International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
In our experiments, we have avoided the use of textures due to 
the simplicity of processing based in colour and the presence of 
non-textured regions in views. 
By discarding small regions below a threshold, and by using 
path-connected constraints regions a topological map is 
generated jointly with a symbolic representation given by a 
graph. Qualitative kinematic information is obtained from 
evaluating growing and decreasing phenomena of “homologue 
regions” along a video sequence. We develop a coarse-to-fine 
approach for kinematics evaluation in terms of cooperative- 
competitive dynamical models. Competitive models work to a 
microlocal (pixel) level, where small differences between 
parameters (specific growth rates of populations and their 
competition effects), are in the issue of relative advantages for 
survivors. Cooperative models contribute to the regions 
homogeneity from the local viewpoint. Along a video sequence, 
mobile objects are in competence for the occupancy of regions; 
thus, global behaviour is controlled by a competitive model 
with three populations which are labelled as child, parents and 
old. Old population concerns to the initialisation of each video 
sequence. The transitions between populations of regions are 
controlled at the intermediate parents level. Prediction concerns 
to the child generation depending on critical values for the 
allowed maximum size. The application of standard 
morphological operators (erosion-dilatation) and their iteration 
(opening-closing), simplity the identification and tracking of 
evolving shapes, without extracting contours. 
The relative linear or angular momentum of regions gives the 
coarsest level for the dynamic model. The mass m; of each 
homogenous region R; is represented by the number of pixels 
with similar colour (modulus a threshold): a) Identify stable or 
inertial regions as belonging to the background (relative 
velocity under a threshold), b) evaluate nearness for mobile 
regions labelled as nodes by using adjacency graphs ,c) 
represent mutations (births, deaths) in terms of unfolding and 
collapsing nodes of the graph d) evaluate relative velocities of 
barycenters of regions with similar colour and localization. 
Any kind of spatial propagation is based on first- or second 
order differences of functions evaluated at pixels. 
Unfortunately, first order differences are very sensitive w.r.t. 
illumination changes and camera motions. To obtain stable, 
robust and accurate results in the static case, we can use LOG 
operators or typical Canny's operator to avoid the dependance 
w.r.t. orientation and illumination. Spatio-temporal version of a 
laplacian is given by a Laplace-Beltrami operator. However, the 
high computational cost for mobile data and troubles for 
dynamic grouping, suggests to introduce some kind of temporal 
average at least for three consecutive images. So, temporal 
average is responsible of small delays to generate meaningful 
regions to be sampled, identified and tracked. Criteria for 
temporal average are based on mediana filters for sampled 
images. 
Cost functions associated to regional segmentation arise from a 
weighted balance between a) the error tolerance at low-level 
and b) the maximum number of regions at high-level. Both 
infinitesimal and local criteria require specific thresholds that 
can be learned in a semiautomatic way depending on the data 
concentration and the critical size of regions. The most accurate 
results are obtained by using information arising from local 
histogram comparisons. Thus, the selection of meaningful 
thresholds can be performed from the beginning by using 
directly a temporal average of two local histograms: a) 
    
Threshold for error tolerance is based on the selection of local 
maxima in histograms corresponding to the most frequent 
values (medianas), and simple propagation mechanisms: If the 
“distance value” is below the threshold, the pixel is assigned to 
the current region, otherwise, a new region is created; b) 
Threshold for maximum number of regions can be understood 
as a mean average problem, which represents a variable version 
of k-means problem, where k represents the maximum number 
of regions, and each pair «position, colour» provides entries for 
the algorithm. This technique allows to maintain constant the 
costs of image processing. However, the variability of data 
contained in video sequences makes difficult the selection of a 
fixed value of k 
If there is no need of a live processing, it is possible to 
decompose each homogenous colour region in monotone or 
convex parts, according to usual algorithms in Computational 
Geometry [Ber97]. In this case, if optimal or at least more 
accurate results are need, our approach is enough flexible to 
support additional constraints. The symbolic management of 
this finer decomposition is labelled as an unfolding of 
centroids. More accurate results linked to boundaries are 
obtained, but matching, indexing and contents retrieval become 
more cumbersome. Thus, results will not be reported here. 
4. AUTOMATIC GENERATION OF DISTANCE MAPS 
AND OPTIMALITY 
We start up with a description of an unsupervised clustering 
technique that is based on a competitive propagation model 
from centroids of homogeneous regions above a critical size. 
An important issue is the integration of low- and high-level 
image features. This integration is related with a coarse colour- 
shape identification (for contents retrieval) and tracking of 
mobile data in general spatio-temporal models. Corresponding 
values at coordinates are weighted according to the distribution 
of frequencies, to increase the relevance of colour homogeneity 
or shape definition. 
The simplest model needs to have in account centroid position 
and typical colours of segmented regions, which gives us a 5- 
dimensional parameter space. The introduction of separating 
hyperplanes in this 5D space is performed in a very similar way 
to a generalized Voronoi diagram, but following a recursive 
pattern with successive subdivisions in half-spaces. So, we 
obtain a coarse subdivision inside the 5D parameters space that 
can be managed in terms of binary trees search. The spatio- 
temporal implementation of this algorithm produces a distance- 
map of contiguous regions with homogenous colour. Instead of 
looking at adjustable weights, we can use a feedback between 
colour-based grouping and shape with good properties for 
search/optimization processes (monotone/convex subdivisions). 
5. EXPERIMENTS 
Two local factors are based in 1) the rate of the new regions 
created per local area unit, and 2) the size of regions. Both local 
factors are related between them by a hyperbolic law. So, if 
many regions are created in a small area, then a complex 
texture is found (wood or leaves in a typical outdoor scene, 
e.g.), and the local error threshold must be increased. 
Contrarily, if we find few regions in a local area unit, the local 
error threshold can be lowered. 
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