Tracking of Features and Edges

Joint Tracking of Features and Edges

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.

巴特西