Apply GPCA to Motion Segmentation - Intelligent Video Event Analysis and Understanding - page 23

segmentation approach under a Bayesian framework by tracking edges between
frames. In the implementation of their proposed scheme, the region edge labels
were not directly applied to the Bayesian model. They were implicitly determined
by the foreground-background orders of the motion layers and the motion layer
labels for each region. Kumar et al. in [8] presented the learning approach of a
generative layered representation of a scene for motion segmentation. In order to
get the initial estimates of model, they utilized the loopy belief propagation, and
further refined the initial estimate by using αβ-swap and α-expansion algorithms.
The large number of undetermined parameters in their Bayesian models leads to
the difficult tracking problem in a high dimensional parameter space. The second
category is the dominant motion approach [9-11]. A single motion is first fitted to
all pixels, and then to test for pixels that agree with that motion. This process can
be repeated recursively on the outlier pixels to provide a full set of layers [10].
The central problem faced by this kind of approaches is that it is extremely diffi-
cult to determine the occluded edges of the moving regions (or motion layers).
Furthermore, this problem can result in the failure of depth ordering of motion
layers. However, analytically reasoning such complex cases is impractical. The
main reasons are three fold. First, the smoothing required by the optical flow algo-
rithms makes it difficult to localize the layer boundaries. Second, the optical flow
field is usually parameterized by some 2D motion models (e.g. 2D affine), which
is the first order approximation of the perspective model. It is unreliable to apply a
2D model to the boundaries of moving regions. Third, pixels in a neighborhood of
the boundaries are in the areas of high intensity gradient. Slight errors or image
noise can result in pixels of a very different intensity, even under the correct
motion estimate [6]. In this paper, we will simplify the problem of motion seg-
mentation based on an algebraic framework. We will first obtain a rough global
segmentation and then refine it afterwards.
Our work is partially inspired by the subspace segmentation approach to motion
model estimation proposed in [14]. This approach can provide a non-iterative and
global estimation of motion layer segmentation. But it is incomplete, since the
depth ordering and the detection of layer boundaries are ignored. In this paper we
provide a complete solution by developing a novel post-processing procedure
using the intensity structures of edges for the detection of (1) motion layer
boundaries and (2) the layer order.
In the remainder of this paper, we first briefly review the subspace segmenta-
tion approach to motion model estimation [14] in section 2. In section 3, a post-
processing procedure is presented for the detection of the layer boundaries and
depth ordering. The experimental results and analysis are given in section 4. Our
conclusion and future work are given in section 5.
2 Motion Segmentation by GPCA-PDA
The core of our proposed motion segmentation approach is the scheme of seg-
menting hyperplanes in R , which is called the generalized PCA (GPCA) in [12].
Applying the GPCA method to motion model estimation has been proposed in