given an image I of type uint8 in matlab
entropy(I)
gives me a very different result from
entropy(im2double(I))
(e.g. 6.98 in the first case, 0.51 in the second case) why the datatype changes this value?
When you read an image using imread, your image is read into a uint m-by-n-by-3 array. Depending on the image format, 16 or fewer bits per color plane (red, green, blue) are used in order to store image pixels.
uint8 (unsigned 8 bits integer) is a numeric format for integers that allows a minimum value of 0 and a maximum value of 255. uint16 (unsigned 16 bits integer) is a numeric format for integers that allows a minimum value of 0 and a maximum value of 65535. When you convert these numerical formats into double, you are basically dividing them by their maximum value:
% Pseudocode
uint8 val = 127;
double val_new = val / 255.0d; % 0.49803921568627450980392156862745
uint16 val = 42133;
double val_new = val / 65535.0d; % 0.64290836957351033798733501182574
The double numerical format is normally used to store very big (64 bits) floating-point values that need to ensure a high precision. This means that your uint values will be converted into 0.something values, where something represents a (variable but potentially) huge amount of digits.
Since the Shannon Entropy (more info here) is defined as the average amount of information produced by a stochastic source of data... your result is easily explained: you are feeding the entropy function with a higher degree of information (greater amount of bytes, greater amount of digits, greater amount of information).