**Abstract**

[Japanese |
Thesis |
Researches in Minoh Lab |
Minoh Lab]

This paper discusses the modeling of a cloth that gives both visual and haptic information to the user for manipulating the cloth in virtual world. The reproduction of human sensing in virtual world created by a computer is one of the main problems for manipulation of virtual object. Although most of the previous work on this problem has focused on rigid objects, it is also important to deal with flexible objects like a cloth. This paper focuses on reproduction of visual and haptic information of a cloth manipulated it in the virtual world.

In the field of computer graphics, many methods for modeling and visualizing a cloth's shape has been proposed. Those methods employ many parameters to represent deformation of a cloth. The most famous example is the spring-model, which is constituted by points with mass connected with each other with springs. Successful reproduction of a real cloth using this model depends on the value of each parameter of the model; the parameters have to be adjusted so that they achieve optimal visual appearance of the cloth. However, manual adjustment of the model parameters is a troublesome work. It has been also proposed to set the model parameters based on measurements of physical properties of real clothes, for stretching, bending shearing and so on. But this measurement require special devices.

In this paper, we aim at estimating the optimal value for the model parameters that reproduces the visual and haptic information given by a real cloth during manipulation by observing it.

The value of each model parameter is adjusted so that the difference between the model and the observed real object in their visual and haptic information is minimized. Our method employs spring-model of square mesh as a simulated cloth. We observe the strain from the cloth at manipulation point as the haptic information and resulting change of shape as the visual information. The parameters are estimated through the observation by minimizing of the evaluation function, which evaluates the difference of the model from the result of actual observation.

In this method, we assume that the observation of a real cloth is continued until the values of the model parameters estimated from visual and haptic information obtained through the observation properly reproduce the visual and haptic information. In this observation, the visual and haptic information is not obtained at once but step by step. Since the evaluation function to be minimized is constituted from the observed visual and haptic information, the evaluation function is not fixed but changes in the process of the observation.

The steepest descent gradient algorithm, which is one of the most common methods to minimize non-linear evaluation function, can not be used to minimize our evaluation function because it changes during observation. Instead, we employ the genetic algorithm (GA) for minimizing our evaluation function. Since the GA is a probabilistic multi-point searching algorithm, the final solution does not depend on the initial condition, and search of an optimal solution can be continual by using the result of search in the previous step, even when the evaluation function is to change in the process of the search. In the conventional GA, each point of the search space is represented by a sequence of binary numbers and it limits the possibility of applying GA to various searching problem. Recently,$B!!(Bthe real-coded GA, which represents each search point by a real vector, and has been proposed. We employ this real-coded GA for minimizing our evaluation function.

We evaluated our method by two kinds of experiments. First we estimate model parameters from the simulated data including visual and haptic information. Second, we employed visual information obtained by observation of a real cloth. In both experiments, the estimated parameters of the model sufficiently reproduced the visual and haptic information. In those experiments we also confirmed that the parameters to minimize the evaluation function is properly searched by the real value GA even when the function dynamically changes.

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