How to obtain piecewise polynomial from the acquired piecewise data?

I am using the following code to obtain the piecewise polynomial :

clc

close all

clear all

%Step 1 : Read Image

X=imread('cameramannn.tif');

figure,imshow(X);

[r c noc]=size(X);

% Step 2 : Gray Scale Conveersion

if noc > 1

Xn=rgb2gray(X);

else

Xn=X;

end

% Step 3 : Extracting Histogram from image

figure,imhist(Xn);

[counts, centers] = imhist(Xn);

bar(centers, counts, 'hist');

histpatch = findobj(gca, 'type', 'patch');

edgemat = get(histpatch, 'XData');

countmat = get(histpatch, 'YData');

counts = countmat(2,:);

centers = mean(edgemat(2,3,:))

% Step 4 : Extracting break points for polynomial

a=1;

while a<=4

for b=1:r*c

y=edgemat(a,b);

%round(y);

disp(y);

end

a=a+1;

end

breaks=[1.5000 2.5000 3.5000 4.5000 5.5000 6.5000 7.5000 8.5000 9.5000 10.5000 11.5000 12.5000 13.5000 14.5000 15.5000 16.5000 17.5000]; % manually taken from step 4

% Step 5 : Acquiring Piecewise Polynomial from the extracted data

pp=mkpp(breaks,Xn);

coefs = pp.coefs ;

breaks = pp.breaks ;

peices = pp.pieces ;

order = pp.order ;

dim = pp.dim ;

disp(pp);

% Step 6 : Obtaining Piecewise Polynomial from the acquired data

a=polyval(breaks,pp);

My Piecewise Output is :

form: 'pp'

breaks: [1x17 double]

coefs: [16x16 uint8]

pieces: 16

order: 16

dim: 1

But when MATLAB is compiling the polyval() I get the following error :

Undefined function 'isfinite' for input arguments of type 'struct'.

Error in polyval (line 54)

if isscalar(x) && (nargin < 3) && nc>0 && isfinite(x) && all(isfinite(p(:)))

Error in extracting_polynomial_try0 (line 50)

a=polyval(breaks,pp);

Please help me in resolving this issue.

Answer 1

[Vidhi Agarwal]

Hi @Avinash Bhatt,

The issue you are facing is due to the misuse of the "polyval" function. The "polyval" function is meant to evaluate a polynomial at specific points, but it expects the coefficients of a single polynomial as its first argument, not a piecewise polynomial structure like "pp" from "mkpp".

• The "mkpp" function returns a structure containing fields like "breaks", "coefs", "pieces", "order", and "dim". Try avoiding to pass this structure directly to "polyval".
• Use "ppval" to evaluate the piecewise polynomial created by "mkpp". This function is designed to handle the "pp" structure.

Revised version of the code is given below:

% Step 1 : Read Image
% Step 2 : Gray Scale Conversion
% Step 3 : Extracting Histogram from image
% Step 4 : Extracting break points for polynomial
% Define manual breakpoints (as provided)
% same as given code

% Step 5 : Acquiring Piecewise Polynomial from the extracted data
% Since Xn is an image matrix, you need to define meaningful coefficients
% For demonstration, let's assume a simple linear fit for each segment
coeffs = repmat([0, 1], length(breaks)-1, 1);  % Example: linear pieces

% Create the piecewise polynomial
pp = mkpp(breaks, coeffs);

% Step 6 : Evaluate the Piecewise Polynomial
x = linspace(min(breaks), max(breaks), 100);  % Define points to evaluate
y = ppval(pp, x);  % Evaluate the piecewise polynomial

% Plot the piecewise polynomial
figure;
plot(x, y, 'r', 'LineWidth', 2);
title('Piecewise Polynomial');
xlabel('Intensity Value');
ylabel('Polynomial Output');
grid on;

For better understanding of "mkpp" and "polyval" function of MATLAB refer to the following documentation:

• https://www.mathworks.com/help/matlab/ref/mkpp.html
• https://www.mathworks.com/help/matlab/ref/polyval.html

Hope this helps!