YouTube, Slideshow, and Mathematical Equations

Despite the seemingly affordable offer from Microsoft, the online storage service aimed for consumer, SkyDrive, is not even close to adequately store the data I have. I’ve to choose certain types of data to be stored on SkyDrive. On the other hand, although Google does allow unlimited uploads of “Private Video” of certain length on YouTube, it’s not exactly an ideal place to store video backups for a couple of reasons.

I’ve been trying to figure out ways to publish mathematical equations online suitable for me. Although it’s fairly easy to type mathematical equations in Microsoft Word, SkyDrive Word Web App renders mathematical equations written in Microsoft Word 2013 as images when that Word document is being viewed; the good thing here is storing or viewing Word document on SkyDrive itself does not change the formatting or contents of the Word document, unlike some other online Word processor solutions. When the mathematical equations are being rendered as images instead of texts, they are subject to pixelation when the “images” are being enlarged. The best viewing experience is obviously to download the Word document and open it with Microsoft Word. But I also like the mathematical equations I wrote can be viewed online without expecting others to use supported version of Microsoft Word, even though I do strongly recommend it.

As I turned my attention to ffmpeg and x264, I found out the existence of ffmpeg-users forum. Over there, I saw some people asked about ways to create slideshow by using ffmpeg years ago. As I began to ponder about it, I found that creating a slideshow video of H.264 lossless compression was indeed viable, at least theoretically. Although ffmpeg did not behave exactly as I initially anticipated when I tried to use video filter “fps” to duplicate frames, after a couple of trial and errors, I did figure out how ffmpeg responded to my video filter “fps” command. Although I was inspired by questions posted by users years ago, I’m not exactly sure that my experience could serve as a direct answer to their questions. I thought, since somebody have asked such questions before, my experience would be helpful to somebody, at least that’s what I thought.

The slideshow I created and share publicly on SkyDrive is made of wallpapers downloaded from The “Wallpapers” slideshow is at I specifically documented the entire process at that forum and posted the link there as well. Well, let’s just say the first response I got is not exactly encouraging or showing gratitude. Without reading carefully what I wrote, someone even declared that my way had failed due to overwhelming large size. Due to large number of frame duplicates, the bit rate is actually quite low even compared with lossy compression; it’s being compressed losslessly. The bit rate is less than 1Mbps. Granted, if it were not a slideshow but an animation or live recording, it bit rate would be much higher. It’s a 720p video.

Later, upon request, I created another slideshow which I meant to remove on August 7, 2013. It’s much shorter in terms of length but features variable-length slides. From what I saw from the responses, the complexity of the process I went through to create a slideshow did not attract ffmpeg-users forums visitors to be interested to adopt the way I wrote. People do seem to prefer simple and straightforward solution. The person who requested me to create a slideshow with variable-length slides did seem to be interested to figure out how I did it. All I can say is good luck to him.

One thing I like about Microsoft Office is the interoperability between applications. Sure enough, I wrote mathematical equations at Microsoft Word. But create a presentation from PowerPoint with equations written at Microsoft Word is merely just “copy & paste”, with minor editing. Since I aimed at create a video slideshow, not a PowerPoint slideshow, I save individual slides as PNG images by click “Save As”; a folder was created automatically with all of my slides in PNG format.

With these PNG formats, I was ready to create my mathematical equations slideshow with ffmpeg.

No matter, I did “finally” figure out a good use of YouTube and a way to publish my mathematical equations for free. Well, it’s certainly viewable directly on web browsers.

Now, let’s talk about why YouTube is not a good solution for private video backups. The slideshow I created was encoded in H.264 lossless with chroma format of 4:4:4. Of course, I knew that YouTube did not decode H.264 lossless or chroma format of 4:4:4 correctly. So, I specifically created another version with constant rate factor of 18 and chroma format of 4:2:0. I uploaded that version of “lossy compression”. Guess what, instead of making use my own version of lossy compression, Google re-encode the video again in lossy encoding mode; but the version encoded by Google is even larger than original lossless version. How is that possible? Well, the automated encoders on YouTube introduced a lot of noises or compression artefacts during the encoding process, resulting in the larger file but less quality. In case you wonder, the file size of the version encoded by Google is more than ten-times larger than my own version of “lossless compression”. Job well done, Google!

Google does have a lot of cash, I’m sure that it can afford it! Regardless, as you can see, the video looks pretty good, is it not? Thank you, Google. I can now write about theories in Physics and Mathematics. It’s kind of hard to write about them without being able to accompany them with mathematical equations. I know that in Stephen Hawking’s book, it’s specifically made without any mathematical equations written on it so that it would sell. It’s called “A Brief History of Time”, I believe.

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