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.

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 this 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 (in frequency space) and polynomials (in the temporal or spatial domain). 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. 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 will be made available for you to take home and use freely after the workshop.