The most difficult aspects of 3D modeling are well represented 
by cultural heritage objects, where current costs can hardly be 
afforded even for the most precious statues. Cultural heritage 
objects are characterized by a number of difficulties such as: 
their shape, typically way more articulated than that of 
mechanical objects; their size, which may not be small; the fact 
that they cannot be taken into a laboratory but almost always 
need portable equipment; the required precision, if physical 
duplication has to be included among the possible model’s uses. 
In this application field, there is a strong demand for automatic 
3D data registration algorithms: solutions for this issue will be a 
major progress for general 3D modeling. 
In the light of topics previously exposed, a fully automatic 
range data registration system has been developed. This system 
is able to execute all the steps needed for 3D modeling of real 
objects in automatic way or at least minimizing as more as 
possible the human intervention, without any other information 
but the range data only. 
The presented work draws the idea from A. E. Johnson[1], 
which proposed an innovative solution for the recognition of 
similarities between 3D surfaces, introducing the spin-image 
concept. The advantage of this approach rely on high compu- 
tational robustness and effectiveness, which allows to employ 
standard market-level CPUs. On the ground of the spin-image 
concept, a full data registration system was developed, in which 
the overlapping areas of two adjacent data set are automatically 
recognized, thus allowing to correctly align the two whole data 
sets. The framework of the registration system can be 
summarized as follows. Given the whole set of range data, 
acquired for instance by a laser scanner, the registration 
procedure is applied to each pair of range data (or range 
images). Firstly, spin-images are computed for each view, then 
a comparison technique is applied in order to build a measure of 
the similarity of the spin-images between two views. As final 
step of this first phase, the above measure is used as input of the 
algorithm that searches for the matching points between the 
view pair. Further filtering and grouping are applied to refine 
the matching and to improve the robustness of the whole 
process. In the second phase the Horn's registration method is 
used to get a first rough estimate of rototranslation between the 
view pair, exploiting the identified matching points only. Then 
this rototranslation is applied to the range data of view pair in 
order to detect the overlapping areas. 
In the third, and final, phase the alignement is refined through 
the application of a cascade of two global registration methods. 
The first is the frequency domain algorithm [2], by which an 
initial estimate of rototranslation parameters is computed using 
all the points of overlapping areas. Then the ICP algorithm is 
applied to compute the optimal estimate. The approximate 
estimate of rototranslation provided by the frequency domain 
method is employed in order to provide a good initial estimate 
of the transformation, in order to avoid the convergence of the 
ICP toward a local minimum, rather than to the global one. 
The paper is structured as follows. Section 2 provides the 
necessary background on the spin image concept, while sections 
3 and 4 give the details of the registration algorithm, with 
section 3 focusing on the local correspondence determination 
between spin images, while section 4 dealing with the automatic 
detection of common areas. 
2. THESPIN IMAGE CONCEPT 
Recent advances in last years in 3-D sensing technology and 
shape recovery algorithms have nade digitized 3D surface data 
widely available. For example, laser scanners return an object 
surface in terms of a dense grid of 3d points, while stereo vision 
systems can passively determine the 3D position of features or 
textured areas from two camera views. Computed Tomography 
or Magnetic Resonance Imaging extract 3D surfaces through 
volumetric image processing. Then, once these 3D data are 
acquired by some kind of sensor, the 3D model of the whole 
sensed object can be reconstructed. A necessary step of this 
process is represented by the pairwise registration of 3D data, 
tipically stored as clouds of points. This step can be carried out 
through surface matching, therefore an appropriate representa- 
tion of the object's shape is needed. In this Work, the surface 
shape is described as in [1], i.e. in terms of the collected 3D 
points and surface normals. Furthermore, each surface point is 
associated with a descriptive image that encodes global 
properties of the surface in an object-coordinate reference 
system. By matching images, correspondences between surface 
points can be established resulting in surface matching. In this 
way, this problem can be broken in many smaller and easier 
affordable problems. Surface normals can be computed using 
sensed 3D points and adjacency among them, i. e. exploiting the 
geometrical relationships among the points. To this aim, object 
surface is represented by polygonal mesh, where its vertices 
correspond to 3D surface points and edges between vertices 
convey the adjacency information. 
A way to encode global properties of object surface is 
represented by spin-images. They are based on the concept of 
oriented point at a surface mesh vertex, which is defined as the 
pair formed by the 3D vertex coordinates and the surface 
normal at this vertex. Through this oriented point, all the object 
points can be mapped on a cylindrical coordinate system 
according to following spin-map: 
So — R° 
Sox) > (8) = (Alix — pi? — (a - (x— p))”, n - (x p) (1) 
where a is the perpendicular distance to the line through the 
surface normal, and is the signed perpendicular distance to the 
tangent plane defined by vertex normal and position (Fig. 1). 
  
  
  
  
  
  
  
  
Figure 1: Oriented point and its surface normal 
Since corresponding points of two views of the same object will 
likely represent two close points on the surface rather than the 
same point, a registration algorithm should have to consider the 
object shape, neglecting the specific position of sample points. 
Therefore a further representation is needed, which is able to 
retain only the information about the spatial distribution of 3D 
points rather than their positions. To this aim, the 2D space (a, 
D) is partitioned in a grid of square cells, which accumulates the 
points of the spin map, resulting in a bidimensional histogram 
(spin-image) of the density of object point distribution (Fig. 
2,3). Essentialy a spin image of a 3D surface is the recording on 
a 2D accumulator of the coordinates of all the points of a 3D 
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