JZUS - Journal of Zhejiang University SCIENCE

ENGINEERING Information Technology & Electronic Engineering

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Image meshing via hierarchical optimization

Author(s): Hao Xie, Ruo-feng Tong
Affiliation(s): Institute of Artificial Intelligence, Zhejiang University, Hangzhou 310027, China
Corresponding email(s): xiehao@zju.edu.cn, trf@zju.edu.cn
Key Words: Image meshing, Hierarchical optimization, Convexification

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Hao Xie, Ruo-feng Tong. Image meshing via hierarchical optimization[J]. Frontiers of Information Technology & Electronic Engineering,in press.https://doi.org/10.1631/FITEE.1500171

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Abstract
Chinese Summary
Academic Network
Reviewer Comment

Abstract: Vector graphic, as a kind of geometric representation of raster images, has many advantages, e.g., definition independence and editing facility. A popular way to convert raster images into vector graphics is image meshing, the aim of which is to find a mesh to represent an image as faithfully as possible. For traditional meshing algorithms, the crux of the problem resides mainly in the high non-linearity and non-smoothness of the objective, which makes it difficult to find a desirable optimal solution. To ameliorate this situation, we present a hierarchical optimization algorithm solving the problem from coarser levels to finer ones, providing initialization for each level with its coarser ascent. To further simplify the problem, the original non-convex problem is converted to a linear least squares one, and thus becomes convex, which makes the problem much easier to solve. A dictionary learning framework is used to combine geometry and topology elegantly. Then an alternating scheme is employed to solve both parts. Experiments show that our algorithm runs fast and achieves better results than existing ones for most images.

Abstract: This paper proposes a new approach to image meshing as a way to compactly represent images. The major new idea is to use a hierarchical optimization with the combined color and location to make the problem more tractable. The experimental results demonstrate that the method produces improved results over state of the art. Overall, it is a nice paper with soild technical contribution and interesting results.

基于层次优化的图像网格化方法

目的：面向数字图像处理领域中的图像表达问题，实现对给定光栅图像生成其对应的三角网格表达，使得通过该网格重建出的图像与原图像尽可能一致。
创新点：使用一种层次优化的方法，将原问题中的高复杂性逐层分散到每一层中，使得每一层中的子问题变得易解。
方法：首先，对给定的光栅图像进行多次双边滤波，从而建立起层次结构（图2），使得处理后的图像在保持局部特征的前提下逐层平滑。接着，对最粗层次的图像生成初始三角网格，与该层的图像一起作为输入，以便后续处理。然后，从最粗一层开始，逐层进行处理；对每一层的子问题均采用几何与拓扑交替迭代的方式进行求解，并将求解的结果作为下一层的初始网格。最后，在最细一层的输出三角网格顶点上赋予图像中对应位置的像素点颜色值，从而形成最终的输出网格（图4b）。当需要重建原始图像时，只需根据三角网格顶点的颜色值对三角形内部点的颜色值进行线性插值即可（图5）。
结论：针对一般的光栅图像，提出了一种基于层次优化的图像网格化方法，可较好地重建出原输入图像。

关键词组：图像网格化；层次优化；凸化

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基于层次优化的图像网格化方法

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