Least Squares Fitting of Circle Curve Using Least Squares Method

针对一组x，y值的基于最小平方方差和的椭圆和圆的拟合，用Matlab实现。

在圆拟合的过程中，直接最小二乘法是用于代数曲面拟合的重要技术。通过将数据点最小化到拟合曲面的距离，可以实现高效、精确的曲面拟合。

在[-1,1]区间上取n=20个等距节点，计算出以相应节点上的e^x的值作为数据样本，以1，x，x²，⋯，x^l为基函数做出l=3,5,7,9次的最小二乘拟合多项式。画出ln(cond(A)) - l曲线，其中A是确定最小二乘多项式系数的矩阵。计算出不同阶最小二乘多项式给出的最小偏差σ(l)。将基函数改为1，P₁(x)，P₂(x)，⋯，Pₗ(x)，其中Pᵢ(x)是勒让德多项式，结果如何？

本工具箱内含有MATLAB解决非线性最小二乘优化问题的所有m函数文件代码，方便用户高效地实现相关计算与优化。

该软件包包含一组工具，允许使用移动最小二乘算法实时变形点和图像。这是一种无需使用薄板样条算法提供的计算扩展技术即可获得良好图像变形的快速技术。该算法发表在Scott Schaefer，Travis McPhail，Joe Warren的论文“使用最小二乘法进行图像变形”中。

Total variation regularized least squares deconvolution is one of the standard problems in image processing. This package uses the concept of Augmented Lagrangian [1] to implement the state-of-the-art algorithm, which can be viewed as a variant of the widely known Alternating Direction Method of Multipliers (ADMM). The deconvtv user interface is similar to the current MATLAB deconvolution tools, including deconvwnr, deconvlucy, and deconvreg: out = deconvtv(img, psf, mu, opt); deconvtv supports direct spatiotemporal processing for image and video deconvolution problems. Its applications include, but are not limited to: image and video deblurring, image and video denoising, depth data enhancement, thermal air turbulence stabilization, and multi-view synthesis. For more information and citations, please refer to: [1] SH Chan, R. Khoshabeh, KB Gibson, PE Gill, and TQ Nguyen, \"Augmented Lagrangian Method for Total Variation Video Restoration\", IEEE Trans. Image.

This tutorial covers curve fitting using cubic numerator and quadratic denominator in Matlab.

In this guide, we will generate random point coordinates within a circle of radius r using the Homogeneous Poisson Point Process (HPPP). The following parameters will be required: % Covered Area: The percentage of the area covered within a circle of radius r. Input Parameters:- Density (λ): The intensity or density of points within the area.- Radius (r): The radius of the circle within which points are randomly distributed. Using these inputs, the HPPP process will calculate random point coordinates to model spatial distributions in the circular region defined by radius r.

经典相机标定程序代码基于matlab编程语言，采用Tsai方法进行相机的标定。