An Adaptive Shape Description Method Based on Implicit Polynomial Curves

WU Gang

doi:10.3969/j.iss.0372-2012-2014.03.013

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An Adaptive Shape Description Method Based on Implicit Polynomial Curves

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- An Adaptive Shape Description Method Based on Implicit Polynomial Curves
- Acta Electronica Sinica Vol. 42, Issue 3, Pages: 505-511(2014)
- 作者机构：
  
  1. 南京财经大学电子商务重点实验室,江苏,南京,210003
  2. 南京财经大学电子商务重点实验室,江苏,南京,210003
- 作者简介：
- 基金信息：
- DOI：10.3969/j.iss.0372-2012-2014.03.013
  CLC： TP391.41
- Published：2014
- 稿件说明：
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WU Gang. An Adaptive Shape Description Method Based on Implicit Polynomial Curves[J]. Acta Electronica Sinica, 2014, 42(3): 505-511.
DOI：

WU Gang. An Adaptive Shape Description Method Based on Implicit Polynomial Curves[J]. Acta Electronica Sinica, 2014, 42(3): 505-511. DOI： 10.3969/j.iss.0372-2012-2014.03.013.

摘要

隐式多项式曲线对目标形状的线性描述算法需要构造隐式多项式曲线的代数残差和梯度残差，但是如何加权平衡这两种残差是一个困难问题.提出了一种平衡这两种残差的自适应权重确定算法.根据隐式多项式曲线稳定性要求，构造了隐式多项式曲线系数向量范数和权重的关系式，进而计算出极小值点并作为最优权重，实现了隐式多项式曲线的自适应描述.从MPEG-7标准测试集中选取不同形状的图形进行描述，实验结果表明，根据自适应权重获取的隐式多项式曲线不仅保证了描述的精确性，而且十分稳定，没有出现多余的曲线.

Abstract

The residual sum of squares of implicit polynomial (IP) and its gradients are constructed as objective function that can be minimized to obtain the fitted IP curve for representing a given shape.However

how to balance the two residual sum of squares using a weight factor is a difficult problem.The adaptive weight algorithm was proposed to determine the weight factor.Firstly

the function formula for the coefficient vector norm of IP curve and the weight were constructed according to the stability of IP curve.Secondly

the minimizer of the the function was computed

and used as the weight.Lastly

the IP curve can be obtained by minimizing the objective function with weight.The performance of the proposed method was evaluated on the standard MPEG-7 shape database

and the experimental results show that the IP curve obtained by proposed algorithm can represent the object shapes both accurately and stably.

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