A parameter independent line fitting method

D. Prasad, Hiok Chai Quek, M. Leung, Siu-Yeung Cho
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引用次数: 39

Abstract

We prove that when a line is approximated using digital line, the error in the slope of the digital line has a definite upper bound and is strongly dependent on the two pixels chosen for defining the digital line. Thus, an analytical expression of the maximum deviation of the pixels from the digital line can be derived. Using this, the conventional line fitting methods that use maximum tolerable deviation as the optimization goal can be made control-parameter independent. This error bound can be used to make the most recent and sophisticated line fitting methods parameter independent and more robust to digitization noises. In our knowledge, this is the first line fitting method completely devoid of any control parameter. Such control-parameter independent line fitting algorithm retains the characteristics of the digital curve with sufficient reliability and precision and provides good dimensionality reduction in representing the digital curves. Extensive results have been generated for 9 datasets comprising of about a hundred thousand images. The proposed method shows robust and repeatable performance across all the datasets with low standard deviation in the performance.
一种参数无关的直线拟合方法
我们证明了当用数字线近似一条线时,数字线斜率的误差有一个确定的上限,并且强烈依赖于选择用于定义数字线的两个像素。因此,可以推导出像素与数字线的最大偏差的解析表达式。利用这种方法,可以使以最大容许偏差为优化目标的传统线拟合方法与控制参数无关。这种误差界限可以使最新和最复杂的线拟合方法与参数无关,并且对数字化噪声具有更强的鲁棒性。据我们所知,这是第一个完全没有任何控制参数的直线拟合方法。这种与控制参数无关的线拟合算法保留了数字曲线的特征,具有足够的可靠性和精度,并且在表示数字曲线时具有良好的降维性。广泛的结果已经产生了9个数据集,包括大约10万张图像。该方法在所有数据集上都具有鲁棒性和可重复性,且性能标准差低。
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