Fujioka Lab.
Todays the spline functions have been widely used in various fields -- such as CAD, computer graphics, numerical analysis, image processing and robotics in general.
In our laboratory, we have studied various problems of optimal design of spline curves and surfaces and their applications in the fields of engineering and sciences.
A basic problem of spline curves that have been considered is to design a curve that passes through or near the given points, while the curve is smooth as much as possible.
For such a problem and its variant problems, we have developed optimal design methods as well as the computational algorithms of interpolating and smoothing spline curves, periodic and constrained splines, and analyzed properties of optimal curves such as statistical and asymptotic properties. Most of the results obtained for curves have been extended to the case of surfaces. By numerical examples, we confirmed that associated algorithm are very stable and reliable numerically.
We have applied the design method of optimal smoothing curves and surfaces to various problems. This includes constructing and reconstructing characters, human calligraphic learning, dynamic contour and movement modeling and edge detection in digital images, extrema detection of curves and surfaces, etc.