value is 0.
• The plane is defined in terms of a normal vector given by joints j1 and j2
and is fixed at joint j3. The function takes the value 1 if joint j4 has a
signed distance greater than θ ∈ ℜ from the oriented plane, else takes the
value 0.
30