I hope my previous walkthrough of the VP8 4×4 intra coding process was educational. Today, I’ll be walking through an example of what happens when my toy VP8 encoder encodes an intra 16×16 block. This may prove educational to those who have never been exposed to the deep details of this or related algorithms. Also, I wanted to illustrate where I think my VP8 encoder process is going bad and generating such grotesque results.

Before I start, let me give a shout-out to Google Docs’ Drawing tool which I used to generate these diagrams. It works quite well.

Results

(Always cut to the chase in a blog post; results first.) I’m glad I composed this post. In the course of doing so, I found the problem, fixed it, and am now able to present this image that was decoded from the bitstream encoded by my toy working VP8 encoder:

Yeah, I know that image doesn’t look like anything you haven’t seen before. The difference is that it has made a successful trip through my VP8 encoder.

Follow along through the encoding process and learn of the mistake…

Original Block and Subblocks

Here is the 16×16 block to be encoded:

The block is broken down into 16 4×4 subblocks for further encoding:

Prediction

The first step is to pick a prediction mode, generate a prediction block, and subtract the predictors from the macroblock. In this case, we will use DC prediction which means the predictor will be the same for each element.

In 4×4 VP8 DC intra prediction, samples outside of the frame are assumed to be 128. It’s a little different in 16×16 DC intra prediction– samples above the top row are assumed to be 127 while samples left of the leftmost column are assumed to be 129. For the top left macroblock, this still works out to 128.

Subtract 128 from each of the samples:

Forward Transform

Run each of the 16 prediction-removed subblocks through the forward transform. This example uses the forward transform from libvpx 0.9.5:

I have highlighted the DC coefficients in each subblock. That’s because those receive special consideration in 16×16 intra coding.

Quantization

The Y plane AC quantizer is 4 in this example, the minimum allowed. (The Y plane DC quantizer is also 4 but doesn’t come into play for intra 16×16 coding since the DC coefficients follow a different process.) Thus, quantize (integer divide) each AC element in each subblock (we’ll ignore the DC coefficient for this part):

The Y2 Round Trip

Those highlighted DC coefficients from each of the 16 subblocks comprise the Y2 block. This block is transformed with a slightly different algorithm called the Walsh-Hadamard Transform (WHT). The results of this transform are then quantized (using 8 for both Y2 DC and AC in this example, as those are the smallest Y2 quantizers that VP8 allows), then zigzagged and entropy-coded along with the rest of the macroblock coefficients.

On the decoder side, the Y2 coefficients are decoded, de-zigzagged, dequantized and run through the inverse WHT.

And this is where I suspect that most of the error is creeping into my VP8 encoder. Observe the round-trip through the Y2 process:

As intimated, this part causes me consternation due to the wide discrepancy between the original and the reconstructed Y2 blocks. Observe the absolute difference between the 2 vectors:

That’s really significant and leads me to believe that this is where the big problem is.

What’s Wrong?

My first suspicion is that the quantization is throwing off the process. I was disabused of this idea when I removed quantization from the equation and immediately reversed the transform:

So perhaps there is a problem with the forward WHT. Just like with the usual subblock transform, the VP8 spec doesn’t define how to perform the forward WHT, only the inverse WHT. Do I need to audition different forward WHTs from various versions of libvpx, similar to what I did with the other transform? That doesn’t make a lot of sense– libvpx doesn’t seem to have so much trouble with basic encoding.

The Punchline

I reviewed the forward WHT code, the stuff that I plagiarized from libvpx 0.9.0. The function takes, among other parameters, a pitch value. There are 2 loops in the code. The first iterates through the rows of the input matrix– which I assumed was a 4×4 matrix. I was puzzled that during each iteration of the row loop, the input pointer was only being advanced by (pitch/2). I removed the division by 2 and the problem went away. I.e., the encoded image looks correct.

What’s up with the (pitch/2), anyway? It seems that the encoder likes to pack 2 4×4 subblocks into an 8×4 block data structure. In fact, the forward DCTs in the libvpx encoder have the same artifact. Remember how I surveyed several variations of forward DCT from different versions of libvpx? The one that proved most accurate in that test was the one I had already modified to advance the input pointer properly. Fixing the other 2 candidates yields similar results:

input:   92 91 89 86 91 90 88 86 89 89 89 88 89 87 88 93 
short 0.9.0: -311 6 2 0 0 11 -6 1 2 -3 3 0 0 0 -2 1 
inverse: 92 91 89 86 91 90 88 87 90 89 89 88 89 87 88 93 
fast  0.9.0: -313 5 1 0 1 11 -6 1 3 -3 4 0 0 0 -2 1 
inverse: 91 91 89 86 90 90 88 86 89 89 89 88 89 87 88 93 
short 0.9.5: -312 7 1 0 1 12 -5 2 2 -3 3 -1 1 0 -2 1 
inverse: 92 91 89 86 91 90 88 86 89 89 89 88 89 87 88 93 

Code cribber beware!

Corrected Y2 Round Trip

Let’s look at that Y2 round trip one more time:

And another look at the error between the original and the reconstruction:

Better.

Dequantization, Prediction, Inverse Transforms, and Reconstruction

To be honest, now that I solved the major problem, I’m getting a little tired of making these pictures. Long story short, all elements of the original 16 subblocks are dequantized and their DC coefficients are filled in with the appropriate item from the reconstructed Y2 block. A base predictor block is generated (all 128 values in this case). And each Y block is run through the inverse transform and added to the predictor block. The following is the reconstruction:

And if you compare that against the original luma macroblock (I don’t feel like doing it right now), you’ll find that it’s pretty close.

I can’t believe how close I was all this time, and how long that pitch bug held me up.