How can I determine what matrix is needed to flip an image upside down?

I need to write a program that will flip an image upside down. This is for a linear algebra class so I am not allowed to use flipud(). I must find a transformation matrix (T) which can be multiplied by an image (X) to give the flipped image.

T*X_original = X_flipped

I'm not sure where to start with this. Thanks!

Answer 1

[Image Analyst]

Try this:

flippedMatrix = originalMatrix(end:-1:1, :);

% Alternatively (less efficient) but what you want.
T = zeros(size(originalMatrix, 1)); % INitialize.
for k = 1 : size(originalMatrix, 1)
  T(k, end-k+1) = 1;
end
T % Print to command window.
flippedMatrix2 = T * originalMatrix

[Youssef Khmou]

good answer .

Answer 2

[Youssef Khmou]

Generally that type of matrices are for euclidean space where a vector or a set of vector can be rotated with a cos and sin rotation matrix, however there might a real matrix that provide what you described , in the mean while you try this way :

X=im2double(imread('circuit.tif')); %  Original image
[m n]=size(X);
Y=X(m:-1:1,n:-1:1);     %  flipped image upside down 
%  gievn T*X=Y  ,  is  T bounded operator ??????? can you answer this equation 

T=Y*pinv(X);     %  Pseudo inverse because Y is not square .