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Figure 1: Hierarchical unsupervised segmentation: algorithm re 
cursively confronts data with models. Regions that do not match 
any proposed model are split. Contribution of this article is men 
tioned in red. 
Model Matching 
The problem is to recognize some proposed models in the facade. 
Given an image region, intensity is compared to one of these 
models in increasing complexity order: the planar model, then 
the generalized cylinders. The process stops when the sub-image 
is considered as a good match for the model: we simply count 
local radiometric differences as follows. Let R- be the sub-image 
at region Rk of a façade image /. Sub-image h is described by 
model M when the deviation (/*.) is small enough and if 
this model is the simplest one. Deviation iV.vi(/ fc ) is defined by 
the number of pixels whose radiometry differs too much from the 
model. 
The planar model assumes that the intensity of the sub-image R 
at pixel p follows an uniform radiometry: R-(p) = A + e(p) with 
A being the uniform radiometry and e(p) being noise (small lo 
cal details, sparse occlusions or Gaussian noise). The generalized 
cylinders are designed either in columns or in rows. The cylin- 
dric model in columns for instance assumes intensities to follow 
Ik(x, y) = A(:r)+e(a;, y) with X(x) being the cylinder value and 
e(x, y) being noise. Figure 2 illustrates instances of such models. 
Figure 2: Instances of radiometric cylindric models: vertical 
cylinders can be detected in window pane or wall railings, hor 
izontal cylinders in window shutter or wall background 
horizontal and vertical dominant alignments are respectively de 
tected at maxima of vertical and horizontal profiles of gradient 
accumulation, vertical profile being obtained by horizontal gradi 
ents. This enforces low but repetitive contrasts. 
The split strategy relies on structures alignment break between 
two facades or inside one facade. Split hypotheses are the previ 
ous detected dominant alignments. If such a vertical hypothesis 
is located at .x*o. horizontal dominant alignments are separately 
detected in the left and right regions. Two new grid patterns are 
thus constituted by vertical dominant alignments and new hori 
zontal ones. An edge of such a grid pattern that covers enough 
strong gradients is named regular edges. Other ones are fictive 
edges: falsely detected edges. The best splitting hypothesis min 
imizes the length of fictive edges in each of the two sub-region. 
Figure 3a shows such split process optimization. 
3 SPLIT ENERGY ADVANCEMENT 
The strength of dominant alignment usage is its independence to 
local isolated structures. (Burochin et al., 2009) aims at mini 
mizing such alignments in best split selection. But alignments 
of edges at two different scales are then compared. They do not 
deal with the same structure types. For instance on figure 3a, the 
fictive edges of the top region nearly coincide with the ones of 
the whole region whereas bottom region contains long contam 
inating fictive edges generated by local high contrasts that were 
insignificant in the whole region. Split energy at this hypothesis 
is negative. Yet it is precisely the split location we are looking for. 
In this typical case, an information about a road sign is compared 
to alignment of window borders. 
3.1 Optimization in Edges Space 
We propose in this paper a static edges structure based split opti 
mization. We have chosen the solution to study edges distribution 
only with dominant alignments grid pattern of the whole region 
unlike approach of (Burochin et al., 2009). We build an edges 
space based on this grid pattern. Now let us introduce the hori 
zontal edges space. 
be the vertical dominant alignment set such that