You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
In this paper, we propose a new framework for segmenting feature-based moving objects under affine subspace model. Since the feature trajectories in practice are high-dimensional and contain a lot of noise, we firstly apply the sparse PCA to represent the original trajectories with a low-dimensional global subspace, which consists of the orthogonal sparse principal vectors. Subsequently, the local subspace separation will be achieved via automatically searching the sparse representation of the nearest neighbors for each projected data. In order to refine the local subspace estimation result and deal with the missing data problem, we propose an error estimation to encourage the projected data that span a same local subspace to be clustered together. In the end, the segmentation of different motions is achieved through the spectral clustering on an affinity matrix, which is constructed with both the error estimation and sparse neighbors optimization. We test our method extensively and compare it with state-of-the-art methods on the Hopkins 155 dataset and Freiburg-Berkeley Motion Segmentation dataset. The results show that our method is comparable with the other motion segmentation methods, and in many cases exceed them in terms of precision and computation time.

Cited Abstract(s):
[1]: We present an approach for motion segmentation using independently detected keypoints instead of commonly used tracklets or trajectories. This allows us to establish correspondences over non- consecutive frames, thus we are able to handle multiple object occlusions consistently. On a frame-to-frame level, we extend the classical split-and-merge algorithm for fast and precise motion segmentation. Globally, we cluster multiple of these segmentations of different time scales with an accurate estimation of the number of motions. On the standard benchmarks, our approach performs best in comparison to all algorithms which are able to handle unconstrained missing data. We further show that it works on benchmark data with more than 98 of the input data missing. Finally, the performance is evaluated on a mobile-phone-recorded sequence with multiple objects occluded at the same time.

[2]: This paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point. When the number of subspaces is known, we show that these polynomials can be estimated linearly from data; hence, subspace segmentation is reduced to classifying one point per subspace. We select these points optimally from the data set by minimizing certain distance function, thus dealing automatically with moderate noise in the data. A basis for the complement of each subspace is then recovered by applying standard PCA to the collection of derivatives (normal vectors). Extensions of GPCA that deal with data in a high-dimensional space and with an unknown number of subspaces are also presented. Our experiments on low-dimensional data show that GPCA outperforms existing algebraic algorithms based on polynomial factorization and provides a good initialization to iterative techniques such as k-subspaces and expectation maximization. We also present applications of GPCA to computer vision problems such as face clustering, temporal video segmentation, and 3D motion segmentation from point correspondences in multiple affine views.
[2] uses the distances of each pair of feature trajectories as the measurement to build the affinity matrix based on a translational motion model. This method can segment motions with unlimited number of missing or incomplete trajectories, which means they are robust to the video with occlusions or moving camera problems. Another approach which is based on the affinity is called Multi-scale Clustering for Motion Segmentation (MSMC) [1] . Based on the conventional image classification technique split and merge, they use the correspondences of each two features between two frames to segment the different motions with many missing data. One of the general problems of affinity-based method is highly time-consuming. They have to be implemented with an optimized platform in order to save the computation times.