Comparing two colored lines
If I consider that your colored lines are multivariate signals (in Red, Green, Blue), that might be related through local offsets and scalings (stretch and squeeze), I would suggest the method in Correlation based dynamic time warping of multivariate time series, Expert Systems with Applications, 2012. 

It combines Dynamic Time Warping (DTW), a widely used technique for comparison of time series data, and Principal Component Analysis (PCA)  to address the correlation between the variables. 

yet, you have to balance, in your metric, the 'shape' part and the 'color' part of the data. The associated quantities do not live in the same space.