In association with HPA's 2009 Technology Retreat
Synopsis:
Mathematics potentially provides deep insight into “how things work” in HDTV and digital cinema. However, many of us either had no serious training in mathematics, or paid little attention to it while we were at school! This workshop will provide a refresher in math. I will show live demonstrations of half a dozen worked examples of mathematics directly applied to HDTV and digital cinema problems. I will use the interactive features – including graphing in 2D and 3D – of one of my favourite tools, Mathematica. Demonstration copies and demo licenses of Mathematica will be available; if you bring a suitably equipped laptop computer, you will be able to install Mathematica and follow along.
We will start by reviewing number theory, showing its application to the choice of scanning and image standards for SDTV and HDTV. I’ll demonstrate a few situations where failure to appreciate number theory has led to awkward choices of parameters in certain video standards.
We will review logarithms and power functions, using examples of opto-electronic (“gamma”) and electro-optical conversion functions used in cameras and displays. How many bits are needed to represent the components of a colour image signal? 8? 10? 12? Or even 14? Using logarithms – and a few properties of human vision – we will answer that question. (The answer depends upon contrast ratio.)
We have all seen RGB colour space represented as a cube. But we have also seen it as a triangle (in CIE x, y space), as a hexagon (on a vectorscope), as a circle (in HLS or HSV space), and as a blob (in Pointer’s gamut). Which is it? We will review affine and projective transforms to answer that question.
The Fourier transform and its first cousin the discrete cosine transform lie at the heart of several important video compression standards. We will review transform theory, showing examples of the effect of transforms on images. Filters are designed using both transforms and polynomials. We will review polynomials, especially the sorts that are important to filter design.
At last year’s seminar, Florian Kainz – senior software developer and colour scientist at ILM – shared his knowledge of colour transforms. This year, a mystery guest credited in several top-tier Hollywood movies will reveal three of his secret software tools of astonishing simplicity. He will reveal how these widely available but little-known tools have contributed greatly to his success in designing, implementing, and performing colour transformations. He will lead a hands-on session showing you how to use these tools, which are available for you to use freely after the workshop.
Materials provided: Course handouts will be provided. Portions of the seminar will be based upon Charles Poynton’s book Digital Video and HDTV Algorithms and Interfaces.
Fee: USD 175. Register at the HPA site.
Charles Poynton -
Courses
& seminars
2009-04-30