A COMPARISON AND EVALUATION OF MOTION INDEXING ...

ased on indexing with inverted lists are used. The feature vectors are used as index
words and indexing is carried out at the segment level rather than at the frame level.
This approach provides fast content-based and fault tolerant retrieval.
3.1.1 Notation for feature-based method
gorithm:
Intially, lets introduce some notations which are used in the feature-based al-
1. Data Stream: A data stream is a sequence of frames and each frame specifies the
3D coordinates of the joints at a certain point in time. Hence, a motion sequence
is represented by a 3-dimensional matrix where the dimensions represent time
(frames), joints in the body, and the axes (x, y, z) for the joint position.
2. Pose: In a geometric context, a frame correspond to a pose. Mathematically, a
pose can be described as P ∈ ℜ 3J , where J is the number of joints in the body.
The j-th column of P , denoted by Pj, corresponds to the 3-D coordinates of
joint j.
3. Document: A motion capture data stream can be expressed as a function Γ :
[1 : T ] → ℜ 3J , where T denotes the number of poses. The document function
Γ maps from the time domain to the set of poses.
4. Motion clip: A subsequence of consecutive frames.
5. Trajectory: The curve described by the 3D coordinates of a single body point.
3.1.2 Feature Functions
A Boolean feature which describes geometric relations can be described as a
function. Mathematically, it is equivalent to a function F : ℜ 3J → {0, 1}, mapping
the set of poses into {0, 1}. The Figure 3.1 shows the output of a boolean feature
function which checks whether the right leg is ahead of the whole body for a walk
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