Properties of linear filters

Several computer vision applications are composed of step by step transformations of an input photo to output. This is easily done due to several properties associated with a common type of filters, that is, linear filters:

• The linear filters are commutative such that we can perform multiplication operations on filters in any order and the result still remains the same:

a * b = b * a 

• They are associative in nature, which means the order of applying the filter does not effect the outcome:

(a * b) * c = a * (b * c)

• Even in cases of summing two filters, we can perform the first summation and then apply the filter, or we can also individually apply the filter and then sum the results. The overall outcome still remains the same:

b = (k+l) * a

• Applying a scaling factor to one filter and multiplying to another filter is equivalent to first multiplying both filters and then applying scaling factor

These properties play a significant role later, when we look at computer vision tasks such as object detection, segmentation, and so on. A suitable combination of these filters enhances the quality of information extraction and as a result, improves the accuracy.