Research

Yukie Nagai, Yutaka Ohtake and Hiromasa Suzuki
Computer Graphics Forum, Vol. 28, No. 5. 2009.
(Eurographics Symposium on Geometry Processing 2009)

We propose a novel method for smoothing partition of unity (PU) implicit surfaces consisting of sets of nonconforming linear functions with spherical supports. We derive new discrete differential operators and Laplacian smoothing using a spherical covering of PU as a grid-like data structure. These new differential operators are applied to the smoothing of PU implicit surfaces. First, Laplacian smoothing is performed for the vector field defined by the gradient of the PU implicit surface, which is then updated to reflect the smoothing of the gradient field. This process achieves a method for noise robust surface reconstruction from scattered points.

Yukie Nagai, Yutaka Ohtake, Hiromasa Suzuki, and Hideo Yokota
Geometric Computing Workshop on Asian Conference on Design and Digital Engineering, GC-2-3,
(Jeju, Korea, 25--28 August, 2010), pp. 454-460, 2010.

In this paper, we propose an algorithm for outlier/noise-robust surface reconstruction based on a partition of unity (PU) approach. PU based surface reconstruction is a local method that covers an area including sampling points with spherical supports of local approximations, and then generates an approximation function whose zero-level sets approximate the surface. This algorithm has many advantages including representation of fine details, and fast and memory efficient computation. Many of these advantages are realized with the locality of PU however, it is also the reason of outlier/noise-instabilities. Unfortunately, scanned data generally contain much amount of noise, and hence improving the robustness of PU based algorithm is required. We achieve an outlier/noise-robust algorithm with integrating Graph-cut and diffusion of local approximations. Since the characteristics of outliers and noise are fundamentally different, overcoming these two with different approaches is reasonable. In our algorithm, first a spherical cover of an area containing input points is generated following the PU manner. And then Graph-cut is performed in order to determine spherical supports which are considered wrongly approximating affected by outliers. Finally, the PU approximation function is updated so that its gradient field smoothed. This smoothing is based on a diffusion of the local approximations. In this paper we show the effects of this integration approach for several scanned data sets.

Yukie Nagai, Yutaka Ohtake and Hiromasa Suzuki
Eurographics 2009 (Short paper), 2009

We present a novel method of reconstructing surfaces from 3D scattered points by combining Partition of Unity (PU) and a Graph-cut approach. PU is a local approximation technique, meaning that the surfaces obtained have high accuracy but are sensitive to noise. Graph-cut, on the other hand, is a global algorithm that is robust to noise but produces low-accuracy results because it is a discrete binary operation. Our algorithm combines these two methods to achieve robust, high accuracy surface reconstruction. First, a PU implicit function is constructed by covering a space containing a point cloud with spherical supports of linear polynomials. Graph-cut is then performed to separate the covered domain into inside and outside areas of the object to be reconstructed. Finally, we extract the zero-level of PU using the marching tetrahedra approach.

Yukie Nagai, Yutaka Ohtake, Kiwamu Kase and Hiromasa Suzuki
CGA'08 (8th Annual International Workshop on Computational Geometry and Applications), 2008

The skeletal structures of solid objects play an important role in medical and industrial applications. Given a volumetrically sampled solid object, our method extracts a well-connected and not-fragmented skeletal structure represented as a polygon mesh. The purpose is to achieve a noise-robust extraction of the skeletal mesh from a realworld object obtained using a scanning technology such as the CT scan method. We first approximate the input image intensity through a set of spherically supported polynomials that provide an adaptively smoothed intensity field, and then perform a polygonization process to find the extremal sheet of the field, which is regarded as a skeletal sheet in this research. In our polygonization, a subset of the weighted Delaunay tetrahedrization defined by a set of spherical supports is used as an adaptively sampled grid. The derivatives for detecting extremality are analytically evaluated at the tetrahedron vertices. We also demonstrate the effectiveness of our method by extracting skeletal meshes from noisy CT images.

Yukie Nagai, Yutaka Ohtake, Kiwamu Kase and Hiromasa Suzuki
SMI'08 (Shape Modeling International) (Poster), 2008

The skeletal structures of solid objects play an important role in medical and industrial applications. Given a volumetrically sampled solid object, our method extracts a nice-looking skeletal structure represented as a polygon mesh. The purpose is to achieve a noise-robust extraction of the skeletal mesh from a real-world object obtained using a scanning technology such as the CT scan method. We first approximate the input through a set of spherically supported polynomials that provide an adaptively smoothed intensity field, and then perform a polygonization process to find the extremal sheet of the field, which is regarded as a skeletal sheet in this research. In our polygonization, a subset of the weighted Delaunay tetrahedrization defined by a set of spherical supports is used as an adaptively sampled grid. The derivatives for detecting extremality are analytically evaluated at the tetrahedron vertices. We also demonstrate the effectiveness of our method by extracting skeletal meshes from noisy CT images.