Clear path detection using edge detection

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There is not standard functionality in OpenCV that provides exactly what you want. However, edges are basically binary maps (or can be represented as such) making it possible for you to detect the amount of white pixels versus the amount of black pixels in a region. This could define a measurement of edge concentration, like you describe it.

In general, if any kind of edge detection is desired it would avoid blurring as it actually makes the edge detection only harder. If filtering is needed then use a median or a bilateral filter as these are edge-preserving.