The Application of Hough Transform in the Detection of Exponent Function Curve
霍夫变换在指数函数型曲线检测中的应用

This paper, by using the strong resistance of Hough transform to noise and its characteristics of extracting points in the vicinity of different lines, studies the curve detection when x i,y i of the discrete data point set M satisfy the exponential function relation. Firstly, the new data points M *( x * i,y * i ) are obtained by logarithmically transforming the discrete data points, and the relation between x * i and y * i becomes linear. Secondly, Hough transform is used to detect the line of M * so that the parameters of lines are obtained. Thirdly, the parameters of lines obtained by Hough transform are used to calculate the distances d ki from the points to the line, and compared d ki with the given threshold d k , so the points in the vicinity of the different lines are extracted and the interferences or noise of data point set M * are deleted. At last, by using the fit line of the least square method and through inverse transform, parameters a and b of the fit curve equation after interferences or noise being deleted are obtained. This paper proposes a new method of detecting the exponential functional curves, which overcomes the three problems existed in the use of the fit curve of the least square method and does not need high accuracy of Hough transform.