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Yet there are 2 issues:

- It is only available to those who purchased Image PRocessing Toolbox.
- It creates the matrix for full convolution shape only.

I implemented the matrix form for imfiter() in Generate the Matrix Form of 2D Convolution Kernel. It was written in simple form (No vectorization tricks) for clarity and simplicity for thos who want to learn.

What I'm after is doing somthing similar for Convolution Matrices for the different shapes: full, same, valid.

Namely a function with the following form:

function [ mK ] = CreateImageConvMtx( mH, numRows, numCols, convShape )

%UNTITLED6 Summary of this function goes here

% Detailed explanation goes here

CONVOLUTION_SHAPE_FULL = 1;

CONVOLUTION_SHAPE_SAME = 2;

CONVOLUTION_SHAPE_VALID = 3;

switch(convShape)

case(CONVOLUTION_SHAPE_FULL)

% Code for the 'full' case

case(CONVOLUTION_SHAPE_SAME)

% Code for the 'same' case

case(CONVOLUTION_SHAPE_VALID)

% Code for the 'valid' case

end

end

I would be happy of someone could assist with that.

Again, prefer clarity over performance.

Thank You.

Matt J
on 15 Jan 2019

Edited: Matt J
on 15 Jan 2019

Readability and clarity over performance.

OK, can't get much simpler and more readable then the following:

function [ mK ] = CreateImageConvMtx( mH, nRows, nCols, convShape )

%convShape is 'full', 'same', or 'valid'

impulse=zeros(nRows,nCols);

for i=numel(impulse):-1:1

impulse(i)=1; %Create impulse image corresponding to i-th output matrix column

tmp=sparse( conv2(impulse,mH,convShape) ); %impulse response

Column{i}=tmp(:);

impulse(i)=0;

end

mK=cell2mat(Column);

end

Matt J
on 15 Jan 2019

Edited: Matt J
on 15 Jan 2019

You can use my func2mat (Download) utility. It will find the matrix form of any linear function and doesn't require any toolboxes. However, there are much better options if your convolution kernels are separable.

function [ mK ] = CreateImageConvMtx( mH, nRows, nCols, convShape )

%convShape is 'full', 'same', or 'valid'

Xtypical=zeros([nRows,nCols]);

fun=@(x) conv2(x,mH,convShape);

mK=func2mat(fun,Xtypical);

end

Royi Avital
on 19 Jan 2019

Edited: Royi Avital
on 22 Jan 2019

Matt J
on 22 Jan 2019

that in case numElements is a large number this becomes inefficient both computationaly and memory wise.

Less efficient, yes, but clearer (are you still prioritizing clarity over performance?), and still very fast even for absurdly large image sizes.

N=5000; %image length

K=7; %kernel length

vK=rand(K,1);

E=eye(N);

tic

mK1 = CreateConvMtxSparse( vK, N, 3 );

toc; %Elapsed time is 0.002846 seconds.

tic;

mK2=sparse(conv2(E,vK,'valid'));

toc %Elapsed time is 0.275314 seconds.

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