Computer graphics

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14 Computer graphics

Many problems in computer graphics can be considered as a case of SIMD programming: an image is a square or rectangular array where each pixel can be manipulated independently, and often with the same operation.

For instance, an image with $1024\times 1024$ pixels, of 8 bits each, takes $2^{20}$ bytes or 1 megabyte. In the context of a movie with a framerate of 60 frames, and a processor with an average instruction rate of 1 GHz, this means that each operation can take about 16 nanoseconds. (While this sounds like a reasonable operation rate, of course we also have to wonder about the bandwidth.)

Examples of operations on a single pixel are thresholding and contrast stretching.

Other operations involve several pixels at once: smoothing operations such as removing noise use a difference stencil . A typical averaging stencil would be \begin{equation} \begin{matrix} 1&1&1\\ 1&8&1\\ 1&1&1 \end{matrix} \end{equation} The stencils you saw in Chapter  Numerical treatment of differential equations represent differentiation; in graphics that can be used for operations such as edge detection. A popular choice for a differentiation stencil is \begin{equation} \hbox{$x$: } \begin{matrix} -1&0&1\\ -2&0&2\\ -1&0&1 \end{matrix} \qquad\hbox{$y$: } \begin{matrix} -1&-2&-1\\ 0&0&0\\ -1&-2&-1 \end{matrix} \end{equation}

The sequential code for applying a $3\times 3$ stencil on an $N\times N$ image would be

for (i=0; i<N; i++) {
  for (j=0; j<N; j++) {
    s = 0;
    for (ii=-1; ii<=1; ii++)
      for (jj=-1; jj<=1; jj++)
        s += frame[i+ii][j+jj];
    avg[i,j] = s;
  }
}

As discussed in section  , this code structure is advantageous for certain types of parallelism. For instance, in \indexac{CUDA} one would write a kernel containing the inner two loops, and instantiate this in parallel on each $[i,j]$ coordinate of the averages array.

On the other hand, this code structure would not be right for vector instructions or \emph{pipeline instructions} where the parallelism has to be in the inner loop, and preferably be as large as possible.

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