Object Modeling in Multiple-Object 3D Scene Using Deformable Simplex Meshes

Research Objectives
The objective of this research is to model multiple objects in a scene using deformable simplex meshes. This method aims at building a new description of the scene for the ultimate purpose of object recognition. The primary emphasis of the research is on breaking the deformable model into multiple pieces when multiple objects compose the scene. Deformable simplex meshes can accurately fit a cloud of 3D points. In addition, simplex meshes are topologically flexible: their number of genus and holes can be modified at any step of their deformation. As these meshes are implicit models with no parameterization, they can take any shape. Simplex meshes are also computationally inexpensive because their deformation is based on simple, local geometric entities. At the end of deformation, there will be a model for each object in the scene.

Methodology
The modeling process begins by encapsulating the entire scene with a single simplex mesh that is then deformed to fit the 3D data points. To initiate the process, a mesh encapsulating the cloud of points is built. Once the initial mesh is constructed, the deformation begins by shrinking the mesh. If a vertex encounters a data point, no further deformation is applied at that point. During this process, the linkage between vertices is modeled as a spring with a maximum length change. When the shrinking stops, the deformation continues by following the equation of motion that calculates the new position of each vertex based on internal and external forces. The internal force deforms the mesh so that a regular shape is taken. The external force pushes the vertices close to the 3D data points. Once the deformation stops, a refinement process is initiated. This process concentrates the vertices in areas of high curvature and changes the topology of the mesh if necessary. After the refinement is completed, a breaking process enables the mesh to split into multiple meshes, one for each object in the scene. To achieve the breaking process, arcs in the mesh are modeled as springs and links are removed when spring tensions exceed a threshold. The breaking process is controlled by heuristics to prevent breaking when high spring tensions are computed on edges of the same object. In addition to modeling, this entire process also effectively segments the scene. The models obtained with this approach will be examined and compared with those obtained from other meshes.

This work was conducted at the IRIS lab by Ernesto Juarez under the supervision of C. Dumont and M. A. Abidi (Thesis Chair). This work was supported by DOE's University Research Program in Robotics under grant DOE-DE-FG02-86NE37968.