NOTE 1003

Motion Segmentation via Robust Subspace Separation in the Presence of Outlying, Incomplete, or Corrupted Trajectories (CVPR08) 和 compressive sensing 有关
motion segmentation problem: given a set of feature points that are tracked through a sequence of video frames, one seeks to cluster the trajectories of those points according to different motions.
Basic Formulation based on affine camera model: Y=AX
Y 为视频中 tracked feature points 的坐标，2FxP (F points, 因为图像为2D，故为 2F，P frames)，X 为真实物体的 3D 坐标，4xP (affine 扩展一维)，A 为 affine motion matrix，2Fx4
Rank(Y) <= 4
Thus the affine camera model postulates that trajectories of feature points from a single rigid motion will all lie in a
linear subspace of R2F of dimension at most four.
对于多个物体，不知道point和物体的对应关系，但是假设属于同一个物体的点的轨迹位于一个 subspace，故有 subspace separation.

 SPARSE REPRESENTATION FOR COLOR IMAGE RESTORATION

是有学习过程的，字典的学习通过 LabelMe 图像的Patches，学习patch大小不同的字典。再用这个字典去做denoise, inpainting

这儿的 inpainting 不能处理连续的一块图像丢失的情况，只能是 small holes of color images,

We now evaluate our extension for color images. We trained some dictionaries
with different sizes of atoms 5 × 5 × 3, 6 × 6 × 3, 7 × 7 × 3 and 8 × 8 × 3, on 200000 patches
taken from a database of 15000 images with the patch-sparsity parameter L = 6 (6 atoms in the
representations). We used the database LabelMe, [50], to build our image database Then we
trained each dictionary with 600 iterations. This provided us a set of generic dictionaries that we
used as initial dictionaries in our denoising algorithm.