How to get the coordinates of the extrema from a plot?

Question

I generated a number of plots. Let us assume that we now have these plots simply as an image. How do I get the coordinates of the extrema in this image?

I am interested in getting the coordinates as pairs of x and y, for each color in the plot.

Here is an example of such an image:

Answer 1

If "image" is a Graphics-object try

pic = Plot[{Sin[x]/x, Exp[-.1 x] Sin[x]}, {x, 0, 20}]  (*two functions*) 

lines = Cases[pic, Line[p_] -> p, Infinity] (*get the points*)

Evaluate all extrema and plot

extrema = Map[Cases[
Partition[#, 3,1], {{_, a_}, p : {_, b_}, {_, c_}} /; a < b && c < b || a > b && c > b -> p] &, lines] 
Show[pic, Graphics[Point[extrema ]]]

Answer 2

If "image" is a pixel image (named pic , sorry, don't know how to include pic="image" in the coding ) try:

dc = Rest@DominantColors[pic] (* dominant colors without white*)

curves = Map[ListPlot[PixelValuePositions[pic, #, .1 ],Axes -> False, PlotStyle -> #] &, dc] (* three colored curves *)

Get the points of the different curves

points = Cases[curves  , Point[pi_] -> pi, Infinity];

...see my first answer

Answer 3

Ulrich's approach for a Graphics-object misses the end points. You can use FindPeaks to also catch the end points.

pic = Plot[{Sin[x]/x, Exp[-.1 x] Sin[x]}, {x, 0, 20}];  (*two functions*)

lines = Cases[pic, Line[p_] -> p, Infinity]; (*get the points*)

max = Flatten[(#[[FindPeaks[#[[All, 2]]][[All, 1]]]] & /@ lines), 1];

min = Flatten[(#[[FindPeaks[(# /. {x_?NumericQ, y_?NumericQ} :> {x, -y})[[All,
             2]]][[All, 1]]]] & /@ lines), 1];

Show[pic, Epilog -> {AbsolutePointSize[4],
   Red, Point[max],
   Blue, Point[min]}]