4 14 6 4 6 14 4 3 9 11 6 11 9 3 1 3 9 14 9 3 1 0 1 3 4 3 1 0

As an exercise, you may wish to verify the accuracy of several of the sample con-


1x5 5x1 5x5

Kernel Kernel Kernel

Figure 14.6 The separability of kernels means a big savings in computer time. To apply a 5x5 kernel to a pixel requires 25 multiplications and 25 additions; whereas computing two 1 x 5 kernels in sequence requires only 10 multiplications and 10 additions—a savings of 60% in computer time.

volutions, since it will help you to appreciate the sheer amount of number-crunch -ing involved in a rather simple image processing operation.

Separability. Because large kernels can be built up from smaller ones, it should come as no surprise that two one-dimensional kernels applied in succession can produce the same result as a convolution with a single large kernel. This property is extremely valuable in synthesizing the effect of a large kernel used in unsharp masking. Below, a 5 x 5 kernel is synthesized from two 5x1 kernels:

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