Atsushi Imiya

Structural, Syntactic, and Statistical Pattern Recognition

Peer-to-Peer (P2P) lending is an online platform to facilitate borrowing and investment transactions. A central problem for these P2P platforms is how to identify the most influential factors that are closely related to the credit risks. This problem is inherently complex due to the various forms of risks and the numerous influencing factors involved. Moreover, raw data of P2P lending are often high-dimension, highly correlated and unstable, making the problem more untractable by traditional statistical and machine learning approaches. To address these problems, we develop a novel filter-based feature selection method for P2P lending analysis. Unlike most traditional feature selection methods that use vectorial features, the proposed method is based on graphbased features and thus incorporates the relationships between pairwise feature samples into the feature selection process. Since the graph-based features are by nature completed weighted graphs, we use the steady state random walk to encapsulate the main characteristics of the graphbased features. Specifically, we compute a probability distribution of the walk visiting the vertices. Furthermore, we measure the discriminant power of each graph-based feature with respect to the target feature, through the Jensen-Shannon divergence measure between the probability distributions from the random walks. We select an optimal subset of features based on the most relevant graph-based features, through the Jensen-Shannon divergence measure. Unlike most existing state-of-theart feature selection methods, the proposed method can accommodate both continuous and discrete target features. Experiments demonstrate the effectiveness and usefulness of the proposed feature selection algorithm on the problem of P2P lending platforms in China.

Linear Scale-Space has First been Proposed in Japan

Linear scale-space is considered to be a modern bottom-up tool in computer vision. The American and European vision community, however, is unaware of the fact that it has already been axiomatically derived in 1959 in a Japanese paper by Taizo Iijima. This result formed the starting point of vast linear scale-space research in Japan ranging from various axiomatic derivations over deep structure analysis to applications to optical character recognition. Since the outcomes of these activities are unknown to western scale-space researchers, we give an overview of the contribution to the development of linear scale-space theories and analyses. In particular, we review four Japanese axiomatic approaches that substantiate linear scale-space theories proposed between 1959 and 1981. By juxtaposing them to ten American or European axiomatics, we present an overview of the state-of-the-art in Gaussian scale-space axiomatics. Furthermore, we show that many techniques for analysing linear scale-space have also been pioneered by Japanese researchers.

On the History of Gaussian Scale-Space Axiomatics

A rapidly increasing number of publications, workshops and conferences which are devoted to scale-space ideas confirms the impression that the scale-space paradigm belongs to the challenging new topics in computer vision.

Digital and Image Geometry

In a series of papers the authors have developed an approach to Digital Topology, which is based on a multilevel architecture. One of the foundations of this approach is an axiomatic definition of the notion of digital space. In this paper we relate this approach with several other approaches to Digital Topology appeared in literature through a deep analysis of the axioms involved in the definition of digital space.

Dominant plane detection from optical flow for robot navigation

Dominant plane is an area which occupies the largest domain in the image. In this paper, we develop an algorithm for dominant plane detection using the optical flow. The dominant plane estimation is an essential task for the autonomous navigation and the path planning of the mobile robot, since the robot moves on the dominant plane. We show that the points on the dominant plane in a pair of two successive images are combined with an affine transformation if the mobile robot obtains successive images for optical flow computation. Therefore, our algorithm detects the dominant plane from images observed by an uncalibrated camera without any assumptions of camera displacement.

Fast Spectral Clustering with Random Projection and Sampling

This paper proposes a fast spectral clustering method for large-scale data. In the present method, random projection and random sampling techniques are adopted for reducing the data dimensionality and cardinality. The computation time of the present method is quasi-linear with respect to the data cardinality. The clustering result can be updated with a small computational cost when data samples or random samples are appended or removed.

Marching cubes method with connectivity

In this paper, we solve the topological problem of isosurfaces generated by the marching cubes method using the approach of combinatorial topology. For each marching cube, we examine the connectivity of polyhedral configuration in the sense of combinatorial topology. For the cubes where the connectivities are not considered, we modify the polyhedral configurations with the connectivity and construct polyhedral isosurfaces with the correct topologies.

The randomized-Hough-transform-based method for great-circle detection on sphere

We propose a randomized-Hough-transform-based method for the detection of great circles on a sphere. We first define transformations from images acquired by central cameras to images on the unit sphere, that is, spherical images. Using the transformations, it is possible to normalize all central-camera images to the spherical image. Therefore, spherical image analysis is a fundamental study for image analysis of central cameras. For geometrical analysis and reconstruction of a three-dimensional space from spherical images, great circles on a sphere are an essential feature since a great circle on a sphere corresponds to a line on a plane in a space. For great-circle detection, we formulate the randomized Hough transform on the basis of the geometric duality of a point and a great circle on a sphere. Finally, as an extension of the randomized Hough transform on a sphere, we propose a method for great-circle detection using a continuous spherical Hough space.

Regularity and scale-space properties of fractional high order linear filtering

We investigate the use of fractional powers of the Laplacian for signal and image simplification. We focus both on their corresponding variational techniques and parabolic pseudodifferential equations. We perform a detailed study of the regularisation properties of energy functionals, where the smoothness term consists of various linear combinations of fractional derivatives. The associated parabolic pseudodifferential equations with constant coefficients are providing the link to linear scale-space theory. These encompass the well-known α-scale-spaces, even those with parameter values α > 1 known to violate common maximum-minimum principles. Nevertheless, we show that it is possible to construct positivity-preserving combinations of high and low-order filters. Numerical experiments in this direction indicate that non-integral orders play an essential role in this construction. The paper reveals the close relation between continuous and semi-discrete filters, and by that helps to facilitate efficient implementations. In additional numerical experiments we compare the variance decay rates for white noise and edge signals through the action of different filter classes.

The Euler Characteristics of Discrete Objects and Discrete Quasi-Objects

Assuming planar 4-connectivity and spatial 6-connectivity, we first introduce the curvature indices of the boundary of a discrete object, and, using these indices of points, we define the vertex angles of discrete surfaces as an extension of the chain codes of digital curves. Second, we prove the relation between the number of point indices and the numbers of holes, genus, and cavities of an object. This is the angular Euler characteristic of a discrete object. Third, we define quasi-objects as the connected simplexes. Geometric relations between discrete quasi-objects and discrete objects permit us to define the Euler characteristic for the planar 8-connected, and the spatial 18- and 26-connected objects using these for the planar 4-connected and the spatial 6-connected objects. Our results show that the planar 4-connectivity and the spatial 6-connectivity define the Euler characteristics of point sets in a discrete space. Finally, we develop an algorithm for the computation of these characteristics of discrete objects.