图形复杂度建模与分析

A Validated Regression Model for Complexity of Polygonal Shape (to be submitted)  

Lingchen Dai, Zhejiang University, China; Xianjun Zheng, Qinghua University, China; Yina Li, Nankai University, China; Kang Zhang, University of Texas at Dallas, USA;  Ralph Martin, Cardiff University, UK; Jinhui Yu, Zhejiang University, China.

Abstract: Quantitative assessment of the visual complexity of 2D shapes is of significant interest, with applications to shape analysis, interpretation, and retrieval as well as to visual design and aesthetic evaluation. The aim is to reproduce manual assessment of visual complexity, using a model based on various contributing factors. Earlier work concentrated on suitable factors, but less well-studied is how best to combine individual factors in a model, and which to use. We propose a linear regression model of 2D shape complexity based on three new variables, edge length entropy, global shape narrowness, and circularity, together with a modified version of a previously used variable, vertex angle entropy. These variables were selected from a large number of candidates by regression analysis; analysis shows that our model can explain 92\% of the variance in manually assessed shape complexity. We take care to achieve a trade off between fitting the training data and generalization to new data by using ridge regression.