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The implementation of Lee Filters in Python can be improved by filtering based on the assigned edge at each pixel by following these steps:

1. First, we need to identify the type of edge at each pixel. For this, we can use an edge detection algorithm like the Canny Edge detector, which provides us with a binary image where the edges are represented by 1 and non-edges by 0.

2. Next, we apply Lee Filters exclusively on the pixels that belong to an edge, i.e., the pixels that have a value of 1 in the edge binary image. The remaining pixels which have a value of 0 in the edge binary image are not subject to any filtering.

3. We then apply the Lee filter algorithm on the edge pixels only, with the window size and threshold parameters adjusted based on the edge type. For example, if the edge is a strong edge, we can choose a larger window size and higher threshold to preserve the edge details, whereas if the edge is a weak edge, we can choose a smaller window size and lower threshold to filter out the noise.

4. Finally, we merge the filtered edge pixels with the non-edge pixels to get the final filtered image.

This approach ensures that the Lee filter is applied only where it is necessary, i.e., on the edges, thereby minimizing the computation time and preserving the edge details.