how to define breaks in mkpp()?

mkpp(breaks,coefs);

If I have 256 coefficients then how can I define breaks?

[Avinash Bhatt]

if I have a matrix of 256 coefficients, suppose :

X=imread('cameraman.tif');

and I want to create the piecewise polynomial structure using mkpp(breaks, coeffs) where coeffs will be the pixel intensity values then how breaks can be defined.

Answer 1

[Vidhi Agarwal]

Hi @Avinash Bhatt,

To use "mkpp" with a matrix of 256 coefficients, you need to define a corresponding set of breakpoints. The number of breakpoints should be one more than the number of polynomial pieces you want to create. If you have 256 coefficients and you want to create a piecewise polynomial where each piece corresponds to a single coefficient, you'll need 257 breakpoints.

Below are the steps to define breakpoints:

• Since "mkpp" expects the number of pieces to be one less than the number of breakpoints, and you have 256 coefficients, you should create 257 breakpoints.
• Assume you want each coefficient to apply over a uniform interval, you can define breakpoints as a simple linear space.

Sample code for the same is given below:

X = imread('cameraman.tif');
Xn = double(X);  % Convert to double for polynomial operations

% Step 2: Define Breakpoints
% Assuming you want each intensity level to be a piece, create 257 breaks
breaks = linspace(0, 256, 257);  % Breakpoints from 0 to 256

% Step 3: Define Coefficients
% Use pixel intensities as coefficients for piecewise constant polynomials
% Assuming each piece is a constant polynomial (order 1)
coeffs = [Xn(:), zeros(numel(Xn), 1)];  % Each row is [a0, a1] for constant a0

For better understanding of breakpoints in "mkpp" refer to the follwoing documentation:

• https://www.mathworks.com/help/matlab/ref/mkpp.html#bvjfcv9breaks:~:text=breaks%20%E2%80%94%20Break,of%20L%20intervals.

Hope that helps!