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If ''I''(''x'') represents the intensity of pixel ''x'', and ''I''′(''x'') represents the first derivative (intensity gradient) at pixel ''x'', we therefore find that:
:<math>I'(x)=-1/2\cdot I(x-1) + 0 \cdot I(x) + 1/2 \cdot I(x+1).\,</math>
For higher performance image processing, the 1st derivative can therefore be calculated (in 1D) by [[convolution|convolving]] the original data with a mask:
<center><table border="1" cellpadding=3>
<tr><td>−1/2</td><td>0</td><td>1/2</td></tr>
</table></center>
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