A good solution would be to identify each line by e.g. Hough transform, determine each intersection (e.g. InterX ) and then find the cluster with the highest density of intersections using e.g hist3.
In this case, it seems the point of interest is also the point with the highest density of white pixels, so you could apply some smoothing filter and then find the highest value in the matrix. Here's an example using a very simple 10x10 pixel average.