3D Shape Modelling through a Constrained Estimation of a Bicubic B-spline Surface

This paper presents a new method to extract the 3D shape of objects from 3D gray level images using a bicubic B-spline surface model. Extraction of object shape is achieved through a hierarchical surface fitting by exploiting the multi-scale representation of the model. A strategy for converting the surface estimation into curve estimations is devised. The model surface is estimated by successively computing a set of cubic B-spline curves consisting of a coordinate curve net defining the surface. A regularising component is incorporated into the curve estimation to encourage the generation of an orthogonal coordinate curve net, preventing the creation of unwanted creases. Experimental results are presented for extracting the 3D shape of objects from real 3D images. 1 Introduction The interpretation of 3D images often needs the shape information of objects in the image. A set of unmodelled 3D structures derived from local low level operations (e.g. edge detection) [10] can hardly ever ..

Implicit meshes:unifying implicit and explicit surface representations for 3D reconstruction and tracking

This thesis proposes novel ways both to represent the static surfaces, and to parameterize their deformations. This can be used both by automated algorithms for efficient 3–D shape reconstruction, and by graphics designers for editing and animation. Deformable 3–D models can be represented either as traditional explicit surfaces, such as triangulated meshes, or as implicit surfaces. Explicit surfaces are widely accepted because they are simple to deform and render, however fitting them involves minimizing a non-differentiable distance function. By contrast, implicit surfaces allow fitting by minimizing a differentiable algebraic distance, but they are harder to meaningfully deform and render. Here we propose a method that combines the strength of both representations to avoid their drawbacks, and in this way build robust surface representation, called implicit mesh, suitable for automated shape recovery from video sequences. This surface representation lets us automatically detect and exploit silhouette constraints in uncontrolled environments that may involve occlusions and changing or cluttered backgrounds, which limit the applicability of most silhouette based methods. We advocate the use of Dirichlet Free Form Deformation (DFFD) as generic surface deformation technique that can be used to parameterize objects of arbitrary geometry defined as explicit meshes. It is based on the small set of control points and the generalized interpolant. Control points become model parameters and their change causes model's shape modification. Using such parameterization the problem dimensionality can be dramatically reduced, which is desirable property for most optimization algorithms, thus makes DFFD good tool for automated fitting. Combining DFFD as a generic parameterization method for explicit surfaces and implicit meshes as a generic surface representation we obtained a powerfull tool for automated shape recovery from images. However, we also argue that any other avaliable surface parameterization can be used. We demonstrate the applicability of our technique to 3–D reconstruction of the human upper-body including – face, neck and shoulders, and the human ear, from noisy stereo and silhouette data. We also reconstruct the shape of a high resolution human faces parametrized in terms of a Principal Component Analysis model from interest points and automatically detected silhouettes. Tracking of deformable objects using implicit meshes from silhouettes and interest points in monocular sequences is shown in following two examples: Modeling the deformations of a piece of paper represented by an ordinary triangulated mesh; tracking a person's shoulders whose deformations are expressed in terms of Dirichlet Free Form Deformations