"PO UU- Um we 
Gonzalo-Tasis, Margarita 
  
5 TRACKING WITH NEURAL FIELDS 
Neural Fields can be understood as some kind of dynamical systems biologically inspired on a geometrical support. 
They are associated to an artificial model of the configuration C or the working space W. Existence of a natural 
projection I1: C — W allow us transfer these Neural Fields between both spaces, and display natural feedback for 
perception-action cycle. 
Dynamical aspects appear in Neural Networks early in the 60s, because the prominent role-played by the time in 
neuronal dynamics. Nonlinearity in the generation, processing and transmission of impulses, are the sources of a lot of 
sophisticated mathematical approaches with biomechanical and neurophysiological basis. However, we can simplify 
adopting here a discrete model based on first-order difference equations for model acquisition and recognition of static 
postures, by excluding another more complex dynamic phenomena linked to gestures (evolving postures along the 
time). The mathematical description of above nonlinear phenomena would require higher-order equations (reaction- 
diffusion equations) and their computational implementation is far from the scope of this paper. 
Our hybrid approach uses symbolic models based on matricial representation which contain information about 
configuration space C as starting point to initiate the network. Features incorporation arising from sensors is one 
permanent challenge, because very often it would be desirable have our disposal horizontal/vertical regional patterns for 
activation/inhibition. Our implementation follows a piecewise linear approach (similar to [DBJ98] for continuous 
models). 
In an independent work [SFP99] we have implemented a multilayer perceptron artificial neural network where we 
have introduced the Little dynamics. This choice is justified by its parallel character (the updating of neurons is carried 
out simultaneously), its simple mathematical formulation (it is given by first-order equations) and its behavior 
(synchronous way in simplest deterministic models without delays). Using systems depending on adjustable parameters 
depending on model diminishes its initial deterministic character (PSOM: Parametrised Self-Organised Maps). In 
addition, there can emerge a nonlinear dynamics from a linear domain (transient from laminar flow to turbulence, e.g. in 
Fluid Mechanics). 
Parallelism condition is meaningful to perform an independent information treatment and control relative to each 
finger, and to correct errors in an independent way, before using the supervisory network controlling global aspects 
relative to complex tasks. In addition, coupling and decoupling processes (cooperative and competitive behavior) are 
easily implemented without using sophisticated simulations. The only information we are considering for control is the 
difference between actual and desired position-orientation parameters for meaningful segments for posture recognition. 
This information is more robust w.r.t. to partial (self)occlusions and noise than those based on nodes corresponding to 
knuckles, and it is able of supporting activation/inhibition muscular effects (measurable in eletrophysiological terms). In 
addition, activation/inhibition elementary patterns are easily modeled in matricial terms, which makes easier their 
extension to massive systems. 
6 EXPERIMENTS 
We have used a six-stage recognition hierarchy from a simulated monocameral and monochrome input image. We 
generate and display in a simultaneous way several high-resolution images corresponding to three orientations of the 
same object in order to select (simulate in real experiments) the best location for a (virtual camera) allowing us to 
identify the current posture. Instead of using a grid or planar lattice, we identify relative orientation of the palm of the 
hand from geometric characteristics of the largest closed region (eventually a segment for certain views). 
REFERENCES 
[Ah95] S. Ahmad "A usable real-time 3D hand tracker" in 28th Asilomar Conference on Signals, Systems and 
Computers, IEEE computer Society Press, 1995. 
[DBJ98] P. Dahm, C. Burckhoff And F. Joublin: "A Neural Field Approach for Robot Motion Control", in IEEE Int. 
Conf. SMC'98 (San Diego, CA, October, 1998), 3460-3465. 
[DS94] J. Davis And M. Shah: "Recognizing Hand Gestures", in J.O.Eklundh (ed.): Computer Vision ECCV'94 
Springer-Verlag, LNCS 800 (1994), 331-340. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 303