Figure 5: y-gradient profiles are separately accumulated in left 
region (yellow profile) and in right region (red profile). 
fictive. Regular edges are located on significant gradient where a 
significant gradient keeps its orientation uniform. A fictive edge 
does not match with any significant gradient. Such a distinction 
is illustrated in figure 6. 
Figure 4: Upper right and bottom left images respectively are 
x-gradient and y-gradient. Bottom right image presents accumu 
lation profiles: green profile for x-gradient and red one for y- 
gradient. extrema of this profiles are our split hypotheses: red 
lines in upper left image. 
Such a rough set of hypotheses supplies initial interesting seg 
mentation. (Lee and Nevatia. 2004) base their window detection 
on similar rough segmentation. They almost use the same pro 
cedure except that they do not accumulate gradients in the same 
orientation: they respectively treat x-gradient and y-gradient hor 
izontally and vertically. Thus they locate valley between two 
extrema blocks of each gradient accumulation profile and they 
frame some floors and windows columns. Their results were rel 
evant in façades composed of a fair windows grid-pattern distri 
bution on a clean background. 
Main buildings structure are detected. Each repetitive objects are 
present in vertical or horizontal alignment as common edges gen 
erate local extrema in accumulation profiles. Local gradient ex 
tremum neighborhood is set a priori. In our case, this neighbor 
hood is set to 30 centimeters. However this last grid-pattern usu 
ally is not enough by itself to summarize façade texture: repeti 
tive elements of our images are not necessarily evenly distributed. 
Thus our split strategy relies on breaks between two façades or 
inside one façade. 
5.2 Choosing the best splitting hypotheses 
The best splitting hypothesis maximizes its pixels number of reg 
ular edges in each of the two sub-region. A regular edge is a 
segment of a main gradient direction that effectively matches to 
a contour of the image. The weight Wh of the split hypoth 
esis H that provides the two regions Ri and Rv is given by 
Wh = f{R\) + /(-R2), where the function / returns the pix 
els number of regular edges in a region. We select the hypothesis 
H* = argmax/i Wh- 
If we try for instance to split image at xo location, we reaccumu 
late y-gradients in left region and in right region separately. Local 
extrema are detected in each of those y-profiles (cf figure 5). 
Previous vertical split hypotheses and those new horizontal split 
hypotheses constitute two new grid patterns for local split hy 
potheses. Each edge of these grid patterns is either regular or 
I 
I 
I 
Figure 6: Regular edges are located on significant gradient where 
a significant gradient keeps its orientation uniform. A fictive edge 
doesn’t match with any significant gradient. 
The weight of each split hypothesis is the sum of regular edge 
lengths. Figure 7 illustrates best split selection. 
Ill 
zzz 
III 
III 
■ ■ 
■ 
m ^ a ▲ 
■■■ 
■■■ 
■ ■ ■ 
Figure 7: Regular edges are drawn in red. Split hypotheses are 
drawn in yellow. Right image presents the best split hypothesis 
whose weight is 8400 regular edge pixels. Left image presents a 
bad split hypothesis: only 7700 regular edge pixels. 
If the given region does not contain any gradient extremum, the 
process stops. Figure 3 shows a region that do not fit with any 
model and that is not split. 
6 RESULTS 
We illustrate our segmentation on a typical instance of our is 
sue: two building façades in the background. We have set maxi 
mum model deviation at 15% of each region area. On our images, 
the depth in the hierarchy of the segmentation tree is represented 
by the thickness of split lines. First the process detects vertical 
structure discontinuities (figure 8). The two façades are sepa 
rated. Then on each of these two new sub-images, background 
is separated from the foreground (figure 9). At this step we have 
obtained four images: two façade images and two images of fore 
ground cars. Then the process recursively keeps analyzing these 
images as shown in figure 10. Figure 11 shows the global seg 
mentation: a tree of about 2000 elementary models.