I recently presented to a group of freshman engineering students at Virginia Commonwealth University. I wanted to show something that was fun, eye-catching, and relatively easy to explain. So I created this image-related demo. I am not an expert in image processing, but I certainly had a lot of fun working on this example. For anyone interested in hardcore image processing, I would suggest also taking a look at Steve's Image Processing blog.
This example demonstrates how to embed an image into another image and how to decompose the images. The embedded image is created by storing two 8-bit RGB image as 16-bit RGB image. The primary image is stored in the most significant byte, while the secondary image is stored in the least significant byte. (See the section titled "Embed Function & Decode Function" of this post for the code). With this method, the secondary image can be concealed inside the primary image, without any loss of information.
This post focuses on the decomposition part of the demo.
This demo uses functions from the Image Processing Toolbox.
curImshowBorder = iptgetpref('ImshowBorder'); iptsetpref('ImshowBorder', 'tight');
Here are two images that look the same. But are they??
Would you believe me if I say these were very different images? Perhaps you'll believe MATLAB:
ans = 0
In fact, they have completely different images embedded in them. You just can't tell with the naked eye.
Let's try to decompose the image and see what's hidden inside.
These are 16-bit RGB images. See the "Embed Function & Decode Function" section of this report to see the function that I used for creating these images.
imData = imread('peppers_BlueHills.png'); whos imData
Name Size Bytes Class Attributes imData 384x512x3 1179648 uint16
The image contains two 8-bit images. The primary image is stored in the most significant byte and the secondary image is stored in the least significant byte.
Convert RGB 3-D Array to a Vector
We'll be using TYPECAST to convert the data type, and the function requires a vector.
pixelVals = imData(:); pixelVals(1:10)
ans = 16097 16352 16862 16348 16346 16344 16087 16854 16082 15822
Convert UINT16 to UINT8
Next, convert the data type from UINT16 to UINT8. In doing so, we'll use TYPECAST (instead of CAST) to preserve the data.
pixelValsConv = typecast(pixelVals, 'uint8'); whos pixelVals*
Name Size Bytes Class Attributes pixelVals 589824x1 1179648 uint16 pixelValsConv 1179648x1 1179648 uint8
Notice that pixelValsConv has twice as many elements. This is because there are two 8-bit values to a 16-bit value.
Separate Two Images
We'll reshape them to separate out the least and the most significant bytes.
pixelValsConv = reshape(pixelValsConv, 2, )'; pixelValsConv(1:10, :)
ans = 225 62 224 63 222 65 220 63 218 63 216 63 215 62 214 65 210 62 206 61
On a system with "little-endian" architecture, the first column is the least significant byte and the second column is the most significant column.
(first pixel) 62*256 + 225 = 16097
On a "big-endian" architecture system, the order is switched.
[cmp,maxsize,endian] = computer if strcmp(endian, 'L') imOrder = [2 1]; else imOrder = [1 2]; end
cmp = PCWIN maxsize = 2.1475e+009 endian = L
We'll take each column and reshape them as the primary and secondary images.
imDataPrimary = reshape(pixelValsConv(:, imOrder(1)), size(imData)); imDataSecondary = reshape(pixelValsConv(:, imOrder(2)), size(imData));
We can see that we end up with two images, both of which are now UINT8 images.
Name Size Bytes Class Attributes imData 384x512x3 1179648 uint16 imData2Primary 384x512x3 589824 uint8 imData2Secondary 384x512x3 589824 uint8 imDataPrimary 384x512x3 589824 uint8 imDataSecondary 384x512x3 589824 uint8
Show Primary and Secondary Images
We'll do the same thing for the second image we read in. Let's see what's embedded in that one. We'll use decodeImage.m which is a function with the above algorithm.
[imData2Primary, imData2Secondary] = decodeImage('peppers_trees.png'); figure; imshow(imData2Primary); figure; imshow(imData2Secondary);
So, how does this work? Why is the secondary image unrecognizable by the naked eye? That's because the secondary image is stored in the least significant byte.
To understand this, let's take a look at a single row of pixels in one of the RGB planes. We'll look at row 150 of the red plane.
pixelRow16 = imData(150, :, 1); % row 150, red plane
We covert this vector to UINT8 using TYPECAST:
pixelRow8 = typecast(pixelRow16, 'uint8'); pixelRow8 = reshape(pixelRow8, 2, ); pixelRow8(:, 1:10)
ans = 64 60 61 61 57 60 61 61 61 61 67 70 71 70 70 72 74 69 63 63
On a little-endian architecture system, the first row is the secondary image, and the second row is the primary image. Next, we'll create a UINT16 vector with only the primary image.
% set the secondary image vector to ZERO pixelRow8Main = [zeros(1, size(pixelRow8, 2), 'uint8'); pixelRow8(2, :)]; pixelRow16Main = typecast(pixelRow8Main(:)', 'uint16');
Now, let's compare the values of the total image vector with those of the primary image vector.
figure; ax1 = axes;hold on; plot(pixelRow16); plot(pixelRow16Main, 'r'); xlabel('Pixel Count'); ylabel('Pixel Value (UINT16)'); legend('Total Image', 'Primary Image', 'Location', 'NorthWest'); rectX = 160; rectY = 15000; rectW = 30; rectH = 3500; rectangle('Position', [rectX, rectY, rectW, rectH]); dar = get(ax1, 'DataAspectRatio'); dar = dar(2)/dar(1); w = .3; h = w*(rectH/rectW)/dar; ax2 = axes(... 'Units', 'Normalized', ... 'Position', [.6 .2 w h], ... 'Box', 'on', ... 'LineWidth', 2, ... 'XTick', , ... 'Ytick', , ... 'Color', [.95 .95 .95]);hold on; xlabel('Magnified Region'); plot(pixelRow16); plot(pixelRow16Main, 'r'); xlim([rectX, rectX+rectW]); ylim([rectY, rectY+rectH]);
As this figure shows, the primary image represents the majority of the information. The information for the secondary image is much smaller relative to the primary image. But if we look at the data for the secondary image by itself, you see that we have the full 8-bit information.
figure; plot(pixelRow8(1, :), 'g'); ylim([0 300]); legend('Secondary Image', 'Location', 'NorthWest'); title('Secondary Image'); xlabel('Pixel Count'); ylabel('Pixel Value (UINT8)');
The following animations show how the secondary image data becomes more apparent as we subtract out the primary image data. Animations created using ANYMATE.
- 2-D Animation
- 3-D Animation
These are the actual functions for creating and decoding embedded images.
EMBEDIMAGE Embed an image into another image EMBEDIMAGE(PRIMARYIMAGE, IMAGETOEMBED) embeds the image file IMAGETOEMBED into the image file PRIMARYIMAGE. Both PRIMARYIMAGE and IMAGETOEMBED must be valid file names. The image files must be 8-bit images. The output image file will be a 16-bit PNG image, named PRIMARYIMAGE_IMAGETOEMBED.png. The primary image data will be stored in the most significant byte and the embedded image data will be stored in the least significant byte. Example: embedImage('trees.tif', 'football.jpg'); See also DECODEIMAGE. Jiro Doke Jan 24, 2009.
DECODEIMAGE Decode embedded image. DECODEIMAGE(IMAGEFILE) decodes embedded image file IMAGEFILE. IMAGEFILE must be a valid file name. It will display a figure with 3 axes. The top axis is the original image. The bottom left is the primary image, and the bottom right is the embedded hidden image. [PRIMARY, HIDDEN] = DECODEIMAGE(IMAGEFILE) returns the primary image and the hidden image data as RGB data. This function only works on images created by embedImage.m. Example: % create embedded image embedImage('trees.tif', 'football.jpg'); decodeImage('trees_football.png'); See also EMBEDIMAGE. Jiro Doke Jan 24, 2009.
I hope you liked this example. Images make nice examples because they are visual. Let me know if you have other fun, pedagogical examples that involve graphics. Put them on the File Exchange, and I'll be sure to take a look at it as a potential Pick of the Week!
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