1л: Paparoditis N., Pieirot-Deseilligny M.. Mallet C.. Tournaire O. (Eds). LAPRS, Vol. XXXV1I1. Part ЗА - Saint-Mandé, France. September 1-3, 2010 
2.3 Extraction of the low-frequency deformation 
A first deviation from the assumption on stochastic model is due 
to the presence of a low-frequency component in the ADEM. 
This might originate from three possible grounds: residual geo- 
referencing errors; instability of the RS; major deformations on 
the cliff (e.g. due to a global displacement of the whole slope). 
Understanding the meaning of a such component is a complex 
issue, requiring context-aware analysis and comparison between 
results obtained on other Regs and w ith geodetic measurements. 
On the other hand, here the main task is to look for low-pass de 
formation. that currently is implemented as the estimation of a 
3D plane Sz = ai + bj 4- c fitting the ADEM. Because some ma 
jor changes might be in the ADEM. the estimation of the linear 
component is carried out first by using a robust approach (Ll- 
nonn). Secondly, the final estimation of the plane parameters 
x = [a b c] r is performed by standard Least Squares. A y 2 test 
on the estimated sigma naught (<7q) allows to check if the linear 
model fit the data well or not. In case of good fit a further statis 
tical testing on the significance of each element of the vector x is 
applied to decide if a low-frequency component is worthy to be 
removed or not. Estimated parameters which are retained to be 
significant are stored in the vector x s \ otherwise, their place in x s 
is put equal zero. Finally the estimated low-frequency component 
is subtracted from the ADEM: 
z'(i, j) = z(i, j) - [ij 1] • x s . (2) 
2.4 Change detection algorithm 
The major changes on a rock face are for the most due to the 
detachment of boulders or to the vegetation growing. Both fea 
ture some specific characteristics that allow to recognize them, 
and some others that are undifferentiated. For example, rock 
falls result in a negative change on the ADEM, while vegeta 
tion gives rise to positive changes during its growth and negative 
when leaves fall. Furthermore, other material could accumulate 
on the cliff resulting in positive changes on the ADEM (e.g. a 
bird nest). 
The procedure that is described here cannot actually account for 
all these factors, but it tries to extract information from the ADEM 
according to a set of basic rules. First of all. rock detachments 
can result only in negative changes (holes) on the ADEM. More 
over, only blocks of significant size deserve to be considered, 
because smaller size rocks are not relevant for geological anal 
yses. Two thresholds have been introduced to recognize holes in 
the ADEM: the min width (w cav ) of a rock-mass which has de 
tached: the min depth (Sz cav ) of the resulting cavity. 
On the other hand, some specific techniques exist to remove the 
vegetated areas before data processing (see Alba et al., 2009; 
2010). This results in the fact that at this stage both original 
DEMs have been already filtered out from vegetation, apart some 
errors which might still remain. How'ever, two thresholds are es 
tablished to detect the vegetation growth only: the min bush width 
(w veg ): the min bush growth along z direction (z veg ). Conversely, 
when leaves fall, the resulting hole in the ADEM can be confused 
with a rock detachment. A final visual inspection of results can 
help in understanding errors, perhaps by texturing the DSM of 
the cliff by using RGB (or NIR) images. 
The basic concept of ChDet algorithm is to perform an analysis 
of volumetric changes by considering relevant variations in the 
ADEM surface. We consider here an approach useful for both 
losses of material and vegetation grow'th. even though each of 
this could be further specialized (e.g. by considering local rough 
ness. curvature, or by integrating further data like RGB and NIR 
images, laser intensity). The assumption made is that changes 
are much larger that data uncertainty and they can be detected 
by fixing suitable thresholds depending on the geomorphology of 
the cliff. The localization of holes is carried out along the two 
following phases. 
2.4.1 Holes localization The convolution of ADEM with a 
square matrix H is computed to define the map of mean displace 
ments M in the nearby of each point: 
M = ADEM 0 H = ADEM 0 —I. (3) 
W c .av 
Secondly, each element i. j of M is tested to check if it belongs 
to a region of detachment (or growth): 
{ D i; = 1, when M,, < Sz cav 
(4) 
D,j = 0. elsewhere. 
The matrix D maps all discovered holes in the ADEM. Accord 
ing to the smoothness of M w.r.t. ADEM, once adequate thresh 
olds w C av and Szcav have been established, commission errors 
are very unlikely. On the other hand, small losses of material 
could not be detected, but usually they are not relevant. 
2.4.2 Improvement of the holes contours To better define 
the contours of each cavity and to improve the accuracy of com 
puted detached volumes, a further procedure has been applied. 
Indeed, errors in the classification of contours by linear filtering 
might be larger when the depth of the holes is deeper. 
First of all. elements of matrix D classified as detachments are 
grouped into clusters of points belonging to the same hole. Un 
der the hypothesis that no commission errors have been made, 
all clusters are held, even though they feature few members only. 
Then the largest cross-section d x of each hole i-th is computed 
according to D. A square window W, sizing 2d t -\ DU is ex 
tracted from the ADEM at corresponding elements. A median 
filtering is applied to W*. This task might result in the loss of the 
smallest cavities found during linear filtering described at Sub 
section 2.4.1. because of the robustness of the median filter of 
size Wcav x w C av For this reason, only holes accounting for a 
minimum number of points n = 0.5 • wij. av + 1 hold. Indeed, 
median filtering is applied only to redefine contours of already 
extracted holes, not to look for new ones. Results of latest fil 
tering are stored into a matrix M . Now the test (4) is applied 
again but considering M instead of M. After the second clas 
sification, the contour is redefined and points with D(i,j) = 1 
clusterized newly. In Figure 2 is shown somehow the use of the 
median filtering preserves the edge of a cavity in a cliff. 
1 
/ 
1 
1 
i 
1 
\ 
\ 
\ 
\ 
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Figure 2: Differences in the definition of contours of a hole when 
applying a linear (left) or a median filtering (right) 
2.4.3 Filtering out the grown vegetation The same proce 
dure is then applied, if needed, to look for vegetation grown in the 
meanwhile of two observation epochs. Here only the localization 
stage is performed, because the precise volume of vegetation is