Hiroyuki Fujioka

Optimal smoothing and interpolating splines with constraints

In this paper, we present a systematic method for designing optimal smoothing splines with equality and/or inequality constraints. The splines are constituted employing normalized uniform B-splines as the basis functions. It is shown that various types of constraints are formulated as linear function of the so-called control points, and the problems reduce to quadratic programming problems. We demonstrate the effectiveness and usefulness by numerical examples.

Constructing and reconstructing characters, words, and sentences by synthesizing writing motions

In this paper, we investigate the problem of generating and manipulating characters, words, and sentences. First, characters are obtained as the trace of the cross-sectional area between a virtual writing plane and a virtual writing device modeled by a circular cone, which is moving in a three-dimensional space. Such a motion is designed as a sum of weighted and time-shifted B-spline functions. A sequence of weight vectors called control points defines the so-called control polygon, and represents the motion and hence, a character. Characters or control polygons designed in this way are then connected in a systematic way to yield words and sentences, which again are represented as a control polygon, either small or large. Then, we consider transforming the typeface of characters or words to the omitted running styles as seen in Japanese calligraphy. Such a scheme is developed by formulating the problem as an optimal function-approximation problem, which minimizes an input energy of writing motions. Finally, a design example of cursive words is included and also the method is implemented for robotic handwriting. Thus, the paper provides a unified framework for generating and manipulating characters, words, and sentences, which are complex planar patterns, in a systematic as well as theoretically sound fashion. Although we describe the method using Japanese Kana characters, the idea and methodology for constructing and reconstructing characters and character strings is general and is not only limited to Japanese characters

OPTIMAL SMOOTHING SPLINE CURVES AND CONTOUR SYNTHESIS

Abstract We consider a problem of designing optimal smoothing spline curves using normalized uniform B-splines as basis functions. Assuming that the data for smoothing is obtained by sampling some curve with noises, an expression for optimal curves is derived when the number of data becomes infinity. It is then shown that, under certain condition, optimal smoothing splines converge to this curve as the number of data increases. The design method and analyses are extended to the case of periodic splines. Results of numerical experiments for periodic case are included for contour synthesizing problem.

Brief paper: Periodic smoothing splines

Periodic smoothing splines appear for example as generators of closed, planar curves, and in this paper they are constructed using a controlled two point boundary value problem in order to generate the desired spline function. The procedure is based on minimum norm problems in Hilbert spaces and a suitable Hilbert space is defined together with a corresponding linear affine variety that captures the constraints. The optimization is then reduced to the computationally stable problem of finding the point in the constraint variety closest to the data points.

Optimal smoothing spline with constraints on its derivatives

This paper considers the problem of designing optimal smoothing spline with constraints on its derivatives. The splines of degree k are constituted by employing normalized uniform B-splines as the basis functions. We then show that the l-th derivative of the spline can be obtained by using B-splines of degree k-l with the control points computed as l-th difference of original control points. This yields systematic treatment of equality and inequality constraints over intervals on derivatives of arbitrary degree. Also, pointwise constraints can readily be incorporated. The problem of optimal smoothing splines with constraints reduce to convex quadratic programming problems. The effectiveness is demonstrated by numerical examples of approximations of probability distribution function and concave function, and trajectory planning with the constraints on velocity and acceleration.

Recovering drawing order of single-stroke handwritten images using probabilistic tabu search

The function of the comparing fingerprints algorithm was to judge whether a new partitioned data chunk was in a storage system a decade ago. At present, in the most de-duplication backup system the fingerprints of the big data chunks are huge and cannot be stored in the memory completely. The performance of the system is unavoidably retarded by data chunks accessing the storage system at the querying stage. Accordingly, a new query mechanism namely Two-stage Bloom Filter (TBF) mechanism is proposed. Firstly, as a representation of the entirety for the first grade bloom filter, each bit of the second grade bloom filter in the TBF represents the chunks having the identical fingerprints reducing the rate of false positives. Secondly, a two-dimensional list is built corresponding to the two grade bloom filter for the absolute addresses of the data chunks with the identical fingerprints. Finally, a new hash function class with the strong global random characteristic is set up according to the data fingerprints’ random characteristics. To reduce the comparing data greatly, TBF decreases the number of accessing disks, improves the speed of detecting the redundant data chunks, and reduces the rate of false positives which helps the improvement of the overall performance of system.

Periodic Smoothing Spline Surface and Its Application to Dynamic Contour Modeling of Wet Material Objects

This paper considers a problem of optimal design of periodic smoothing spline surfaces employing normalized uniform B-splines as the basis functions. The surface can be periodic in either of two variables or in both. The expressions for optimal solutions are concise and are readily solved numerically. These periodic surfaces can be used to construct closed or semiclosed surfaces in the 3-D space. Assuming that the data are obtained by sampling some surface with noises, we present convergent properties of optimal spline surface when the number of data becomes infinity. The results are applied to the problem of modeling contour of wet material objects with deforming motion. The effectiveness is examined by numerical and experimental studies.

Optimal Smoothing Splines for Detecting Extrema from Observational Data

In this paper, we present a method for detecting and computing the extrema from observational data by using spline curves. First, we approximate a given set of discrete data by designing optimal smoothing spline curves using normalized uniform B-splines as the basis functions. Then, we show the method for detecting and computing all the extrema of designed splines and/or of its first derivative. Here, utilizing the fact that splines are continuously differentiable piecewise polynomials, we only need to detect and compute the extrema of the polynomial and its first derivative in turn for each interval between the knot points. This process is easily carried out since the polynomial in each interval is characterized by a few control points. Finally we verified the validities by numerical experiments. In particular, the detection and computation of the extrema of the first derivative are used for edge detection in digital images.

3D analysis of contact in peg-hole insertion

Contact types of chamfered cylindrical peg and cylindrical hole are analyzed in three dimensional space heading for the task understanding of insertion of the peg into the hole. Considering deviation and tilt angle of the center axis of the peg to center axis of the hole as parameters, relationships between the contact types and the parameters are investigated and a region map of the contact types in the parameter space is shown. These results are a basis for force analysis of the insertion operation.

Vector optimal smoothing spline curves with constraints

In this paper, we consider the problem of designing optimal smoothing vectorized spline curves with equality and/or inequality constraints. The constraints include cross-coupled constraints among the element curves. The splines are constituted employing normalized uniform B-splines as the basis functions. Then various types of constraints are formulated as linear function of the so-called control points, and the problem is reduced to convex quadratic programming problem. The performance is examined by some numerical examples.