We were asked to obtain a grayscale image, and make sure its dimensions are multiples of 8.
The image I chose whose dimensions are 240x240:
We needed to extract an 8x8 pixel block, apply the 2D-DCT, quantize, and reconstruct the block. Code for the DCT, quantizing, and dequantizing: a-d code
My original 8x8 block (left) DCT matrix (right):
My reconstructed 8x8 blocks with their YQ matrices p=1(top), p=2(middle), p=4(bottom):
Now reconstructing the entire image using 8x8 blocks: Image reconstruction
p=1 (left) p=2 (middle) p=4 (right):
Next we were asked to repeat but with the JPEG-suggested matrix with p=1. The only change in the code was the Q matrix.
My original 8x8 pixel block is the same as above, and my reconstructed pixel block, DCT matrix, and YQ matrix are:
My reconstructed entire image:
The next part required us to obtain a color image and repeat the process. The color image I chose:
The 8x8 color pixel block with code for the following parts: Color code
The DCT matrices or R, G and B respectively are:
The YQ matrices for quantinization for p=1 are (for R, G and B respectively):
For p=2:
For p=4
The reconstructed 8x8 pixel blocks (for R, G and B respectively):
The entire reconstructed image from combining R G and B with p = 1,2,4 respectively: Code given here: Reconstructed color
We were now asked to repeat the steps with the color image but now transforming the RGB values into luminance/color difference coordinates and using the JPEG quantinization.
The same 8x8 color pixel block from above will be used.
The YQ matrices for Y, U, and V respectively are:
The reconstruction of the 8x8 pixel block for Y, U, V respectively are (with code given here): Luminance/color difference
Combining Y, U and V together to reconstruct the picture yielded for p=1,2,4 respectively (with code given here): Luminance reconstruction
