Writing an image with floating point values

Question

My code reads an RGB image, processing it to produce floating-point results. How can I write these values as an image, maintaining these floating-point values, in Matlab 7.6.0 (R2008a)?

Answer 1

It is actually possible to fit 64 bits of pixel data (i.e. the number of bits needed to represent a double-precision floating-point value) into certain image formats, specifically a PNG. And you can even recover the data exactly. The key is to encode everything as uint16 values and use a Truecolor RGB image (3 color planes of 16 bit data) along with an alpha transparency map (another 16 bits). Here's the encoding step:

data = rand(4);              % Just some sample data, a small 4-by-4 matrix
hexData = num2hex(data(:));  % Get the 16 digit hex codes for each pixel
C = mat2cell(hexData, numel(data), [4 4 4 4]);  % Split the hex codes into 4 groups of 4
C = cellfun(@(c) {uint16(hex2dec(c))}, C);  % Convert each hex value into a 16 bit integer
colorData = reshape([C{1:3}], [size(data) 3]);  % 4-by-4-by-3 uint16 color data
alphaData = reshape(C{4}, size(data));          % 4-by-4 uint16 alpha data
imwrite(colorData, 'double_data.png', 'Alpha', alphaData);  % Save image

You now have a valid image file, although it'll probably looks like random garbage if you view it. Now, you can decode it like so:

[imColor, ~, imAlpha] = imread('double_data.png');  % Load image
imSize = size(imColor);  % Get image size
imHex = [dec2hex(imColor(:, :, 1)) ...  % Convert each uint16 to hex and concatenate
         dec2hex(imColor(:, :, 2)) ...
         dec2hex(imColor(:, :, 3)) ...
         dec2hex(imAlpha)];
imdata = reshape(hex2num(imHex), imSize(1:2));  % Reproduce data

And an equality check:

>> isequal(imdata, data)

ans =

  logical

   1           % it's the same!

Answer 2

The number of bits used to represent each element of a digital image is called the bit-depth of the image. The bit-depth tells us the number of discrete levels which an element of the image can take. Whether these elements will be stored as an integral type or a floating-point type is irrelevant: the bit-depth determines exactly how many discrete levels there may be.

How the bit-depth is interpreted depends on whether an image is grayscale or color. For example, an 8-bit grayscale image will have intensities in [0,255], while a 24-bit color image will also have intensities in [0,255]. This nomenclature is used because storing a color pixel with 8-bit red, green and blue components requires 24-bits. In order to avoid confusion, color images are often called by the number of bits per color channel. For example, the PNG format supports up to 16 bits per channel, or 48-bits total for truecolor (RGB) with an alpha layer.

The documentation for imwrite lists the formats and the bit-depths available in MATLAB.

Saving a color image (MxNx3 matrix) from MATLAB with the highest level of precision:

%// Assume an image called 'im' of type double.
%// First normalize to fall into [0,1].
im = im - min(im(:)); %// Save these numbers somewhere
im = im / max(im(:)); %// if you need to recover the original values later!
%// Best PNG quality.
imwrite(im,'image.png','bitdepth',16);

If you need more precision, you must save your image in a general data format rather than a specialized image format.