使用Matlab进行拟合是图像处理中线条变换的一个重点内容，本文将详解Matlab中的直线拟合和曲线拟合用法。
关键函数：
Fit type for curve and surface fitting
/***********************************线性拟合***********************************/
线性拟合公式：
coeff1 * term1 + coeff2 * term2 + coeff3 * term3 + ...其中，coefficient是系数，term都是x的一次项。
线性拟合Example：
Example1: y=kx+b;
法1：
[csharp] view plain copy print ? x=[1,1.5,2,2.5,3];y=[0.9,1.7,2.2,2.6,3]; p=polyfit(x,y,1); x1=linspace(min(x),max(x)); y1=polyval(p,x1); plot(x,y,'*',x1,y1); x=[1,1.5,2,2.5,3];y=[0.9,1.7,2.2,2.6,3]; p=polyfit(x,y,1); x1=linspace(min(x),max(x)); y1=polyval(p,x1); plot(x,y,'*',x1,y1);结果：p = 1.0200 0.0400
即y=1.0200 *x+ 0.0400
法2：
[csharp] view plain copy print ? x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; p=fittype('poly1') f=fit(x,y,p) plot(f,x,y); x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; p=fittype('poly1') f=fit(x,y,p) plot(f,x,y);运行结果：
[csharp] view plain copy print ? x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; p=fittype('poly1') f=fit(x,y,p) plot(f,x,y); p = Linear model Poly1: p(p1,p2,x) = p1*x + p2 f = Linear model Poly1: f(x) = p1*x + p2 Coefficients (with 95% confidence bounds): p1 = 1.02 (0.7192, 1.321) p2 = 0.04 (-0.5981, 0.6781) x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; p=fittype('poly1') f=fit(x,y,p) plot(f,x,y); p = Linear model Poly1: p(p1,p2,x) = p1*x + p2 f = Linear model Poly1: f(x) = p1*x + p2 Coefficients (with 95% confidence bounds): p1 = 1.02 (0.7192, 1.321) p2 = 0.04 (-0.5981, 0.6781) Example2:y=a*x + b*sin(x) + c
法1：
[csharp] view plain copy print ? x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; EXPR = {'x','sin(x)','1'}; p=fittype(EXPR) f=fit(x,y,p) plot(f,x,y); x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; EXPR = {'x','sin(x)','1'}; p=fittype(EXPR) f=fit(x,y,p) plot(f,x,y);
运行结果：
[csharp] view plain copy print ? x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; EXPR = {'x','sin(x)','1'}; p=fittype(EXPR) f=fit(x,y,p) plot(f,x,y); p = Linear model: p(a,b,c,x) = a*x + b*sin(x) + c f = Linear model: f(x) = a*x + b*sin(x) + c Coefficients (with 95% confidence bounds): a = 1.249 (0.9856, 1.512) b = 0.6357 (0.03185, 1.24) c = -0.8611 (-1.773, 0.05094) x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; EXPR = {'x','sin(x)','1'}; p=fittype(EXPR) f=fit(x,y,p) plot(f,x,y); p = Linear model: p(a,b,c,x) = a*x + b*sin(x) + c f = Linear model: f(x) = a*x + b*sin(x) + c Coefficients (with 95% confidence bounds): a = 1.249 (0.9856, 1.512) b = 0.6357 (0.03185, 1.24) c = -0.8611 (-1.773, 0.05094)
法2： [csharp] view plain copy print ? x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; p=fittype('a*x+b*sin(x)+c','independent','x') f=fit(x,y,p) plot(f,x,y); x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; p=fittype('a*x+b*sin(x)+c','independent','x') f=fit(x,y,p) plot(f,x,y); 运行结果： [csharp] view plain copy print ? x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; p=fittype('a*x+b*sin(x)+c','independent','x') f=fit(x,y,p) plot(f,x,y); p = General model: p(a,b,c,x) = a*x+b*sin(x)+c Warning: Start point not provided, choosing random start point. > In fit>iCreateWarningFunction/nThrowWarning at 738 In fit>iFit at 320 In fit at 109 f = General model: f(x) = a*x+b*sin(x)+c Coefficients (with 95% confidence bounds): a = 1.249 (0.9856, 1.512) b = 0.6357 (0.03185, 1.24) c = -0.8611 (-1.773, 0.05094) x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; p=fittype('a*x+b*sin(x)+c','independent','x') f=fit(x,y,p) plot(f,x,y); p = General model: p(a,b,c,x) = a*x+b*sin(x)+c Warning: Start point not provided, choosing random start point. > In fit>iCreateWarningFunction/nThrowWarning at 738 In fit>iFit at 320 In fit at 109 f = General model: f(x) = a*x+b*sin(x)+c Coefficients (with 95% confidence bounds): a = 1.249 (0.9856, 1.512) b = 0.6357 (0.03185, 1.24) c = -0.8611 (-1.773, 0.05094)
/***********************************非线性拟合***********************************/
Example：y=a*x^2+b*x+c
法1：
[cpp] view plain copy print ? x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; p=fittype('a*x.^2+b*x+c','independent','x') f=fit(x,y,p) plot(f,x,y); x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; p=fittype('a*x.^2+b*x+c','independent','x') f=fit(x,y,p) plot(f,x,y); 运行结果：
[csharp] view plain copy print ? p = General model: p(a,b,c,x) = a*x.^2+b*x+c Warning: Start point not provided, choosing random start point. > In fit>iCreateWarningFunction/nThrowWarning at 738 In fit>iFit at 320 In fit at 109 f = General model: f(x) = a*x.^2+b*x+c Coefficients (with 95% confidence bounds): a = -0.2571 (-0.5681, 0.05386) b = 2.049 (0.791, 3.306) c = -0.86 (-2.016, 0.2964) p = General model: p(a,b,c,x) = a*x.^2+b*x+c Warning: Start point not provided, choosing random start point. > In fit>iCreateWarningFunction/nThrowWarning at 738 In fit>iFit at 320 In fit at 109 f = General model: f(x) = a*x.^2+b*x+c Coefficients (with 95% confidence bounds): a = -0.2571 (-0.5681, 0.05386) b = 2.049 (0.791, 3.306) c = -0.86 (-2.016, 0.2964)
法2：
[csharp] view plain copy print ? x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; %use c=0; c=0; p1=fittype(@(a,b,x) a*x.^2+b*x+c) f1=fit(x,y,p1) %use c=1; c=1; p2=fittype(@(a,b,x) a*x.^2+b*x+c) f2=fit(x,y,p2) %predict c p3=fittype(@(a,b,c,x) a*x.^2+b*x+c) f3=fit(x,y,p3) %show results scatter(x,y);%scatter point c1=plot(f1,'b:*');%blue hold on plot(f2,'g:+');%green hold on plot(f3,'m:*');%purple hold off x=[1;1.5;2;2.5;3];y=[0.9;1.7;2.2;2.6;3]; %use c=0; c=0; p1=fittype(@(a,b,x) a*x.^2+b*x+c) f1=fit(x,y,p1) %use c=1; c=1; p2=fittype(@(a,b,x) a*x.^2+b*x+c) f2=fit(x,y,p2) %predict c p3=fittype(@(a,b,c,x) a*x.^2+b*x+c) f3=fit(x,y,p3) %show results scatter(x,y);%scatter point c1=plot(f1,'b:*');%blue hold on plot(f2,'g:+');%green hold on plot(f3,'m:*');%purple hold off
