无序点云的B曲线拟合

step 1
主元素分析法PCA初始化B样条曲面
step 2
拟合B样条曲面
step 3
循环初始化B样条曲线
step 4
拟合B样条曲线
step 5
三角化B样条曲面

Gestalt principles
Monte Carlo particle filter (MCPF)蒙特卡洛粒子滤波
tracking-state-detection(TSD)This allows to learn or extend a
probabilistic motion model.

一些符号约定

S ——savings of a surface model hypothesis
κ0,1,2 ——MDL weights
Ξ —— knot vector
ξi ——element of the knot vector
ξ —— parameter of a B-spline curve
u,v —— parameters of a B-spline surface
Ω ——parameter space of a B-spline curve or surface
Ni,p ——i-th B-spline basis function of p-th order
Mj,p ——j-th B-spline basis function of p-th order
c ——B-spline curve
b ——control vector
S ——B-spline surface
B ——control grid
p ——point
n ——normal vector
t ——tangent vector
o ——outward pointing normal vector
e ——error function
f ——objective function
w ——weighting factor or -function
d ——signed distance to B-spline curve
ρ ——curvature of the B-spline curve
σ ——standard deviation or transition width
ε ——threshold
f ——force vector
K ——stiffness matrix
R ——regularisation matrix
t ——time steps t∈N∪{0}
I ——colour image
T ——rigid transformation (rotation, translation)
t ——translation
R ——rotation (matrix form)
i,j,k ——imaginary units
q ——quaternion
r ——real value of quaternion
θx,y,z ——imaginary value of quaternion
θ ——vector of imaginary values of quaternion, i.e. rotation
x ——state vector of a particle
x~ ——posterior particle
N ——normal distributed noise
σ ——standard deviation
c ——confidence
p ——probability
P ——discrete probability
i ——particle index
N ——number of particles
w ——importance weight
y ——observation
g ——colour gradient
M ——object model projected to image space
m ——match value
s ——normalizing factor
h ——hue value of the HSV colour space
δ(x) ——delta-Dirac mass located in x
u,v ——pixel coordinates in image space
Xft ——set of fixed particles
o ——detection success
qk ——fixed point on the object surface
e ——tracking error
A,B,O ——coordinate frames

第一章 介绍

认知机器人的子任务：
• Knowledge representation: Represent knowledge that allows for extension and
modification over time.
• Reasoning: Reason about the world using and updating the current knowledge.
• Autonomous robot: Integrate knowledge about the embodiment of the robot
and consider its possibilities.
• Dynamic world: Detect and observe changes in the environment as well as in
the present state of knowledge.
• Incomplete world: Identify knowledge gaps, i.e. missing information.

1.1Problem statement: modelling objects

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建模的要求：
shape
colour颜色对环境光照比较敏感，但是颜色的梯度信息A strong cue is provided by the gradients of a colour image
since colour itself strongly depends on the lighting conditions. A more suitable way is to use histograms of colour and gradients of image patches.

一个更合适的方法是使用颜色和图像块的梯度直方图。 SIFT和SURF
Physical behaviour

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系统的抓取在模型建立不完全的时候也能工作。这就暗示了模型的建立不能是一步一步的，而应该是平行建立的。

第二章 分割与重建

收敛的时候使某些距离最小。
point distance（PD）
tangent distance（TD）
squared distance （SD）