Image Processing Reference
In-Depth Information
Table 3.3. A possible set of principal curvatures in a 4D curved surface.
Simple principal
Absolute value
Mean curvature
Number curvature criterion
criterion
criterion
1
k 1 >k 2 >k 3 > 0 |k 1 | > |k 2 | > |k 3 | > 0 k 1 + k 2 + k 3 > 0
2
k 1 >k 2 >k 3 = 0 |k 1 | > |k 2 | > |k 3 | = 0
3
k 1 >k 2 = k 3 > 0 |k 1 | > |k 2 | = |k 3 | > 0
4
k 1 >k 2 = k 3 = 0 |k 1 | > |k 2 | = |k 3 | = 0
5
k 1 = k 2 >k 3 > 0 |k 1 | = |k 2 | > |k 3 | > 0
6
k 1 = k 2 >k 3 =
0 |
k 1 |
=
|
k 2 |
>
|
k 3 |
=
0
7
k 1 = k 2 = k 3 > 0 |k 1 | = |k 2 | = |k 3 | > 0
8
k 1 = k 2 = k 3 = 0 |k 1 | = |k 2 | = |k 3 | = 0 k 1 + k 2 + k 3 = 0
9
k 1 >k 2 > 0 >k 3 |k 1 | > |k 2 | > |k 3 | > 0 k 1 + k 2 + k 3 > 0
10
|k 1 | > |k 2 | = |k 3 | > 0
11
|k 1 | > |k 3 | > |k 2 | > 0
|k 1 | = |k 3 | > |k 2 | > 0
12
13
|k 3 | > |k 1 | > |k 2 | > 0
14
k 1 + k 2 + k 3 = 0
15
k 1 + k 2 + k 3 < 0
16
k 1 >k 2 = 0 >k 3 |k 1 | > |k 3 | > |k 2 | = 0 k 1 + k 2 + k 3 > 0
17
|k 1 | = |k 3 | > |k 2 | = 0 k 1 + k 2 + k 3 = 0
18
|k 3 | > |k 1 | > |k 2 | = 0 k 1 + k 2 + k 3 < 0
19
k 1 = k 2 > 0 >k 3 |k 1 | = |k 2 | > |k 3 | > 0 k 1 + k 2 + k 3 > 0
20
|
k 1 |
=
|
k 2 |
=
|
k 3 |
>
0
21
|k 3 | > |k 1 | = |k 2 | > 0
22
k 1 + k 2 + k 3 = 0
23
k 1 + k 2 + k 3 < 0
24
k 1 = k 2 = 0 >k 3 |k 3 | > |k 1 | = |k 2 | = 0
25
k 1 > 0 >k 2 >k 3 |k 1 | > |k 3 | > |k 2 | > 0 k 1 + k 2 + k 3 > 0
k 1 + k 2 + k 3 = 0
26
27
k 1 + k 2 + k 3 < 0
28
|k 1 | = |k 3 | > |k 2 | > 0
29
|k 3 | > |k 2 | > |k 1 | > 0
30
|k 3 | > |k 1 | = |k 2 | > 0
31
|k 3 | > |k 1 | > |k 2 | > 0
32
k 1 > 0 >k 2 = k 3 |k 1 | > |k 2 | = |k 3 | > 0 k 1 + k 2 + k 3 > 0
33
k 1 + k 2 + k 3 = 0
34
k 1 + k 2 + k 3 <
0
35
|k 1 | = |k 2 | = |k 3 | > 0
36
|k 2 | = |k 3 | > |k 1 | > 0
37
k 1 = 0 >k 2 >k 3 |k 3 | > |k 2 | > |k 1 | = 0
38
k 1 = 0 >k 2 = k 3 |k 2 | = |k 3 | > |k 1 | = 0
39
0 >k 1 >k 2 >k 3 |k 3 | > |k 2 | > |k 1 | > 0
0 >k 1 >k 2 = k 3 |k 2 | = |k 3 | > |k 1 | > 0
40
41
0 >k 1 = k 2 >k 3 |k 3 | > |k 2 | = |k 1 | > 0
42
0 >k 1 = k 2 = k 3 |k 1 | = |k 2 | = |k 3 | > 0
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