The spin image is …rst introduced by Andrew E. Johnson in.The key concept of generating the spin image is the use of oriented points.There are two kinds of oriented coordinate sys-tems.One is object-otriented coordinate systems which are coordinate systems …xed on a surface.Another is viewer-oriented coordinate systems which are based on the viewpoint of the oberserver of the surface.Johnson [31] adopted the object-oriented coordinate systems for the view independent of the description of a surface under the changing viewpoint.
An oriented point at a surface mesh vertex can be de…ned by the 3D position of the surface vertex and a surface normal which are denoted by and respectively [31].By using the tangent plane through which is perpandicular to and the line
through which parallel to ,it will achieve a representation in a form ( ) based on cylindrical coordinate system where is the perpendicular distance to and is the signed perpendicular distance to the plane [29].Fig.13 illustrate the detail of the creation of cylindrical coordinate system.
Figure 13:Parameters of Spin Image
We can de…ne the transformation precedure as a projection function of the 3D points
to 2D coordinate ( ) associated with the 2D basis ( ) that corresponds to the oriented point [18].The projection function (spin map) is shown as following [16]:
0 : 3! 2
0()! ( ) = (p
jj ¡ jj2¡ ( ¢ ( ¡ )2) ¢ ( ¡ ))
Before we introduce how to generate the spin image,there are four paremeters,bin size
,image width ,support distance and support angle ,need to be recommanded
…rst.Bin size is an important parameter in spin image generation.It not only determines the storage size of the spin image but has an e¤ect on the descriptiveness of the spin images.A saitable bin size can reduce the in‡uence of indivisual point position.It is better to set the bin size based on mesh resolution.The reason is that the size of the shape features
on an object and the density of points in surface mesh e¤act the mesh resolution.Johnson in [31] indicated that if the bin size was set to be one or two times the mesh resolution,the resulting spin image can properly describe the global shape.Three spin image of decreasing bin size for a point on the duckie modal are shown in Fig.14 [31].Johnson [31] let the number of rows and columns in a spin image equaled to each other and de…ned the number of rows or columns in a square spin image as image width.A image width can decide the amount of global information in a spin image.Support distnace is de…ned as the product of the image width and the bin size.The amount of global information swept ot by spin image can be determined by the support distance.The last parameter,support angle,is the maximum angle between the direction of the oriented point and the surface normal of points which can contribute to the spin image.
Figyre 14:The e¤ect of bin size on spin image appearance [31].
To create aspin image,the procedure can be introduced in detail in the following [31].First,we have to select an oriented point from a vertex of the surface mesh.Then the spin map coordinates with respect to the oriented point are computed for each vertex on the surface mesh.The next step is to screen the vertex which meets some criteria based on the distance from the oriented point and the support angle.For example,suppose
that the oriented point with its position and normal is set as ( ), and there exists another point on the surface mesh with the position and normal as ( ).If satis…es cos¡1(¢ ) , can be accumulated in the spin image respect to the oriented point
.Once the vertex can be accumulated in the spin image,the gridding index of the bin which is projected in is determined.The index of the bin ( ) can be computed as follow
=b
2 ¡
c =b
c (2.9)
where is the bin size , is the image width,( ) is the spin map coordinate and b¢c is the ‡oor operator.By using the formula we can grid the 2D points into the spin image bins.In the gridding procedure,an error is produced by the ‡oor operator.We can use the spin map coordinates,( ),and the gridding indices to do bilinear interpolation.The result of the bilinear interpolation is the contribution of a point to its surrounding grid locations.We can calculate the bilinear interpolation weights acoording to the formula [31]
as follow
= ¡ = ¡ (2.10)
And we can see the total procedure of the creation of the spin image described in pseudo code in Figure 15.
Figure 15:The procedure of the creation of the spin image description [31].
Spin image can show the global propertires of any surface in an object oriented coor-dinate system rather than a viewer oriented coorcoor-dinate system.It transform the 3D points into 2D cyclindrical coordinate system.( ) Sice coordinates are measured according to the oriented point and its normal,we can infer that the spin images are rotation and translation invariant,but they are not scale invariant.If there are two surfaces with the same shape but di¤erent scale,the spin image of the two surfaces will be di¤erent.Even so,we still can see the strong robustness and good adapatability descriptiveness of the 3D shape.