In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Vol. XXXVIII, Part 3A/V4 — Paris, France, 3-4 September, 2009 
225 
Figure 2: The rectification process, upper left: original image 
only; upper right: original image with segments that support main 
vanishing points (green and blue ones are those for the main ver 
tical direction, yellow and white ones for the main horizontal di 
rection and red ones for an aberrant vanishing point); bottom left: 
rectified image with rectified segments that support the two se 
lected directions; bottom right: rectified image only 
4 MODEL MATCHING 
Given a region of a rectified image, we try to match two geomet 
ric models with data in increasing complexity order: the planar 
model Mi, then the generalized cylinders one M 2 - This de 
cision tree indeed provides a good compromise between quality 
and compression rate. 
To match an image region with a model, we simply count local 
radiometric differences as follows. Let I k be the sub-image at 
region Rk of a façade image I. Sub-image I k is described by 
model M when the deviation NmÎR) is small enough and if 
this model is the simplest one. Deviation Nm(Iic) is defined by 
the number of pixels whose radiometry differs too much from the 
model. Radiometric medians provide some significative robust 
ness: the influence of parasite structures such as tree branches or 
lighting posts, is significantly reduced. Figure 3 illustrates mod 
els we use. 
Figure 3: Description of our radiometric 2Z)-models 
An instance of a planar model is depicted on the lower-right cor 
ner of figure 3. 
Mi : Vp € Rk, h{p) = median(h) + e(p) (1) 
where e(p) is the difference between the image Ik and the model 
M\ at the pixel p. If this difference is smaller than an arbi 
trary threshold, it is tolerated. It refers to the acquisition noise 
or some texture defects. Otherwise, the deviation NM(h) is in 
cremented. 
4.2 Generalized Cylinder Model 
A generalized cylinder model is designed either in columns (M 2 ) 
or in rows (Mo)- The model in columns is composed of medi 
ans of columns and the cylinder model in rows is composed of 
medians of rows. They are is defined by equation 2. Functions 
mediarix and median y respectively return the median of the 
column at x abscissa and the row at y ordinate. Figure 3 shows 
an instance of each generalized cylinder model. 
V(x,2/) € Rk, 
M 2 : h(x,y) = mediarix (I k{x,y)) + e(x,y) (2) 
M l 2 : h{x,y) = mediany (I k (x,y)) + e(x,y) 
where e(x,y) is the difference between the image I k and the 
model M 2 at the pixel (x,y). In the same manner as planar 
model, the deviation NM(h) is incremented when this differ 
ence is greater than an arbitrary threshold. 
5 SPLIT PROCESS BY ENERGY MAXIMIZATION 
Given a region of a rectified image that does not match with any 
model, we try to split it by measuring the internal gradient distri 
bution energy. 
5.1 Generating splitting hypotheses 
4.1 Planar Model 
A planar model is an image with an uniform radiometry. Let Mi 
be the planar model of a sub-image I k - It is defined by equation 1. 
We select split hypotheses with a technique close to (Lee and 
Nevatia, 2004). We accumulate x-gradient absolute values by 
column and y-gradient absolute values by row, where x-gradient 
and y-gradients are related respectively to vertical and horizontal