How to detect anomalous points As is clear from the figure, the blue points, which don't follow the trend, are anomalous points. 

I'm wondering about the best non-parametric method to detect those points. I have tested some outlier detection methods such as standard deviation, etc. but they don't provide good results while it is clear from the figure.
In your example what differentiates the clusters is not the raw value but rapid departure from previous points.  I might look into change-point detection. Nonparametic, but still requires some fiddling with tuning parameters.