wi p— N 
Gonzalo-Tasis, Margarita 
To fix ideas, the i-th finger has three DOF (in the configuration space) represented by a column vector is 
i ! pi gi. : ; i p n i . i ; . 
Gg =, 5,0;) to which we associate NO) = sl eta where s, = sin(0;) with 1< j£3 .In 
particular the entries of each vertex are binary i.e. extended knuckle is 0 and flexioned knuckle is 1; additionally we can 
round off values of 3 in order to know the nearest extremal posture for each finger. 
Binary values for each finger can be represented as vertices of a 3D cube that we associate to each finger. Similarly, 
each edge of this cube does correspond to replace a 0 by means an 1; thus, it represents an evolving posture from an 
extension to a flexion for two adjacent segments (representing adjacent phalanxes) in a vertex (common knuckle). 
  
  
  
  
  
  
Fig2: Successive process of an image 
The exact position for each finger must be acquired and learned along edges connecting adjacent vertices, depending on 
parameters controlling kinematic and dynamic restrictions (these effects have not been considered here). From the 
kinematic viewpoint, each vertex in each cube corresponding to i-th finger acts as a possible attractor between 
competitive postures, in such way that we can label the posture in terms of the nearest attractor. Then, elementary 
dynamical aspects for evolving postures are formulated in terms of competitive neural fields for each finger [SFP99]. 
Nevertheless their appearance, this formulation gives a discrete low-level non-deterministic representation, which is 
dynamically preserved in unions of 3D cubes for each finger. This algebraic representation of each geometric posture as 
a 3x3-matrix for each finger is matched in a 3x3k-matrix corresponding to coordinated tasks controlled by a parallel 
processor. Evolving postures (gestures) are modeled as paths, whose binary matrices (obtained by rounding inputs) 
change only one datum each time they arrive to some vertex. Due to parallel character of this updating for each 3x3- 
matrix, we can have several simultaneous mechanical events represented as a simultaneous change in each box. This 
presentation has several advantages from the geometrical viewpoint based on some elementary applications of 
Grassmannians as mathematical tool ([FG98]), and from the block dynamics acting on the columns of matrix, instead of 
an individual activation/inhibition phenomenon. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 301