The optimum surface-fitting method for binary images is extended in order to treat gray images, and a new method to extract edges in three-dimensional gray images is proposed. If voxels that have similar values to the voxel of interest (VOI) are distributed like a two-dimensional curved surface, it is thought that there would be a curved surface at the VOI. To apply the fitting method to gray i...

When designing curves on surfaces the need arises to approximate a given noisy target shape by a smooth fitting shape. We discuss the problem of fitting a B-spline curve to a point cloud by squared distance minimization in the case that both, the point cloud and the fitting curve, are constrained to lie on a smooth manifold. The on-manifold constraint is included by using the first fundamental ...

Although, most of the abnormal structures of human brain do not alter the shape of outer envelope of brain (surface), some abnormalities can deform the surface extensively. However, this may be a major problem in a surface-based registration technique, since two nearly identical surfaces are required for surface fitting process. A type of verification known as the circularity check for th...

Implicit planar curve and surface fitting to a set of scattered points plays an important role in solving a wide variety of problems occurring in computer graphics modelling, computer graphics animation, and computer assisted surgery. The fitted implicit surfaces can be either algebraic or non-algebraic. The main problem with most algebraic surface fitting algorithms is that the surface fitted ...

This paper presents a robust and efficient surface flattening approach based on fitting a woven-like mesh model on a 3D freeform surface. The fitting algorithm is based on tendon node mapping (TNM) and diagonal node mapping (DNM), where TNM determines the position of a new node on the surface along the warp or weft direction and DNM locates a node along the diagonal direction. During the 3D fit...

A new implicit surface fitting method for surface reconstruction from scattered point data is proposed. The method combines an adaptive partition of unity approximation with least-squares RBF fitting and is capable of generating a high quality surface reconstruction. Given a set of points scattered over a smooth surface, first a sparse set of overlapped local approximations is constructed. The ...