Nonlinear Least Squares Optimization Toolbox in MATLAB

This resource demonstrates the use of Least Squares Method to fit a circle curve. The output includes the coordinates of the center and the radius of the fitted circle.

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。

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。

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？

配套案例26粒子群算法的寻优算法-非线性函数极值寻优.zip

[使用优化工具箱的二维互信息匹配]这是新墨西哥大学的Kateryna Artyushkova编码的IP工具箱用户使用互信息更新的自动图像配准。对象函数'image_registr_MI.m'最初是由人编码并由我修改的。我使用优化工具箱为完整的图像配准添加了一个比例因子。因此，运行此程序需要优化工具箱。zip文件包含三个文件：- opti_MI_scaling.m %主要代码- image_registr_MI.m %对象函数- image.mat %图像矩阵。在“image.mat”中，IM1和IM2仅用于示例目的。- IM1：230 X 230 MRI 8位图像- IM2：512 X 512 CT 8位图像要运行此代码，请输入以下命令： x0=[50; -15; 0.5];[x, fval]=fminsear

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.

MATLAB非线性拟合课件，教你怎样熟练运用MATLAB进行非线性拟合处理。