Tracking of Features and Edges
目录
Joint Tracking of Features and Edges
1. LK光流
基本LK光流
运动假设:
\[I(x+u,y+v,t+1) = I(x,y,t)
\]
一阶近似得到:
\[f(u,v,I) = I_xu+I_yv+I_t =0
\]
由于Aperture problem
,需要假设领域像素运动相同,并作为约束,便可以求解
\[E_{LK}(u,v) = K_{\rho}*(f(u,v;I))^2
\]
2. Horn-Schunck光流
\[E_{HS}(u,v) = \int _{\Omega} (f(u,v;I))^2+\lambda( |\nabla u|^2 +|\nabla v|^2)dxdy
\]
\(\lambda\)为正则项参数,相当于加了个平滑约束.
\(\nabla ^2u, \nabla ^2v\) 为\(u,v\)的拉普拉斯算子,可以近似为:
\[\nabla ^2u \approx h(\overline u - u)
\]
领域\(u\)的均值来表示.
3. Joint Tracking
\[E_{JLK} = \sum_{i=1}^N (E_D(i)+\lambda_i E_S(i))
\]
\[E_D(i) = K_{\rho}*(f(u_i,v_i;I))^2\\
E_S(i) = ((u_i-\hat{u}_i)^2+(v_i-\hat{v}_i)^2)
\]
\((\hat{u}_i,\hat{v}_i)^T\) 为期望的偏移量,可以通过任何一种方式获取.
Instead, we predict the motion displacement of a pixel by fitting an affine motion model
to the displacements of the surrounding features, which are inversely weighted according to their distance to the pixel.
We use a Gaussian weighting function on the distance, with σ = 10 pixels.
对于周围的特征拟合一个Affine变换来获取?
利用特征周围的特征点求解一个预测值:
- 直接利用领域内\((u,v)\)的平均值
特征选择:
\[max(e_{min},\eta e_{max}), \eta <1
\]
本文取: \(\eta=0.1\)
4. Unified Point-Edgelet Feature tracking
- 进一步优化,选取
Edgelet
而不是边缘的点作为track的目标 - 预测的\((\hat{u},\hat{v})\)不是平均值,而是拟合一个Affine变换获得(u,v),并且拟合变换的权重根据距离和scale进行计算
5. \(u,v\)预测值如何计算
利用领域特征的\(u,v\)取加权来进行计算获得
6. 接下来工作
这些方法的思路都是利用点和边缘来互补操作,使得二者能够互相提升各自的缺陷,接下来基本参考joint_tracking的思路,但是不取平均值,而是进行加权操作,简单尝试.
7. 参考文献
- Birchfield S T , Pundlik S J . Joint tracking of features and edges
CVPR 2008
- Sundararajan K . Unified point-edgelet feature tracking[J]. Dissertations & Theses - Gradworks, 2011.