Combinatorial Boundary Tracking of a 3D Lattice Point Set

Boundary tracking and surface generation are ones of main topological topics for three-dimensional digital image analysis. However, there is no adequate theory to make relations between these different topological properties in a completely discrete way. In this paper, we present a new boundary tracking algorithm which gives not only a set of border points but also the surface structures by using the concepts of combinatorial/algebraic topologies. We also show that our boundary becomes a triangulation of border points (in the sense of general topology), that is, we clarify relations between border points and their surface structures

不完全投影からの画像再構成の研究

金沢大学工学部研究課題/領域番号:61750325, 研究期間(年度):1986出典：研究課題「不完全投影からの画像再構成の研究」課題番号61750325（KAKEN：科学研究費助成事業データベース（国立情報学研究所）） （https://kaken.nii.ac.jp/ja/grant/KAKENHI-PROJECT-61750325/）を加工して作

回転する三次元画像の投影からの再構成に関する研究

金沢大学工学部研究課題/領域番号:63750346, 研究期間(年度):1988出典：研究課題「回転する三次元画像の投影からの再構成に関する研究」課題番号63750346（KAKEN：科学研究費助成事業データベース（国立情報学研究所）） （https://kaken.nii.ac.jp/ja/grant/KAKENHI-PROJECT-63750346/）を加工して作

不完全投影からの三次元画像直接再構成に関する研究

金沢大学工学部研究課題/領域番号:62750313, 研究期間(年度):1987出典：研究課題「不完全投影からの三次元画像直接再構成に関する研究」課題番号62750313（KAKEN：科学研究費助成事業データベース（国立情報学研究所）） （https://kaken.nii.ac.jp/ja/grant/KAKENHI-PROJECT-62750313/）を加工して作

RI放射線からの3次元画像直接再構成に関する研究

金沢大学工学部研究課題/領域番号:01750325, 研究期間(年度):1989出典：研究課題「RI放射線からの3次元画像直接再構成に関する研究」課題番号01750325（KAKEN：科学研究費助成事業データベース（国立情報学研究所）） （https://kaken.nii.ac.jp/ja/grant/KAKENHI-PROJECT-01750325/）を加工して作

Image hierarchy in gaussian scale space

We investigate the topological structure of an image and the hierarchical relationship between local and global structures provided by spatial gradients at different levels of scale in the Gaussian scale space. The gradient field curves link stationary points of an image, including a local minimum at infinity, and construct the topological structure of the image. The evolution of the topological structure with respect to scale is analyzed using pseudograph representation. The hierarchical relationships among the structures at different scales are expressed as trajectories of the stationary points in the scale space, which we call the stationary curves. Each top point of the local extremum curve generically has a specific gradient field curve, which we call the antidirectional figure-flow curve. The antidirectional figure-flow curve connects the top-point and another local extremum to which the toppoint is subordinate. A point at infinity can also be connected to the top points of local minimum curves. These hierarchical relationships among the stationary points are expressed as a tree. This tree expresses a hierarchical structure of dominant parts. We clarify the graphical grammar for the construction of this tree in the Gaussian scale space. Furthermore, we show a combinatorial structure of singular points in the Gaussian scale space using conformal mapping from Euclidean space to the spherical surface. We define segment edges as a zero-crossing set in the Gaussian scale space using the singular points. An image in the Gaussian scale space is the convolution of the image and the Gaussian kernel. The Gaussian kernel of an appropriate variance is a typical presmoothing operator for segmentation. The variance is heuristically selected using statistics of images such as the noise distribution in images. The variance of the kernel is determined using the singular-point configuration in the Gaussian scale space, since singular points in the Gaussian scale space allow the extraction of the dominant parts of an image. This scale-selection strategy derives the hierarchical structure of the segments. Unsupervised segmentation methods, however, have difficulty in distinguishing valid segments associated with the objects from invalid random segments due to noise. By showing that the number of invalid segments monotonically decreases with increasing scale, we characterize the valid and invalid segments in the Gaussian scale space. This property allows us to identify the valid segments from coarse to fine and does us to prevent undersegmentation and oversegmentation. Finally, we develop principal component analysis (PCA) of a point cloud on the basis of the scale-space representation of its probability density function. We explain the geometric features of a point cloud in the Gaussian scale space and observe reduced dimensionality with respect to the loss of information. Furthermore, we introduce a hierarchical clustering of the point cloud and analyze the statistical significance of the clusters and their subspaces. Moreover, we present a mathematical framework of the scale-based PCA, which derives a statistically reasonable criterion for choosing the number of components to retain or reduce the dimensionality of a point cloud. Finally, we also develop a segmentation algorithm using configurations of singular points in the Gaussian scale space

Navigation of Nonholonomic Mobile Robot Using Visual Potential Field

In this paper, we develop an algorithm for the navigation of a nonholonomic mobile robot using the visual potential. The robot is equipped with a camera system which dynamically captures the environment. The visual potential is computed from an image sequence and optical flow computed from successive images captured by the camera mounted on the robot. Our robot selects a local pathway using the visual potential computed from its vision system without any knowledge of a robot workspace. We present experimental results of the obstacle avoidance in the real environment

Discrete Polyhedrization of a Lattice Point Set

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