Segmentation of a Vector Field: Dominant Parameter and Shape Optimization

Abstract

Vector field segmentation methods usually belong to either of three classes: methods which segment regions homogeneous in direction and/or norm, methods which detect discontinuities in the vector field, and region growing or classification methods. The first two classes of method do not allow segmentation of complex vector fields and control of the type of fields to be segmented, respectively. The third class does not directly allow a smooth representation of the segmentation boundaries. In the particular case where the vector field actually represents an optical flow, a fourth class of methods acts as a detector of main motion. The proposed method combines a vector field model and a theoretically founded minimization approach. Compared to existing methods following the same philosophy, it relies on an intuitive, geometric way to define the model while preserving a general point of view adapted to the segmentation of potentially complex vector fields with the condition that they can be described by a finite number of parameters. The energy to be minimized is deduced from the choice of a specific class of field lines, e.g. straight lines or circles, described by the general form of their parametric equations. In that sense, the proposed method is a principled approach for segmenting parametric vector fields. The minimization problem was rewritten into a shape optimization and implemented by splinebased active contours. The algorithm was applied to the segmentation of precomputed optical flow fields given by an external, independent algorithm.

Hierarchical patch generation for multilevel statistical shape analysis by principal factor analysis decomposition

“…The PDM is able to describe the shape variability of the structure as a surface or point cloud embedded in the 3D space. Let P = {p 1 A clusterization across the surface was initially presented in [10], which was conducted for vector field segmentation of moving objects in 2D image sequences. We extend this work to unstructured 3D displacement vector fields across a surface.…”

“…Through functional minimization and the tradeoff between sparseness of the deformations and clusters size, the algorithm provides a clusterization of the 2D surface embedded in the 3D space (we emphasizes again the tailoring of this approach compared to [10]) with no preconditioning on the expected number of clusters. Our method was designed to assess the interpretability of the decompositions by PFA in conjunction with anatomical variability.…”

Local Region Descriptors for Active Contours Evolution

“…is then written as (14) and it can be interpreted similarly to the 1-D case. Only LRDs which describe the inside of the object are computed, and letting all the variables describe the object only, the energy to be minimized is changed to The energy is minimal when for each with , i.e., each pixel in the segmented object must be similar to its neighbors in the object, with similarity measured by .…”

“…Recently, many other types of information have been included in the energy functional: a vector field, as the optical flow field [14], [15], motion detection [16], [17], texture filters [17]- [19], image description by vectors of features [20], measures of shape similarity [21], [22], or the geometry of the active contour [23].…”

Segmentation of Vectorial Image Features Using Shape Gradients and Information Measures

“…Some authors choose to minimize the image differences (Jehan-Besson et al, 2002), while other consider parametric models for each region (Cremers and Soatto, 2003). Another approach consists in using the length of the motion vectors (Ranchin and Dibos, 2004) or the dominant direction (Roy et al, 2006). In this paper we are able to consider both the length and the direction of motion vectors by using the joint entropy.…”