Yukie Nagai, Yutaka Ohtake and Hiromasa Suzuki,
Computers & Graphics Special Issue on Shape Modeling International (short paper),
Vol. 46, February 2015, pp.55–63, 2014.

Inspired by computed tomography (CT), this paper presents a novel surface reconstruction algorithm, {\em tomographic surface reconstruction}, to reconstruct a surface mesh from a point cloud equipped with oriented normals. In the process of scanning a real object using an X-ray CT system, it generates a sinogram consisting of projection images that are maps of X-ray transmission lengths, and then, a tomogram (CT volume) is reconstructed from the sinogram. A hole-free surface mesh is then easily obtained by polygonizing an isosurface. To adopt this CT paradigm to surface reconstruction from a point cloud, only a scheme to generate a sinogram from a point cloud is required. The value of a sinogram for surface reconstruction can be defined as the sum of the distances between the intersecting points of a ray and the underlying surface, which are defined as the maxima of the point density. While ordinary CT scanning uses projection directions which share a single rotation axis, tomographic surface reconstruction adopts randomly selected projection directions and successfully improved the reconstruction robustness. By applying an iterative CT reconstruction to the sinogram, the algorithm generates a tomogram whose boundary between the foreground and background approximates the surface of the object. The effectiveness for a point cloud with a lack of sampling and outliers is demonstrated from experimental results.

Yukie Nagai, Yutaka Ohtake, Hideo Yokota and Hiromasa Suzuki
Science China Information Sciences, Vol. 56, No. 11. 2013.

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.

Mitsuru Negishi, Yutaka Ohtake, Hiromasa Suzuki, Yukie Nagai
In Proceedings of the 6th Conference on Industrial Computed Tomography (iCT2016), 9-12 February, Wels, Austria, 2016

Seungki Kim, Akitsune Sakane, Yutaka Ohtake, Hiromasa Suzuki, Yukie Nagai, Katsutoshi Satoh, Hiroyuki Fujimoto, Makoto Abe, Osamu Satoh, Toshiyuki Takatsuji
In Proceedings of the 6th Conference on Industrial Computed Tomography (iCT2016), 9-12 February, Wels, Austria, 2016

S. Kondo, H. Suzuki, Y. Ohtake, Y. Nagai, H. Hishida, K. Inagaki, T. Nakamura, F. Watanabe
Digital Industrial Radiology and Computed Tomography (DIR 2015), 22-25 June 2015, Belgium, Ghent, 2015

Deepak Keshwani, Hiromasa Suzuki, Ohtake Yutaka, Yukie Nagai
DE-ll-l, P.42, Proc. Asian Conference on Design and Digital Engineering, Shandong, China, 2014, Oct. 31st - Nov.2nd, 2014

Takashi Seno, Yutaka Ohtake, Yuji Kikuchi, Noriaki Saito, Suzuki Hiromasa, Nagai Yukie
DE-ll-3, P. 47, Proc. Asian Conference on Design and Digital Engineering, Shandong, China, 2014, Oct. 31st - Nov.2nd, 2014

Kotaro Morioka, Yutaka Ohtake, Hiromasa Suzuki, Yukie Nagai, Hiroyuki Hishida, Koichi Inagaki, Takeshi Nakamura, Fumiaki Watanabe
Materials, DE-ll-2, P. 06, Proc. Asian Conference on Design and Digital Engineering, Shandong, China, 2014, Oct. 31st - Nov.2nd, 2014

Trung Vuong Pham, Yutaka Ohtake, Yukie Nagai, Hiromasa Suzuki
11th IMEKO Symposium LMPMI 2014 (Laser Metrology for Precision Measurement and Inspection in Industry),
B10, Sept. 2-5, 2014, Tsukuba

Ryo Jinnouchi, Yutaka Ohtake, Hiromasa Suzuki, Yukie Nagai
in Proc. Conference on Industrial Computed Tomography (iCT 2014),
Poster Presentation, Shaker Verlag ISBN 978-3-8440-2557-6, pp.439-446 (2014).

S. Flöry, Y. Nagai, F. Isvoranu, H.Pottmann and J.Wallner
Advances in Architectural Geometry 2012, Springer Verlag,
2012.

Yukie Nagai, Yutaka Ohtake, Hideo Yokota, and Hiromasa Suzuki
Geometric Computing and CAD Workshop on Asian Conference on Design and Digital Engineering,
2012.

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.