*Forma,* Vol. 6 (No. 2), pp. 147-169, 1991

*Original Paper*

## Representation Method of Form

Yoshio Shimizu^{1}, Takao Furukawa^{1}, Shouichi Maeda^{1}, Atsuo Konda^{1}, Kazuaki Daiyasu^{1}, and Hiroko Shimizu^{2}

^{1}Faculty of Textile Science and Technology, Shinshu University, Ueda 386, Japan

^{2}Faculty of Education, Utsunomiya University, Utsunomiya 321, Japan

(Received January 20, 1991; Accepted February 12, 1991)

**Keywords: **
Form Representation, Form Composition, Form Clustering, Form Aesthetic, Neural Network, *N*-Dimensional Outline Form

**Abstract. **
This paper describes methods of a representation, a composition, a clustering, and an aesthetic estimation for a form. The form is represented by a planer curve. Any planer curve can be defined by the set of {*W*(*j*)}. {*W*(*j*)} is represented by a point series on the cylinder surface where the bottom is a unit circle on a complex number plane. The composite curve of plural curves defined as the linear combination of *C*_{a},(*k*) which is the Fourier coefficients of curve *a*. Some composite examples are shown for human body silhouettes or other simple figures. UESAKA's *N*-dimensional body outlines were used in cluster analysis and factor analysis. By means of squared Euclidian distances of power spectrums or Fourier coefficients, the cluster analysis of human body forms were done. For 64dimensional body outlines, the results of the cluster analysis differ from the subjective classification.. For 3-dimensional body outlines, the cluster analysis results agree with the subjective's. Several factors were extracted from the factor analysis of human body forms. In order to estimate aesthetic evaluation of forms automatically, a neural network system was used. Birkhoff's 90 forms were used as learning samples. Power spectrums of Birkhoff's forms were input into the neural system. After learning, this system could evaluate the aesthetic estimation of an arbitrary form.