Implementation of Euclidean Distance Transforms Using Erosion and Dilation with Form Correction

doi:10.11834/jig.20100217

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Implementation of Euclidean Distance Transforms Using Erosion and Dilation with Form Correction
Vol. 15, Issue 2, Pages: 294(2010)
Published：2010
DOI： 10.11834/jig.20100217
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DOI：

Implementation of Euclidean Distance Transforms Using Erosion and Dilation with Form Correction[J]. Journal of Image and Graphics, 2010, 15(2): 294. DOI： 10.11834/jig.20100217.

摘要

提出一种用带形状校正的腐蚀膨胀实现的Euclidean距离变换新算法。该方法的特点是采用新的数据结构——线段表来表示区域与边界。对于用线段表表示的区域作腐蚀膨胀比用卷积型腐蚀膨胀算法效率提高数十倍。通过总结腐蚀膨胀造成失真的规律，设计出形状校正的方法来消除所造成的误差。与传统基于局部距离累加的Chamfer算法相比较，该方法在保真度与处理效率两方面都有提高。新的距离变换算法也可用于数字图像的合成，优点是生成羽化蒙板时形状保真度高并且运行速度快。特别适用于任意形状区域可选宽度边界条带上的羽化处理。

Abstract

A novel method of implementation for Euclidean distance transform using erosion and dilation with form correction is proposed in this paper. The characteristic of the method is a new data structure

which uses line segment table to represent region and edge. Compared with traditional convolution mask

the efficiency of erosion and dilation operation for region expressed by line segment table is improved more than 10 times. Through analyzing the rules of distortions caused by erosion and dilation

we propose a form correction method to decrease the errors. Compared with the Chamfer algorithm

our new approach is better for fidelity and efficiency. The new distance transform can also be used for image blend thanks to the advantage of fidelity and high speed when creating feather mask. Furthermore

it is especially propitious to feather operation of selected boundary in arbitrarily shape regions. The principle and implementation are discussed in detail. And the efficiencies of different processing methods are compared.