The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
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considered to be the weight of its normal. Second, according to 
the statistics distribution getting from the first step, the three- 
dimension normal vectors are projected to two-dimension space 
(like the definition of longitude and latitude). As result of these 
two steps, a statistics chart of the triangles’ normal shows the 
distribution of these three-dimension vectors. Third, to find a 
gray-scale image threshold, the image getting from the second 
step is processed by Otsu algorithm Then the weighted 
average normal and the approximate number of the object’s 
major surfaces can be obtained. 
There are three examples of using Normal distribution analysis 
methods to analysis.Fig 1 (a) shows weighted normal 
distribution of hexahedral object. The object is similar to that of 
the mathematic hexahedral object, but all the surfaces of the 
object are not a plane. Figl (b) shows the normal distribution of 
the green rectangle region in Figl (a). The background colour 
of Figl (b) is yellow, that represents the absence of the 
corresponding normal in the actual surface, while the graduated 
tint from white to black represent the concentration degree from 
low to high. 
Fig2 shows the weighted normal distribution of car. Fig3 shows 
the weighted normal distribution of human face. 
Compared Figl (a) and Figl (b), there are six significantly 
concentrated distribution points in Figl (a). And every 
concentrated distribution point represents a major surface. As a 
result, the weighted average normal (the Pixel coordinates of 
corresponding pixel), area (the sum of all the pixels’ gray in one 
concentrated distribution point) and the number of major 
surface (the number of concentrated distribution points) can be 
extracted from the statistics chart. 
Compared Figl (a), Fig2 and Fig3, a special phenomenon of 
normal distribution concentration can be found that the 
polyhedron is most obvious, the human face is the least and the 
car is between these two situations. The human face has amount 
of complex surface, as a result, the normal distribution 
concentration of is least. While the surfaces of the car are 
curved surface, the main shape of the car is approximate to a 
complex polyhedron, so the statistics chart of it show some 
concentrated points. 
Though these examples, Normal distribution analysis can get 
the number, average normal and area of the major surface of 
polyhedron object. 
% 
* 
0 
(b) 
Fig.l Statistics chart of hexahedral object. Fig.l (a) shows the 
weighted normal distribution of hexahedral object. Figl (b) 
shows the normal distribution of the green rectangle region in 
Figl (a). 
Fig.2 Statistics chart of the weighted normal distribution of car. 
Fig.3 Statistics chart of the weighted normal distribution of 
human face. 
2.1.2 Recursive algorithm of Growth Triangles 
Classification: All the triangles, through recursive algorithm, 
are classified into several classes, according to the normal and 
the contiguous relation of the triangles. 
The main processes of the Growth Triangles Classification are 
as follow: 
1. Input one triangle as the initial growth triangle (from the 
triangle mesh of the object), and add its adjacent triangles into 
the growth candidate array. 
2. Traverse the adjacent triangles of the initial growth triangle, 
if the difference of the normal between the initial growth 
triangle and its adjacent triangle is less than the threshold 
provisions, its adjacent triangle is classified as the same class of 
itself. And its adjacent triangles are also added to the growth 
candidate array. 
3. Calculate the average normal and the total area of the current 
class. 
4. Traverse all the triangles in the growth candidate array, and 
use the triangle as input of step 1. The process from 1 to 3 will 
repeat until no triangle meets the condition of step 2. 
5. Traverse all the unclassified triangles, and use the triangle as 
input of step 1). The process from 1) to 3) will repeat until all 
the triangles are classified. 
In this process, Recursive algorithm can accelerate the Growth 
Triangles Classification. The main substance of recursive 
algorithm is expressed in Fig 4. At end of every recursive 
process, there is a new class.