The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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3.4 Hough Space Characterization 
The Hough Space is a 3D space whose dimensions are a, b and 
- (a,b) being the translation and being the rotation angle 
(rotation center being the image center). We will not focus a lot 
on the Hough Space representation because the data associated 
with each dimension is represented homogeneously, and thus 
we only have to use a classical scheme for representing this data 
(i.e. cells in which we capitalize votes,). 
An item (a,b, ) of the Hough Space is calculated as the 
transformation that makes a primitive (xl,yl, 1) of Image 1 
matching with a primitive (x2,y2, 2) of Image2. It provides a 
classical non-linear system of three equations with three 
unknown variables (a, b and ), whose solution is classical. 
Once we obtain all these items - i.e. (ai,bi, i) points in the 
Hough Space - we have to classified them in order to find the 
densest area that is characteristic from the expected 
transformation. This process is also very classical because of 
the Hough Space homogeneity. 
distance below dmin of any other point selected 
previously 
We obtain two sets of primitives SI = {(xi,yi, i), i ei..nl} (in 
ImBl) and S2 = {(xj,yj, j), j ei..n2} (in ImB2) to be paired. 
A primitive P1 ,i of SI is paired with a primitive P2,j of S2 when 
they satisfy a proximity constraint that is “the distance between 
points is below dmax” and “the difference of their orientations 
is below max”). Then, we can compute Tij - represented by 
(aij,bij, ij) - that transforms P2j into Pl,i. The 
transformation Tij is a “point” (or item) of the Hough Space. 
The key point of this algorithm is that we replace a set of 
possible landmarks (the one-dimensional structures) whose size, 
distribution, complexity and reliability is variable, by a larger 
set of primitives that all have the same complexity and 
reliability, and that are more uniformly distributed. 
4. RESULTS 
The only difficulty, and it is an important one, is to find 
primitives in both images and to pair them efficiently. 
3.5 Primitive detection and matching 
In this section, we introduce our contribution in finding and 
pairing primitives, and we describe precisely the algorithm we 
have designed for that. Then, in the next section, we show some 
results we obtained using this algorithm. 
Let us consider two images Iml and Im2 to be registered. 
We first compute two corresponding binary images ImBl and 
ImB2 by applying a Touzi filter and morphological 
transformations as opening and thinning. Thus, ImB 1 and ImB2 
only (or mainly) contain one-dimensional structures (i.e. based 
on arcs of curve). Most of these arcs of curve appear in both 
images (ImB 1 and ImB2) but some of them only appear in one 
image (ImB 1 or ImB2) and not in the other one. 
We assign an orientation to each point of ImBl (from now, 
when writing “a point” - in a binary image - we mean a point 
whose value is 1). This orientation is obtained by using a simple 
but efficient algorithm: we define a (small) neighborhood and 
we consider all the possible “discrete thick lines” centered on 
this point; then, we keep the direction of such a line that covers 
most points of ImBl within this point neighborhood (this 
number of points is the “score” s that characterizes the 
relevance of the selected orientation). Finally, we represent each 
point of ImBl by four values ((x,y, ),s) and we provide a 
selection on this set of points in order to obtain the set SI of 
primitives P1 ,i of ImB 1 (and we proceed in the same way for 
ImB2). Let us see now how we provide this selection. 
We experienced our approach on actual data in order to 
illustrate its feasibility. We used the Tsunami Dataset Package 
provided by ESA, and we chose two pre-tsunami images from 
ENVISAT/ASAR (*). 
Figure 2. ENVISAT/ASAR images. 
We only keep the points whose orientation is relevant enough Fi S“" 3 - Bi " aI y images obtained by using the Touzi algorithm. 
and we impose a constraint that is formulated as follows: “the 
distance between two primitives must not be lower than a given 
value dmin”. For ImBl (and then for ImB2), our algorithm 
consists in: 
1. eliminating all the points whose score is below a given 
threshold 
2. sorting all the remaining points by decreasing values of s 
3. selecting the first point of the list (i.e. whose score is 
maximum) and then, sequentially, doing the same for all 
the other points under the condition they are not at a