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Normalized Cut Based Edge Detection

机译：基于归一化切割的边缘检测

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摘要

This work introduces a new technique for edge detection based on a graph theory tool known as normalized cut. The problem involves to find certain eigenvector of a matrix called normalized laplacian, which is constructed in such way that it represents the relation of color and distance between the image's pixels. The matrix dimensions and the fact that it is dense represents a trouble for the common eigensolvers. The power method seemed a good option to tackle this problem. The first results were not very impressive, but a modification of the function that relates the image pixels lead us to a more convenient laplacian structure and to a segmentation result known as edge detection. A deeper analysis showed that this procedure does not even need of the power method, because the eigenvector that defines the segmentation can be obtained with a closed form.
机译：这项工作介绍了一种基于称为归一化割的图论工具的边缘检测新技术。问题涉及找到矩阵的某些特征向量，称为归一化拉普拉斯矩阵，该矩阵以表示颜色与图像像素之间距离的关系的方式构造。矩阵尺寸及其密集的事实给普通的特征求解器带来了麻烦。功率方法似乎是解决此问题的不错选择。最初的结果不是很令人印象深刻，但是对与图像像素相关的函数的修改使我们得到了更方便的拉普拉斯结构和称为边缘检测的分割结果。更深入的分析表明，此过程甚至不需要幂方法，因为定义细分的特征向量可以用封闭形式获得。

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