The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part B3b. Beijing 2008 
Image pre-processing 
1 
Remove image 
background noise 
' 
’ 
Extract image Features 
1 
' 
Image matching 
Figure 2. The process of quick image matching 
2.3 3D Reconstruction and Registration for Non- 
cooperative Target 
Image matching only can provide discrete and non-structured 
3D target information. However, for the determination of 
relative navigation parameters and motion rules of non- 
cooperative target, 3D metric geometric model must be built to 
locate precisely the target centroid and shape. Constructive 
Solid Geometry (CSG) model is conveniently used to describe 
artificial spatial target because the artificial target has relatively 
regular appearance and shape. CSG uses some basic geometric 
entities, such as cube, cylinder and cone, to construct complex 
3D entities according to some proper positive Boolean 
operations. Basic geometric entities can be transformed from 
basic condition to combined condition by way of some 
transformations, such as translation, rotation and scaling, and 
can be used to construct intermediate entities by means of some 
positive Boolean operations, such as intersection, union and 
difference. Then the intermediate entities are as basic entities to 
combine at a more high degree. 3D objects can be described as 
a CSG tree, also called as binary tree, in which basic geometric 
entities and its transformation parameters are leaf nodes and 
positive Boolean operations and transformation operations are 
other nodes. Basic geometric entities in CSG are mainly regular 
geometric entities which can be represented easily because of 
more simple data structure. And the model can be edited by 
mathematic operations such as adding, changing, modifying and 
deleting leaf nodes and intermediate entities to alter 3D objects 
conveniently. In addition, CSG can describe geometric shapes 
of objects precisely and strictly and construct a clearer 
mathematic model to query, add and delete shape data structure 
easily and expediently. 
If 3D geometric model of non-cooperative target is known, the 
3D data field must be matched with the known model to locate 
the target centroid and principal axis and construct quickly the 
body coordinate system of the tracked spacecraft. But if it is 
unknown, the whole 3D model of the target will be built based 
on long-time tracking and observing. The process is shown in 
Figure 3. 
Figure 3. 3D Reconstruction and Registration for Non- 
cooperative Target 
2.4 Real-time Solution for Relative Navigation 
The relative navigation parameters between targets, such as 
relative location, relative attitude, can be obtained by CSG 
model of non-cooperative target, and then the relative velocity 
and angular velocity can also be acquired using time relation of 
sequence images. In the algorithm, the above process is 
integrated closely into image matching and 3D reconstructing 
and the combined adjustment algorithm will be adopted to solve 
jointly the parameters for image matching, 3D reconstruction 
and navigation and at the same time Extended Kalman Filtering 
is used to realize real-time relative navigation. 
In the resolution process, the key to the problem is to describe 
the rotation relation between two coordinate systems effectively 
and reliably. There are many parameters to describe the rotation 
relation in mathematics, which include Euler-angle, Gibbs 
vector, Cayley-Klein parameters, Paul spin matrices, orthogonal 
rotation matrix, the coordinate axes and angles, orthogonal 
matrix, Hamilton quaternions and others. In Photogrammetry, 
Euler-angle and orthogonal rotation matrix are commonly used 
but the latter cannot be used widely because it needs six 
constraints. The primary researches present the quaternions 
have clear superiority in resolution. They have an efficient 
algorithm because it does not execute the operation of 
trigonometric functions and they are calculated easily because 
they need only a constraint. And they can describe the rotation 
axis and the rotation angle directly because they have obvious 
geometric sense. At the same time, the quaternions are not 
singular and they are steady to describe the transformation 
between two coordinate systems. Therefore, the quaternions and 
dual-quaternions can be adopted to describe relevant 
transformation relation between the coordinate systems entirely 
[15-16]. 
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