What is a low-pass filter for a sequence of tuples? I am currently reading SEGMENTATION AND RECOGNITION OF SYMBOLS WITHIN HANDWRITTEN MATHEMATICAL EXPRESSIONS. There is one sentence I don't understand:


  The preprocessing stage is subdivided into three steps: 
  
  
  smoothing the input data by lowpass-filtering.
  


In this context your data usually looks like this:

[[(x1, y1), (x2, y2), ...], 
 [(x12, y12), ...],
 ...
]


So you have list of coordinates that are ordered by time. Each sublist is exactly one line or a single point.

I've only heard of low-pass filters in the context of acoustics / electronics so far (I don't know much about these topics). In those contexts it's obvious what it means to let low frequencies pass / cut high frequencies.

So what is a low-pass filter in the context of handwritten symbol recogntion?
'Frequency' for a sequence of values is the measure of how sharp the values in that sequence change.

For example, the sequence $x_1(n)=[\begin{array}[cccccccc]&amp;\cdots &amp;1, &amp;1, &amp;1, &amp;1, &amp;\cdots\end{array}]$ has a frequency 0 but the  $x_2(n)=[\begin{array}[cccccccc] &amp;\cdots &amp;1 &amp;1 &amp;7 &amp;1 &amp;\cdots\end{array}]$ is a  higher frequency signal since there is a sharp change in sequence value (1 to 7 and 7 to 1).

A low pass filter is a system which attenuates the high frequency components. OR it reduces the sharpness (or introduces blur) in case of an image. OR a low pass filter does not allow sudden changes in values and smoothens these changes. Figure below shows low passing various sequences ($\style{color:blue}{blue:input}$ $\style{color:red}{red:output}$).



Consider a system whose output is a sequence $y(n)$ where n$^{th}$ value in $y(n)$ is the average of n$^{th}$, (n-1)$^{th}$ and (n+1)$^{th}$ value of input sequence is a simple low pass filter. If $x_2(n)$ is fed as input to this filter, then output, will  be $[\begin{array}[cccccccc] &amp;\cdots &amp;1 &amp;3 &amp;3 &amp;3 &amp;1 &amp;\cdots\end{array}]$ and it is clear that the magnitude of change between consecutive values are reduced. or the high frequency components are attenuated. 

Since you have a tuple, you have to separate it into two sequences ([x1,x2,....] and [y1,y2,....]). The low pass filtering should be done on these sequences separately. 

In character recognition algorithms, low pass filtering is used in pre-processing to remove noises or unwanted small dots, having a width of one or two pixels. see an example of low pass filtering used for noise removal in image processing.