ABSTRACT. This is a short introduction to the efficient calculation of image compositions. Some of the techniques shown here are not well known, and should be. In particular, we explain the difference between premultiplied alpha and not. These two related notions are often confused, or not even understood. We show that premultiplied alpha is more efficient, yields more elegant formulas, and occurs commonly in practice. We show that the non-premultiplied alpha formulation is not closed on over, the fundamental image compositing operator - as usually defined. Most importantly, the notion of premultiplied alpha leads directly to the notion of image object, or sprite - a shaped image with partial transparencies.

ABSTRACT. This paper is an introduction to a theory of image computing. The theory, or model, underlies everything I say or think about images and imaging. The primary idea behind the model to be presented here, the sprite theory or model of image computing, was that one was needed at all. It came from my realization, in the 1980s, that the reason the “image processing” market had not taken off was that it had no center—it was undefined. As opposed to the 2D geometry market—also known as desktop publishing—which was founded on the careful definition of 2D geometry embodied in the PostScript language, there was no accepted definition of 2D image computing. Every company or institution in the business had an internal idea, often vague, of a model that, of course, differed from the others. So I spent about a year at Pixar defining a language, called IceMan, to accomplish for images what PostScript did for 2D geometry. Many of these concepts, but not the IceMan language itself, I embodied in a prototype application that eventually became Altamira Composer. The concepts grew and matured in Altamira Composer, and they are those presented here.

ABSTRACT. My purpose here is to, once and for all, rid the world of the misconception that a pixel is a little geometric square. This is not a religious issue. This is an issue that strikes right at the root of correct image (sprite) computing and the ability to correctly integrate (converge) the discrete and the continuous. The little square model is simply incorrect. It harms. It gets in the way. If you find yourself thinking that a pixel is a little square, please read this paper. I will have succeeded if you at least understand that you are using the model and why it is permissible in your case to do so (is it?).

Everything I say about little squares and pixels in the 2D case applies equally well to little cubes and voxels in 3D. The generalization is straightforward, so I won’t mention it from hereon.

I discuss why the little square model continues to dominate our collective minds. I show why it is wrong in general. I show when it is appropriate to use a little square in the context of a pixel. I propose a discrete to continuous mapping—because this is where the problem arises—that always works and does not assume too much.

I presented some of this argument in Tech Memo 5 but have encountered a serious enough misuse of the little square model since I wrote that paper to make me believe a full frontal attack is necessary.

Alpha and the History of Digital Compositing, Tech Memo 7, Aug 15, 1995

ABSTRACT. The history of digital image compositing - other than simple digital implementation of known film art - is essentially the history of the alpha channel. Distinctions are drawn between digital printing and digital compositing, between matte creation and matte usage, and between (binary) masking and (subtle) matting. The history of the integral alpha channel and premultiplied alpha ideas are presented and their importance in the development of digital compositing in its current modern form is made clear.

Varieties of Digital Painting, Tech Memo 8, Aug 30, 1995

ABSTRACT. The purpose of this memo is to distinguish between the various meanings that digital painting may have. It is important to have a taxonomy so that intelligent conversation may proceed on such important issues as multi-resolution paint programs. Each type of painting will be discussed in its multi-resolution generalization. The taxonomy here splits painting into discrete and continuous categories and each of these into maxing and non-maxing subcategories.

Gamma Correction, Tech Memo 9, Sep 1, 1995

ABSTRACT. Gamma is one of the most misunderstood concepts in computer imaging applications. Part of the reason is that the term is used to mean several different things, completely confusing the user. The purpose of this memo is to draw distinctions between the several uses and to propose a fixed meaning for the term: Gamma is the term used to describe the nonlinearity of a display monitor. This is the historical first meaning of the term. A corollary of this definition is that all other uses of the term gamma should be dropped, or the imaging industry will continue to stumble. In particular, this means that gamma should not be used to describe nonlinearity introduced into the image data itself. Image data, especially images intended for reuse, should always contain linear data, as commonly assumed by all computer graphics algorithms.

Digital Paint Systems: Historical Overview, Tech Memo 14, May 30, 1997

INTRODUCTION. The period I will cover is from the late 1960s to the early 1980s, from the beginnings of the technology of digital painting up to the first consumer products that implemented it. I include a little information about major developments in the later 1980s. Two surveys that cover this later period fairly well - when the emergence of the personal computer completely changed the software universe - were both published in the magazine Computer Graphics World. My emphasis, of course, is on those systems I knew firsthand. I begin with a simple timeline of programs and systems. I will attempt a weighting and a "genealogy" of these in a later section, where I will also narrow the field to those painting systems that have directly affected the movie industry.

Should Alpha Be Nonlinear If RGB Is? Tech Memo 17, Dec 14, 1998

INTRODUCTION. The title question provides an excellent case study for the Fundamental Tenets of multimedia authoring. I argue that whenever a difficult problem is posed in the multimedia domain, one should fall back on the Fundamental Tenets to find the solution. They frequently serve as incisive probes into a problem. Having said this, I must admit that I failed to do so for the title question for an embarrassingly long time. It wasn’t until I remembered the Fundamental Tenets that I was able to solve the problem cleanly. The problem itself is interesting too. This is the record of a problem arising in an actual standards battle.

Eigenpolygon Decomposition of Polygons, Tech Memo 19, Oct 24, 1998

INTRODUCTION. Eigenvectors and eigenvalues play powerful roles in linear algebra. A remarkable example of their use in geometry is presented here: Any n-gon can be represented as a complex linear sum of n eigenvectors. Since these eigenvectors are themselves n-gons, I call them eigenpolygons. For example, any hexagon can be represented by a linear sum of six eigenhexagons, or, as the title suggests, it can be decomposed into six eigenhexagons. And any hexagon can be decomposed into a sum of the same six eigenhexagons—hence the "eigen". The rightmost column of Figure 1 shows these characteristic, or fundamental, hexagons. The columns of this figure, in fact, are the eigenpolygons for triangles, quadrilaterals, pentagons, and hexagons, respectively. Details of the eigenpolygon decomposition of 2-dimensional polygons are presented below.